messages
listlengths 2
2
|
|---|
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: FStar.Pervasives.norm [\n FStar.Pervasives.iota;\n FStar.Pervasives.zeta;\n FStar.Pervasives.delta_attr [\"Vale.Arch.HeapTypes_s.__reduce__\"; \"FStar.BigOps.__reduce__\"];\n FStar.Pervasives.delta_only [\n \"Vale.Interop.Base.uu___is_TD_Buffer\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_ok\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_regs\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_flags\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_heap\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_stack\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_stackTaint\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_trace\";\n \"FStar.FunctionalExtensionality.on_dom\"; \"FStar.FunctionalExtensionality.on\";\n \"FStar.List.Tot.Base.fold_right_gtot\"; \"FStar.List.Tot.Base.map_gtot\";\n \"FStar.List.Tot.Base.length\"; \"FStar.Pervasives.Native.fst\"; \"FStar.Pervasives.Native.snd\";\n \"FStar.Pervasives.Native.__proj__Mktuple2__item___1\";\n \"FStar.Pervasives.Native.__proj__Mktuple2__item___2\"\n ];\n FStar.Pervasives.primops;\n FStar.Pervasives.simplify\n ]\n Vale.Inline.X64.Fadd_inline.lowstar_add1_t\n<:\nType0\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nPartial implementation:\nlet lowstar_add1_normal_t:normal lowstar_add1_t =\n \n"
},
{
"role": "assistant",
"content": "as_normal_t #lowstar_add1_t lowstar_add1"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_pre Vale.Inline.X64.Fadd_inline.fadd_dom\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n\nPartial implementation:\nlet fadd_pre:VSig.vale_pre fadd_dom =\n \n"
},
{
"role": "assistant",
"content": "fun (c: V.va_code) (out: b64) (f1: b64) (f2: b64) (va_s0: V.va_state) ->\n FH.va_req_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_verify_bn_st t ke modBits\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n [@inline_let] let bits = size (bits t) in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n\n let n = sub pkey 0ul nLen in\n let r2 = sub pkey nLen nLen in\n let e = sub pkey (nLen +! nLen) eLen in\n\n let mask = BN.bn_lt_mask nLen s n in\n let h = ST.get () in\n SB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\n\n let res =\n if BB.unsafe_bool_of_limb mask then begin\n Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n\n if bn_lt_pow2 modBits m_def then true\n else false end\n else false in\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_to_msg_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n saltLen:size_t\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h ->\n live h msg /\\ live h m /\\ disjoint m msg /\\\n\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_bn_to_msg a (v modBits) (v saltLen) (v msgLen) (as_seq h0 msg) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_bn_to_msg_st t a modBits\n\nlet rsapss_verify_bn_to_msg #t a modBits saltLen msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n let em = create emLen (u8 0) in\n\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits == v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let m1 = sub m 0ul mLen in\n BN.bn_to_bytes_be emLen m1 em;\n let res = RP.pss_verify a saltLen msgLen msg emBits em in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_compute_msg_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> m:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h pkey /\\ live h m /\\\n disjoint m sgnt /\\ disjoint m pkey /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m) h0 h1 /\\\n (r, as_seq h1 m) == LS.rsapss_verify_compute_msg (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_verify_compute_msg:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_verify_compute_msg_st t ke modBits\n\nlet rsapss_verify_compute_msg #t ke modBits eBits pkey sgnt m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n let k = blocks modBits 8ul in\n\n let s = create nLen (uint #t 0) in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_from_bytes_be k sgnt s;\n\n let b = rsapss_verify_bn #t ke modBits eBits pkey m s in\n pop_frame ();\n b\n\nPartial implementation:\nlet rsapss_verify_st1\n (t: limb_t)\n (ke: BE.exp t)\n (a: Hash.hash_alg{S.hash_is_supported a})\n (modBits: modBits_t t)\n =\n \n"
},
{
"role": "assistant",
"content": "let len = blocks modBits (size (bits t)) in\n\n eBits: size_t{LS.pkey_len_pre t (v modBits) (v eBits)} ->\n pkey: lbignum t (2ul *! len +! blocks eBits (size (bits t))) ->\n saltLen: size_t ->\n sgnt: lbuffer uint8 (blocks modBits 8ul) ->\n msgLen: size_t ->\n msg: lbuffer uint8 msgLen\n -> Stack bool\n (requires\n fun h ->\n len == ke.BE.bn.BN.len /\\ live h msg /\\ live h sgnt /\\ live h pkey /\\ disjoint msg sgnt /\\\n disjoint msg pkey /\\ LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey) /\\\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures\n fun h0 r h1 ->\n modifies0 h0 h1 /\\\n r ==\n LS.rsapss_verify_ a\n (v modBits)\n (v eBits)\n (as_seq h0 pkey)\n (v saltLen)\n (as_seq h0 sgnt)\n (v msgLen)\n (as_seq h0 msg))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n min: Prims.nat ->\n max: Prims.nat{min <= max /\\ max < 4294967296} ->\n hp: LowParse.Spec.Base.parser hk ht ->\n dlf: (_: ht -> LowParse.Spec.BoundedInt.bounded_int32 min max) ->\n ps: LowParse.Spec.Base.serializer pp ->\n input: LowParse.Bytes.bytes\n -> FStar.Pervasives.Lemma\n (ensures\n LowParse.Spec.Base.parse (LowParse.Spec.DepLen.parse_deplen min max hp dlf ps) input ==\n (match LowParse.Spec.Base.parse hp input with\n | FStar.Pervasives.Native.None #_ -> FStar.Pervasives.Native.None\n | FStar.Pervasives.Native.Some #_ (FStar.Pervasives.Native.Mktuple2 #_ #_ h consumed) ->\n (match FStar.UInt32.v (dlf h) + consumed > FStar.Seq.Base.length input with\n | true -> FStar.Pervasives.Native.None\n | _ ->\n let input' =\n FStar.Seq.Base.slice input consumed (FStar.UInt32.v (dlf h) + consumed)\n in\n (match LowParse.Spec.Base.parse pp input' with\n | FStar.Pervasives.Native.None #_ -> FStar.Pervasives.Native.None\n | FStar.Pervasives.Native.Some\n #_\n (FStar.Pervasives.Native.Mktuple2 #_ #_ t consumed') ->\n (match\n consumed' = FStar.UInt32.v (dlf h) &&\n FStar.Seq.Base.length (LowParse.Spec.Base.serialize ps t) = consumed'\n with\n | true ->\n FStar.Pervasives.Native.Some ((h, t), consumed + FStar.UInt32.v (dlf h))\n | _ -> FStar.Pervasives.Native.None)\n <:\n FStar.Pervasives.Native.option (LowParse.Spec.DepLen.parse_deplen_data_t min\n max\n dlf\n ps *\n LowParse.Spec.Base.consumed_length input))\n <:\n FStar.Pervasives.Native.option (LowParse.Spec.DepLen.parse_deplen_data_t min\n max\n dlf\n ps *\n LowParse.Spec.Base.consumed_length input))\n <:\n FStar.Pervasives.Native.option (LowParse.Spec.DepLen.parse_deplen_data_t min max dlf ps *\n LowParse.Spec.Base.consumed_length input)))\nEffect: FStar.Pervasives.Lemma\n\nContext:\nmodule LowParse.Spec.DepLen\n\n(* LowParse specification module for parsing structures with dependent length\n\n Example:\n\n struct {\n uint len;\n uint foo;\n uint buf[len];\n };\n\n*)\n\ninclude LowParse.Spec.Combinators\ninclude LowParse.Spec.AllIntegers\ninclude LowParse.Spec.VLGen\n\nmodule U32 = FStar.UInt32\nmodule Seq = FStar.Seq\n\n\n(* arguments\n\n @min :\n @max : integer bounds\n @ht : header type\n @hk : header parser metadata\n @hp : header parser\n @h : header data\n @dlf : dependent length function\n @pt : payload type\n @pk : payload parser metadata\n @pp : payload parser\n @ps : payload serializer\n @x : data\n\n*)\n\n(* data type of the dependent length parser, which is a pair of the header and the payload *)\n\nlet parse_deplen_data_t \n (min : nat)\n (max : nat { min <= max /\\ max < 4294967296 } )\n (#ht : Type)\n (#pt : Type)\n (dlf : ht -> Tot (bounded_int32 min max) )\n (#pk : parser_kind)\n (#pp : parser pk pt)\n (ps : serializer pp)\n= x:(ht & pt) {U32.v (dlf (fst x)) == Seq.length (serialize ps (snd x) ) }\n\n\n(* the tag for a piece of dependent length data is just its header *)\n\nlet calc_tag_of_deplen_data\n (min : nat)\n (max : nat { min <= max /\\ max < 4294967296 } )\n (#ht : Type)\n (#pt : Type)\n (dlf : ht -> Tot (bounded_int32 min max) )\n (#pk : parser_kind)\n (#pp : parser pk pt)\n (ps : serializer pp)\n (x : parse_deplen_data_t min max dlf ps)\n: GTot ht\n= fst x\n\n\n(* synth put the header and the payload together to get the data *)\n\nlet synth_deplen_data\n (min : nat)\n (max : nat { min <= max /\\ max < 4294967296 } )\n (#ht : Type)\n (#pt : Type)\n (dlf : ht -> Tot (bounded_int32 min max) )\n (#pk : parser_kind)\n (#pp : parser pk pt)\n (ps : serializer pp)\n (h : ht)\n (x : parse_fldata_strong_t ps (U32.v (dlf h)))\n: Tot (refine_with_tag (calc_tag_of_deplen_data min max dlf ps) h) \n= (h, x)\n\n\n(* metadata of the payload, reuse bounded_vlgen_payload *)\n\nlet parse_deplen_payload_kind = parse_bounded_vlgen_payload_kind\n\n\n(* parser spec for the dependent length payload which attaches the header to generate the data *)\n\nlet parse_deplen_payload\n (min : nat)\n (max : nat { min <= max /\\ max < 4294967296 } )\n (#ht : Type)\n (#pt : Type)\n (dlf : ht -> Tot (bounded_int32 min max) )\n (#pk : parser_kind)\n (#pp : parser pk pt)\n (ps : serializer pp)\n (h : ht)\n: Tot (parser (parse_deplen_payload_kind min max pk) (refine_with_tag (calc_tag_of_deplen_data min max dlf ps) h)) \n= let sz = (U32.v (dlf h)) in\n let bounds_off =\n pk.parser_kind_low > sz || (\n match pk.parser_kind_high with\n | None -> false\n | Some pkmax -> pkmax < sz\n )\n in\n if bounds_off\n then fail_parser (parse_deplen_payload_kind min max pk) (refine_with_tag (calc_tag_of_deplen_data min max dlf ps) h)\n else\n weaken (parse_deplen_payload_kind min max pk)\n (parse_fldata_strong ps sz\n `parse_synth`\n synth_deplen_data min max dlf ps h)\n\n\n(* unfold is a more human readable version and do double-check of the definition\n\n This lemma says using the parser defined above is equivalent to using a fixed-length\n parser with the calculated size and then attach the header\n*) \n\nlet parse_deplen_payload_unfold\n (min : nat)\n (max : nat { min <= max /\\ max < 4294967296 } )\n (#ht : Type)\n (#pt : Type)\n (dlf : ht -> Tot (bounded_int32 min max) )\n (#pk : parser_kind)\n (#pp : parser pk pt)\n (ps : serializer pp)\n (h : ht)\n (input: bytes)\n: Lemma\n (parse (parse_deplen_payload min max dlf ps h) input == (match (parse (parse_fldata_strong ps (U32.v (dlf h))) input) with\n | None -> None\n | Some (x, consumed) -> Some (synth_deplen_data min max dlf ps h x, consumed)))\n = let sz = (U32.v (dlf h)) in\n let bounds_off =\n pk.parser_kind_low > sz || (\n match pk.parser_kind_high with\n | None -> false\n | Some pkmax -> pkmax < sz\n )\n in\n if bounds_off\n then ()\n else\n parse_synth_eq\n (parse_fldata_strong ps sz)\n (synth_deplen_data min max dlf ps h)\n input\n\n(* metadata for dependent length parser\n\n @min : \n @max : integer bounds\n @hk : header metadata\n @pk : payload metadata\n*)\n\nlet parse_deplen_kind\n (min : nat)\n (max : nat { min <= max /\\ max < 4294967296 } )\n (hk : parser_kind)\n (pk : parser_kind)\n= and_then_kind hk (parse_deplen_payload_kind min max pk)\n\n\n(* parse spec for dependent length structures *)\n\nlet parse_deplen\n (min: nat)\n (max: nat { min <= max /\\ max < 4294967296 } )\n (#hk: parser_kind)\n (#ht: Type)\n (hp: parser hk ht)\n (dlf: ht -> Tot (bounded_int32 min max))\n (#pk: parser_kind)\n (#pt: Type)\n (#pp: parser pk pt)\n (ps: serializer pp)\n: Tot (parser (parse_deplen_kind min max hk pk) (parse_deplen_data_t min max dlf ps))\n= parse_tagged_union\n hp\n (calc_tag_of_deplen_data min max dlf ps)\n (parse_deplen_payload min max dlf ps)\n\n(* This lemma says using the parser above is equivalent to using the header parser and then\n the deplen_payload parser\n*)\n\nlet parse_deplen_unfold\n (min: nat)\n (max: nat { min <= max /\\ max < 4294967296 } )\n (#hk: parser_kind)\n (#ht: Type)\n (hp: parser hk ht)\n (dlf: ht -> Tot (bounded_int32 min max))\n (#pk: parser_kind)\n (#pt: Type)\n (#pp: parser pk pt)\n (ps: serializer pp)\n (input : bytes)\n: Lemma\n (parse (parse_deplen min max hp dlf ps) input ==\n (match parse hp input with\n | None -> None\n | Some (h, consumed) ->\n begin\n if (U32.v (dlf h) + consumed) > (Seq.length input) then\n None\n else\n let input' = Seq.slice input consumed (Seq.length input) in\n match parse (parse_deplen_payload min max dlf ps h) input' with\n | None -> None\n | Some(x, consumed') -> \n if consumed' = U32.v (dlf h) then\n Some (x, consumed + (U32.v (dlf h)))\n else\n None\n end)\n )\n= parse_tagged_union_eq\n hp\n (calc_tag_of_deplen_data min max dlf ps)\n (parse_deplen_payload min max dlf ps)\n input;\n match parse hp input with\n | None -> ()\n | Some (h, consumed) ->\n let input' = Seq.slice input consumed (Seq.length input) in\n parse_deplen_payload_unfold min max dlf ps h input';\n let sz = (U32.v (dlf h)) in\n if Seq.length input < consumed + sz then\n ()\n else\n Seq.slice_slice input consumed (Seq.length input) 0 sz\n\n(* a stronger version that further unfolds the payload *)\n\nPartial implementation:\nlet parse_deplen_unfold2\n (min: nat)\n (max: nat{min <= max /\\ max < 4294967296})\n (#hk: parser_kind)\n (#ht: Type)\n (hp: parser hk ht)\n (dlf: (ht -> Tot (bounded_int32 min max)))\n (#pk: parser_kind)\n (#pt: Type)\n (#pp: parser pk pt)\n (ps: serializer pp)\n (input: bytes)\n : Lemma\n (parse (parse_deplen min max hp dlf ps) input ==\n (match parse hp input with\n | None -> None\n | Some (h, consumed) ->\n if (U32.v (dlf h) + consumed) > (Seq.length input)\n then None\n else\n let input' = Seq.slice input consumed (U32.v (dlf h) + consumed) in\n match parse pp input' with\n | None -> None\n | Some (t, consumed') ->\n if consumed' = U32.v (dlf h) && Seq.length (serialize ps t) = consumed'\n then Some ((h, t), consumed + (U32.v (dlf h)))\n else None)) =\n \n"
},
{
"role": "assistant",
"content": "parse_tagged_union_eq hp\n (calc_tag_of_deplen_data min max dlf ps)\n (parse_deplen_payload min max dlf ps)\n input;\nmatch parse hp input with\n| None -> ()\n| Some (h, consumed) ->\n let input' = Seq.slice input consumed (Seq.length input) in\n parse_deplen_payload_unfold min max dlf ps h input';\n let sz = (U32.v (dlf h)) in\n if Seq.length input < consumed + sz\n then ()\n else Seq.slice_slice input consumed (Seq.length input) 0 sz"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\nPartial implementation:\nlet rsapss_sign_st1\n (t: limb_t)\n (ke: BE.exp t)\n (a: Hash.hash_alg{S.hash_is_supported a})\n (modBits: modBits_t t)\n =\n \n"
},
{
"role": "assistant",
"content": "let len = blocks modBits (size (bits t)) in\n\n eBits: size_t ->\n dBits: size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)} ->\n skey: lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t))) ->\n saltLen: size_t ->\n salt: lbuffer uint8 saltLen ->\n msgLen: size_t ->\n msg: lbuffer uint8 msgLen ->\n sgnt: lbuffer uint8 (blocks modBits 8ul)\n -> Stack bool\n (requires\n fun h ->\n len == ke.BE.bn.BN.len /\\ live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\ LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures\n fun h0 eq_m h1 ->\n modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) ==\n LS.rsapss_sign_ a\n (v modBits)\n (v eBits)\n (v dBits)\n (as_seq h0 skey)\n (v saltLen)\n (as_seq h0 salt)\n (v msgLen)\n (as_seq h0 msg))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.X64.Decls.va_code\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nPartial implementation:\nlet code_Fadd =\n \n"
},
{
"role": "assistant",
"content": "FH.va_code_Fadd ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: wfr: FStar.WellFoundedRelation.wfr_t a\n -> wfr':\n FStar.WellFoundedRelation.wfr_t (FStar.Pervasives.Native.option a)\n {Mkwfr_t?.relation wfr' == FStar.WellFoundedRelation.option_relation wfr}\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2022 Jay Lorch and Nikhil Swamy, Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\n(* This library is intended to simplify using well-founded relations\n in decreases clauses.\n*)\n\nmodule FStar.WellFoundedRelation\n\nopen FStar.Universe\nmodule WF = FStar.WellFounded\nmodule WFU = FStar.WellFounded.Util\n\nlet rec default_decreaser (#a: Type u#a) (x: a)\n : Tot (acc_classical (default_relation #a) x) (decreases x) =\n let smaller (y: a{default_relation y x}) : acc_classical (default_relation #a) y =\n default_decreaser y\n in\n AccClassicalIntro smaller\n\nlet default_wfr (a: Type u#a) : (wfr: wfr_t a{wfr.relation == default_relation}) =\n let proof (x1: a) (x2: a)\n : Lemma (requires default_relation x1 x2)\n (ensures default_decreaser x1 << default_decreaser x2) =\n assert ((default_decreaser x2).access_smaller x1 == default_decreaser x1)\n in\n { relation = default_relation; decreaser = default_decreaser; proof = proof; }\n\nlet rec empty_decreaser (#a: Type u#a) (x: a)\n : Tot (acc_classical (empty_relation #a) x) (decreases x) =\n let smaller (y: a{empty_relation y x}) : acc_classical (empty_relation #a) y =\n empty_decreaser y\n in\n AccClassicalIntro smaller\n\nlet empty_wfr (a: Type u#a) : (wfr: wfr_t a{wfr.relation == empty_relation}) =\n let proof (x1: a) (x2: a)\n : Lemma (requires empty_relation x1 x2) (ensures empty_decreaser x1 << empty_decreaser x2) =\n assert ((empty_decreaser x2).access_smaller x1 == empty_decreaser x1)\n in\n { relation = empty_relation; decreaser = empty_decreaser; proof = proof; }\n\nlet rec acc_decreaser\n (#a: Type u#a)\n (r: a -> a -> Type0)\n (f: WF.well_founded r{forall x1 x2 (p: r x1 x2). (f x2).access_smaller x1 p == f x1})\n (x: a)\n : Tot (acc_classical (acc_relation r) x) (decreases (f x)) =\n let smaller (y: a{(acc_relation r) y x}) : (acc_classical (acc_relation r) y) = (\n eliminate exists (p: r y x). True\n returns f y << f x\n with _. assert ((f x).access_smaller y p == f y);\n acc_decreaser r f y\n ) in\n AccClassicalIntro smaller\n\nlet rec eta_expand_well_founded (#a: Type) (r: WF.binrel a) (wf_r: WF.well_founded r) (x: a)\n : Tot (WF.acc r x)\n (decreases {:well-founded (WFU.lift_binrel_as_well_founded_relation wf_r) (| a, x |)})\n = WF.AccIntro (let g_smaller (y: a) (u: r y x) : WF.acc r y =\n WFU.intro_lift_binrel r y x;\n eta_expand_well_founded r wf_r y\n in g_smaller)\n\nlet acc_to_wfr (#a: Type u#a) (r: WF.binrel u#a u#0 a) (f: WF.well_founded r)\n : (wfr: wfr_t a{wfr.relation == acc_relation r}) =\n let f = eta_expand_well_founded r f in\n let proof (x1: a) (x2: a)\n : Lemma (requires acc_relation r x1 x2)\n (ensures acc_decreaser r f x1 << acc_decreaser r f x2) =\n assert ((acc_decreaser r f x2).access_smaller x1 == acc_decreaser r f x1)\n in\n { relation = acc_relation r; decreaser = acc_decreaser r f; proof = proof; }\n\nlet rec subrelation_decreaser (#a: Type u#a) (r: a -> a -> Type0)\n (wfr: wfr_t a{forall x1 x2. r x1 x2 ==> wfr.relation x1 x2}) (x: a)\n : Tot (acc_classical r x) (decreases wfr.decreaser x) =\n let smaller (y: a{r y x}) : (acc_classical r y) =\n subrelation_decreaser r wfr y\n in\n AccClassicalIntro smaller\n\nlet subrelation_to_wfr (#a: Type u#a) (r: a -> a -> Type0)\n (wfr: wfr_t a{forall x1 x2. r x1 x2 ==> wfr.relation x1 x2})\n : (wfr': wfr_t a{wfr'.relation == r}) =\n let proof (x1: a) (x2: a)\n : Lemma (requires r x1 x2)\n (ensures subrelation_decreaser r wfr x1 << subrelation_decreaser r wfr x2) =\n assert ((subrelation_decreaser r wfr x2).access_smaller x1 == subrelation_decreaser r wfr x1)\n in\n { relation = r; decreaser = subrelation_decreaser r wfr; proof = proof; }\n\nlet rec inverse_image_decreaser (#a: Type u#a) (#b: Type u#b) (r: a -> a -> Type0) (f: a -> b)\n (wfr: wfr_t b{forall x1 x2. r x1 x2 ==> wfr.relation (f x1) (f x2)})\n (x: a)\n : Tot (acc_classical r x) (decreases wfr.decreaser (f x)) =\n let smaller (y: a{r y x}) : (acc_classical r y) =\n inverse_image_decreaser r f wfr y\n in\n AccClassicalIntro smaller\n\nlet inverse_image_to_wfr (#a: Type u#a) (#b: Type u#b) (r: a -> a -> Type0) (f: a -> b)\n (wfr: wfr_t b{forall x1 x2. r x1 x2 ==> wfr.relation (f x1) (f x2)})\n : (wfr': wfr_t a{wfr'.relation == r}) =\n let proof (x1: a) (x2: a)\n : Lemma (requires r x1 x2)\n (ensures inverse_image_decreaser r f wfr x1 << inverse_image_decreaser r f wfr x2) =\n assert ((inverse_image_decreaser r f wfr x2).access_smaller x1 ==\n inverse_image_decreaser r f wfr x1)\n in\n { relation = r; decreaser = inverse_image_decreaser r f wfr; proof = proof; }\n\nlet rec lex_nondep_decreaser (#a: Type u#a) (#b: Type u#b) (wfr_a: wfr_t a) (wfr_b: wfr_t b)\n (xy: a * b)\n : Tot (acc_classical (lex_nondep_relation wfr_a wfr_b) xy)\n (decreases %[wfr_a.decreaser (fst xy); wfr_b.decreaser (snd xy)]) =\n let smaller (xy': a * b{lex_nondep_relation wfr_a wfr_b xy' xy})\n : (acc_classical (lex_nondep_relation wfr_a wfr_b) xy') =\n lex_nondep_decreaser wfr_a wfr_b xy'\n in\n AccClassicalIntro smaller\n\nlet lex_nondep_wfr (#a: Type u#a) (#b: Type u#b) (wfr_a: wfr_t a) (wfr_b: wfr_t b)\n : wfr: wfr_t (a * b){wfr.relation == lex_nondep_relation wfr_a wfr_b} =\n let proof (xy1: a * b) (xy2: a * b)\n : Lemma (requires lex_nondep_relation wfr_a wfr_b xy1 xy2)\n (ensures lex_nondep_decreaser wfr_a wfr_b xy1 <<\n lex_nondep_decreaser wfr_a wfr_b xy2) =\n assert ((lex_nondep_decreaser wfr_a wfr_b xy2).access_smaller xy1 ==\n lex_nondep_decreaser wfr_a wfr_b xy1)\n in\n { relation = lex_nondep_relation wfr_a wfr_b;\n decreaser = lex_nondep_decreaser wfr_a wfr_b;\n proof = proof; }\n\nlet rec lex_dep_decreaser (#a: Type u#a) (#b: a -> Type u#b) (wfr_a: wfr_t a)\n (a_to_wfr_b: (x: a -> wfr_t (b x))) (xy: (x: a & b x))\n : Tot (acc_classical (lex_dep_relation wfr_a a_to_wfr_b) xy)\n (decreases %[wfr_a.decreaser (dfst xy); (a_to_wfr_b (dfst xy)).decreaser (dsnd xy)]) =\n let smaller (xy': (x: a & b x){lex_dep_relation wfr_a a_to_wfr_b xy' xy})\n : (acc_classical (lex_dep_relation wfr_a a_to_wfr_b) xy') =\n lex_dep_decreaser wfr_a a_to_wfr_b xy'\n in\n AccClassicalIntro smaller\n\nlet lex_dep_wfr (#a: Type u#a) (#b: a -> Type u#b) (wfr_a: wfr_t a)\n (a_to_wfr_b: (x: a -> wfr_t (b x)))\n : wfr: wfr_t (x: a & b x){wfr.relation == lex_dep_relation wfr_a a_to_wfr_b} =\n let proof (xy1: (x: a & b x)) (xy2: (x: a & b x))\n : Lemma (requires lex_dep_relation wfr_a a_to_wfr_b xy1 xy2)\n (ensures lex_dep_decreaser wfr_a a_to_wfr_b xy1 <<\n lex_dep_decreaser wfr_a a_to_wfr_b xy2) =\n assert ((lex_dep_decreaser wfr_a a_to_wfr_b xy2).access_smaller xy1 ==\n lex_dep_decreaser wfr_a a_to_wfr_b xy1)\n in\n { relation = lex_dep_relation wfr_a a_to_wfr_b;\n decreaser = lex_dep_decreaser wfr_a a_to_wfr_b;\n proof = proof; }\n\nlet bool_wfr: (wfr: wfr_t bool{wfr.relation == bool_relation}) =\n inverse_image_to_wfr #bool #nat bool_relation (fun b -> if b then 1 else 0) (default_wfr nat)\n\nPartial implementation:\nlet option_wfr (#a: Type u#a) (wfr: wfr_t a)\n : wfr': wfr_t (option a) {wfr'.relation == option_relation wfr} =\n \n"
},
{
"role": "assistant",
"content": "let unit_a:Type u#a = raise_t unit in\nlet f: option a -> (b: bool & (if b then a else unit_a)) =\n fun opt ->\n (match opt with\n | Some x -> (| true, x |)\n | None -> (| false, raise_val () |))\nin\nlet bool_to_wfr_a (b: bool) : wfr_t (if b then a else unit_a) =\n if b then wfr else empty_wfr unit_a\nin\nlet wfr_bool_a:wfr_t (b: bool & (if b then a else unit_a)) = lex_dep_wfr bool_wfr bool_to_wfr_a in\nassert (forall (bx1: (b: bool & (if b then a else unit_a)))\n (bx2: (b: bool & (if b then a else unit_a))).\n wfr_bool_a.relation bx1 bx2 <==>\n (let (| b1 , x1 |), (| b2 , x2 |) = bx1, bx2 in\n (not b1 && b2) \\/ (b1 && b2 /\\ wfr.relation x1 x2)));\nassert (forall opt1 opt2. (option_relation wfr) opt1 opt2 ==> wfr_bool_a.relation (f opt1) (f opt2));\ninverse_image_to_wfr (option_relation wfr) f wfr_bool_a"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: n: Prims.nat -> Prims.string\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nPartial implementation:\nlet fadd_names (n: nat) =\n \n"
},
{
"role": "assistant",
"content": "match n with\n| 0 -> \"out\"\n| 1 -> \"f1\"\n| 2 -> \"f2\"\n| _ -> \"\""
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n modBits: Lib.IntTypes.size_t{1 < Lib.IntTypes.v modBits} ->\n m:\n Hacl.Bignum.Definitions.lbignum t\n (Hacl.Bignum.Definitions.blocks modBits (Lib.IntTypes.size (Lib.IntTypes.bits t)))\n -> FStar.HyperStack.ST.Stack Prims.bool\nEffect: FStar.HyperStack.ST.Stack\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nPartial implementation:\nlet bn_lt_pow2 #t modBits m =\n \n"
},
{
"role": "assistant",
"content": "if not ((modBits -! 1ul) %. 8ul =. 0ul)\nthen true\nelse\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\nPartial implementation:\nlet rsapss_sign_st\n (t: limb_t)\n (ke: BE.exp t)\n (a: Hash.hash_alg{S.hash_is_supported a})\n (modBits: modBits_t t)\n =\n \n"
},
{
"role": "assistant",
"content": "let len = blocks modBits (size (bits t)) in\n\n eBits: size_t ->\n dBits: size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)} ->\n skey: lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t))) ->\n saltLen: size_t ->\n salt: lbuffer uint8 saltLen ->\n msgLen: size_t ->\n msg: lbuffer uint8 msgLen ->\n sgnt: lbuffer uint8 (blocks modBits 8ul)\n -> Stack bool\n (requires\n fun h ->\n len == ke.BE.bn.BN.len /\\ live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\ LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures\n fun h0 b h1 ->\n modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) ==\n LS.rsapss_sign a (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (v saltLen)\n (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Lib.IntTypes.size_t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_verify_bn_st t ke modBits\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n [@inline_let] let bits = size (bits t) in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n\n let n = sub pkey 0ul nLen in\n let r2 = sub pkey nLen nLen in\n let e = sub pkey (nLen +! nLen) eLen in\n\n let mask = BN.bn_lt_mask nLen s n in\n let h = ST.get () in\n SB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\n\n let res =\n if BB.unsafe_bool_of_limb mask then begin\n Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n\n if bn_lt_pow2 modBits m_def then true\n else false end\n else false in\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_to_msg_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n saltLen:size_t\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h ->\n live h msg /\\ live h m /\\ disjoint m msg /\\\n\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_bn_to_msg a (v modBits) (v saltLen) (v msgLen) (as_seq h0 msg) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_bn_to_msg_st t a modBits\n\nlet rsapss_verify_bn_to_msg #t a modBits saltLen msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n let em = create emLen (u8 0) in\n\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits == v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let m1 = sub m 0ul mLen in\n BN.bn_to_bytes_be emLen m1 em;\n let res = RP.pss_verify a saltLen msgLen msg emBits em in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_compute_msg_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> m:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h pkey /\\ live h m /\\\n disjoint m sgnt /\\ disjoint m pkey /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m) h0 h1 /\\\n (r, as_seq h1 m) == LS.rsapss_verify_compute_msg (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_verify_compute_msg:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_verify_compute_msg_st t ke modBits\n\nlet rsapss_verify_compute_msg #t ke modBits eBits pkey sgnt m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n let k = blocks modBits 8ul in\n\n let s = create nLen (uint #t 0) in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_from_bytes_be k sgnt s;\n\n let b = rsapss_verify_bn #t ke modBits eBits pkey m s in\n pop_frame ();\n b\n\n\ninline_for_extraction noextract\nlet rsapss_verify_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> saltLen:size_t\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h msg /\\ live h sgnt /\\ live h pkey /\\\n disjoint msg sgnt /\\ disjoint msg pkey /\\\n\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey) /\\\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_ a (v modBits) (v eBits) (as_seq h0 pkey)\n (v saltLen) (as_seq h0 sgnt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_verify_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_st1 t ke a modBits\n\nlet rsapss_verify_ #t ke a modBits eBits pkey saltLen sgnt msgLen msg =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n let b = rsapss_verify_compute_msg ke modBits eBits pkey sgnt m in\n let res = if b then rsapss_verify_bn_to_msg a modBits saltLen msgLen msg m else false in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> saltLen:size_t\n -> sgntLen:size_t\n -> sgnt:lbuffer uint8 sgntLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h msg /\\ live h sgnt /\\ live h pkey /\\\n disjoint msg sgnt /\\ disjoint msg pkey /\\\n\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify a (v modBits) (v eBits) (as_seq h0 pkey)\n (v saltLen) (v sgntLen) (as_seq h0 sgnt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_verify:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_st t ke a modBits\n\nlet rsapss_verify #t ke a modBits eBits pkey saltLen sgntLen sgnt msgLen msg =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n assert (v msgLen <= max_size_t);\n assert (v hLen + 8 < max_size_t);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n sgntLen =. blocks modBits 8ul in\n\n if b then\n rsapss_verify_ ke a modBits eBits pkey saltLen sgnt msgLen msg\n else\n false\n\n\ninline_for_extraction noextract\nlet rsapss_skey_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:size_t) =\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> nb:lbuffer uint8 (blocks modBits 8ul)\n -> eb:lbuffer uint8 (blocks eBits 8ul)\n -> db:lbuffer uint8 (blocks dBits 8ul)\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h ->\n blocks modBits (size (bits t)) == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\\n live h nb /\\ live h eb /\\ live h db /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\\n disjoint sgnt nb /\\ disjoint sgnt eb /\\ disjoint sgnt db /\\\n disjoint salt msg)\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (let sgnt_s = S.rsapss_skey_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 nb) (as_seq h0 eb) (as_seq h0 db) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) in\n if b then Some? sgnt_s /\\ as_seq h1 sgnt == Some?.v sgnt_s else None? sgnt_s))\n\n\ninline_for_extraction noextract\nval rsapss_skey_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t\n -> rsapss_load_skey:RK.rsapss_load_skey_st t ke modBits\n -> rsapss_sign:rsapss_sign_st t ke a modBits ->\n rsapss_skey_sign_st t ke a modBits\n\nlet rsapss_skey_sign #t ke a modBits rsapss_load_skey rsapss_sign eBits dBits nb eb db saltLen salt msgLen msg sgnt =\n [@inline_let] let bits = size (bits t) in\n let h0 = ST.get () in\n push_frame ();\n let skey = create (2ul *! blocks modBits bits +! blocks eBits bits +! blocks dBits bits) (uint #t 0) in\n let b = rsapss_load_skey eBits dBits nb eb db skey in\n LS.rsapss_load_skey_lemma #t (v modBits) (v eBits) (v dBits) (as_seq h0 nb) (as_seq h0 eb) (as_seq h0 db);\n\n let res =\n if b then\n rsapss_sign eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false in\n pop_frame ();\n let h1 = ST.get () in\n assert ((res, as_seq h1 sgnt) == LS.rsapss_skey_sign #t a (v modBits) (v eBits) (v dBits)\n (as_seq h0 nb) (as_seq h0 eb) (as_seq h0 db) (v saltLen) (as_seq h0 salt)\n (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt));\n res\n\nPartial implementation:\nlet rsapss_pkey_verify_st\n (t: limb_t)\n (ke: BE.exp t)\n (a: Hash.hash_alg{S.hash_is_supported a})\n (modBits: size_t)\n =\n \n"
},
{
"role": "assistant",
"content": "\n eBits: size_t{LS.pkey_len_pre t (v modBits) (v eBits)} ->\n nb: lbuffer uint8 (blocks modBits 8ul) ->\n eb: lbuffer uint8 (blocks eBits 8ul) ->\n saltLen: size_t ->\n sgntLen: size_t ->\n sgnt: lbuffer uint8 sgntLen ->\n msgLen: size_t ->\n msg: lbuffer uint8 msgLen\n -> Stack bool\n (requires\n fun h ->\n blocks modBits (size (bits t)) == ke.BE.bn.BN.len /\\ live h msg /\\ live h sgnt /\\\n live h nb /\\ live h eb /\\ disjoint msg sgnt /\\ disjoint nb eb /\\ disjoint sgnt nb /\\\n disjoint sgnt eb /\\ disjoint msg nb /\\ disjoint msg eb)\n (ensures\n fun h0 r h1 ->\n modifies0 h0 h1 /\\\n r ==\n S.rsapss_pkey_verify a (v modBits) (v eBits) (as_seq h0 nb) (as_seq h0 eb) (v saltLen)\n (v sgntLen) (as_seq h0 sgnt) (v msgLen) (as_seq h0 msg))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\nPartial implementation:\nlet rsapss_verify_bn_st (t: limb_t) (ke: BE.exp t) (modBits: modBits_t t) =\n \n"
},
{
"role": "assistant",
"content": "let len = blocks modBits (size (bits t)) in\n\n eBits: size_t{LS.pkey_len_pre t (v modBits) (v eBits)} ->\n pkey: lbignum t (2ul *! len +! blocks eBits (size (bits t))) ->\n m_def: lbignum t len ->\n s: lbignum t len\n -> Stack bool\n (requires\n fun h ->\n len == ke.BE.bn.BN.len /\\ live h pkey /\\ live h m_def /\\ live h s /\\ disjoint m_def pkey /\\\n disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures\n fun h0 r h1 ->\n modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) ==\n LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s)\n )"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_verify_bn_st t ke modBits\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n [@inline_let] let bits = size (bits t) in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n\n let n = sub pkey 0ul nLen in\n let r2 = sub pkey nLen nLen in\n let e = sub pkey (nLen +! nLen) eLen in\n\n let mask = BN.bn_lt_mask nLen s n in\n let h = ST.get () in\n SB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\n\n let res =\n if BB.unsafe_bool_of_limb mask then begin\n Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n\n if bn_lt_pow2 modBits m_def then true\n else false end\n else false in\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_to_msg_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n saltLen:size_t\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h ->\n live h msg /\\ live h m /\\ disjoint m msg /\\\n\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_bn_to_msg a (v modBits) (v saltLen) (v msgLen) (as_seq h0 msg) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_bn_to_msg_st t a modBits\n\nlet rsapss_verify_bn_to_msg #t a modBits saltLen msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n let em = create emLen (u8 0) in\n\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits == v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let m1 = sub m 0ul mLen in\n BN.bn_to_bytes_be emLen m1 em;\n let res = RP.pss_verify a saltLen msgLen msg emBits em in\n pop_frame ();\n res\n\nPartial implementation:\nlet rsapss_verify_compute_msg_st (t: limb_t) (ke: BE.exp t) (modBits: modBits_t t) =\n \n"
},
{
"role": "assistant",
"content": "let len = blocks modBits (size (bits t)) in\n\n eBits: size_t{LS.pkey_len_pre t (v modBits) (v eBits)} ->\n pkey: lbignum t (2ul *! len +! blocks eBits (size (bits t))) ->\n sgnt: lbuffer uint8 (blocks modBits 8ul) ->\n m: lbignum t len\n -> Stack bool\n (requires\n fun h ->\n len == ke.BE.bn.BN.len /\\ live h sgnt /\\ live h pkey /\\ live h m /\\ disjoint m sgnt /\\\n disjoint m pkey /\\ as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures\n fun h0 r h1 ->\n modifies (loc m) h0 h1 /\\\n (r, as_seq h1 m) ==\n LS.rsapss_verify_compute_msg (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 sgnt))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Prims.list Prims.string\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nPartial implementation:\nlet fadd_comments:list string =\n \n"
},
{
"role": "assistant",
"content": "[\"Computes the field addition of two field elements\"]"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: FStar.Pervasives.norm [\n FStar.Pervasives.iota;\n FStar.Pervasives.zeta;\n FStar.Pervasives.delta_attr [\"Vale.Arch.HeapTypes_s.__reduce__\"; \"FStar.BigOps.__reduce__\"];\n FStar.Pervasives.delta_only [\n \"Vale.Interop.Base.uu___is_TD_Buffer\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_ok\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_regs\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_flags\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_heap\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_stack\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_stackTaint\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_trace\";\n \"FStar.FunctionalExtensionality.on_dom\"; \"FStar.FunctionalExtensionality.on\";\n \"FStar.List.Tot.Base.fold_right_gtot\"; \"FStar.List.Tot.Base.map_gtot\";\n \"FStar.List.Tot.Base.length\"; \"FStar.Pervasives.Native.fst\"; \"FStar.Pervasives.Native.snd\";\n \"FStar.Pervasives.Native.__proj__Mktuple2__item___1\";\n \"FStar.Pervasives.Native.__proj__Mktuple2__item___2\"\n ];\n FStar.Pervasives.primops;\n FStar.Pervasives.simplify\n ]\n Vale.Inline.X64.Fadd_inline.lowstar_fadd_t\n<:\nType0\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nPartial implementation:\nlet lowstar_fadd_normal_t:normal lowstar_fadd_t =\n \n"
},
{
"role": "assistant",
"content": "as_normal_t #lowstar_fadd_t lowstar_fadd"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n a: Type ->\n framed: Prims.bool ->\n pre: Steel.Effect.Common.pre_t ->\n post: Steel.Effect.Common.post_t a ->\n req: Prims.pure_pre ->\n ens: Prims.pure_post a\n -> Type\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.ST.Effect\nfriend Steel.Effect\nopen Steel.Memory\nopen FStar.Ghost\nmodule Mem = Steel.Memory\nmodule T = FStar.Tactics\ninclude Steel.Effect.Common\nopen Steel.Effect\n#set-options \"--warn_error -330\" //turn off the experimental feature warning\n#set-options \"--ide_id_info_off\"\n\nPartial implementation:\nlet repr a framed pre post req ens : Type u#2 =\n \n"
},
{
"role": "assistant",
"content": "Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\nPartial implementation:\nlet rsapss_sign_bn_st (t: limb_t) (ke: BE.exp t) (modBits: modBits_t t) =\n \n"
},
{
"role": "assistant",
"content": "let len = blocks modBits (size (bits t)) in\n\n eBits: size_t ->\n dBits: size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)} ->\n skey: lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t))) ->\n m: lbignum t len ->\n m': lbignum t len ->\n s: lbignum t len\n -> Stack bool\n (requires\n fun h ->\n len == ke.BE.bn.BN.len /\\ live h skey /\\ live h m /\\ live h s /\\ live h m' /\\ disjoint s m /\\\n disjoint s skey /\\ disjoint m skey /\\ disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures\n fun h0 r h1 ->\n modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) ==\n LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_pre Vale.Inline.X64.Fadd_inline.fsub_dom\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n\nPartial implementation:\nlet fsub_pre:VSig.vale_pre fsub_dom =\n \n"
},
{
"role": "assistant",
"content": "fun (c: V.va_code) (out: b64) (f1: b64) (f2: b64) (va_s0: V.va_state) ->\n FH.va_req_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: _: _ -> Prims.bool\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nPartial implementation:\nlet fsub_xmms_modified =\n \n"
},
{
"role": "assistant",
"content": "fun _ -> false"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.X64.Decls.va_code\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that fsub_lemma' has the required type *)\nlet fsub_lemma = as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'\n\nPartial implementation:\nlet code_Fsub =\n \n"
},
{
"role": "assistant",
"content": "FH.va_code_Fsub ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_post Vale.Inline.X64.Fadd_inline.fsub_dom\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\nPartial implementation:\nlet fsub_post:VSig.vale_post fsub_dom =\n \n"
},
{
"role": "assistant",
"content": "fun\n (c: V.va_code)\n (out: b64)\n (f1: b64)\n (f2: b64)\n (va_s0: V.va_state)\n (va_s1: V.va_state)\n (f: V.va_fuel)\n ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\nPartial implementation:\nlet rsapss_sign_compute_sgnt_st (t: limb_t) (ke: BE.exp t) (modBits: modBits_t t) =\n \n"
},
{
"role": "assistant",
"content": "let len = blocks modBits (size (bits t)) in\n\n eBits: size_t ->\n dBits: size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)} ->\n skey: lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t))) ->\n m: lbignum t len ->\n sgnt: lbuffer uint8 (blocks modBits 8ul)\n -> Stack bool\n (requires\n fun h ->\n len == ke.BE.bn.BN.len /\\ live h sgnt /\\ live h skey /\\ live h m /\\ disjoint sgnt skey /\\\n disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures\n fun h0 eq_m h1 ->\n modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) ==\n LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m)\n )"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n bit: FStar.UInt64.t{FStar.UInt64.v bit <= 1} ->\n p0: Vale.Inline.X64.Fswap_inline.u512 ->\n p1: Vale.Inline.X64.Fswap_inline.u512\n -> FStar.HyperStack.ST.Stack Prims.unit\nEffect: FStar.HyperStack.ST.Stack\n\nContext:\nmodule Vale.Inline.X64.Fswap_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet cswap_dom: IX64.arity_ok 3 td =\n let y = [tuint64; t64_mod; t64_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet cswap_pre : VSig.vale_pre cswap_dom =\n fun (c:V.va_code)\n (bit:uint64)\n (p0:b64)\n (p1:b64)\n (va_s0:V.va_state) ->\n FU.va_req_Cswap2 c va_s0\n (UInt64.v bit) (as_vale_buffer p0) (as_vale_buffer p1)\n\n[@__reduce__]\nlet cswap_post : VSig.vale_post cswap_dom =\n fun (c:V.va_code)\n (bit:uint64)\n (p0:b64)\n (p1:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Cswap2 c va_s0 (UInt64.v bit) (as_vale_buffer p0) (as_vale_buffer p1) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet cswap_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRdi || r = rR8 || r = rR9 || r = rR10 then true\n else false\n\nlet cswap_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet cswap_lemma'\n (code:V.va_code)\n (_win:bool)\n (bit:uint64)\n (p0:b64)\n (p1:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n cswap_pre code bit p0 p1 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 cswap_regs_modified cswap_xmms_modified /\\\n cswap_post code bit p0 p1 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer p0) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer p1) /\\\n ME.buffer_writeable (as_vale_buffer p0) /\\\n ME.buffer_writeable (as_vale_buffer p1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer p0))\n (ME.loc_union (ME.loc_buffer (as_vale_buffer p1))\n ME.loc_none)) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Cswap2 code va_s0 (UInt64.v bit) (as_vale_buffer p0) (as_vale_buffer p1) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 p0;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 p1;\n (va_s1, f)\n\n(* Prove that cswap_lemma' has the required type *)\nlet cswap_lemma = as_t #(VSig.vale_sig cswap_regs_modified cswap_xmms_modified cswap_pre cswap_post) cswap_lemma'\n\nlet code_cswap = FU.va_code_Cswap2 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the cswap wrapper *)\n[@__reduce__]\nlet lowstar_cswap_t =\n assert_norm (List.length cswap_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n cswap_regs_modified\n cswap_xmms_modified\n code_cswap\n cswap_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_cswap cswap_dom [] (cswap_lemma code_cswap IA.win))\n\n(* And here's the cswap wrapper itself *)\nlet lowstar_cswap : lowstar_cswap_t =\n assert_norm (List.length cswap_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n cswap_regs_modified\n cswap_xmms_modified\n code_cswap\n cswap_dom\n (W.mk_prediction code_cswap cswap_dom [] (cswap_lemma code_cswap IA.win))\n\nlet lowstar_cswap_normal_t : normal lowstar_cswap_t\n = as_normal_t #lowstar_cswap_t lowstar_cswap\n\nopen Vale.AsLowStar.MemoryHelpers\n\nPartial implementation:\nlet cswap2 bit p0 p1 =\n \n"
},
{
"role": "assistant",
"content": "DV.length_eq (get_downview p0);\nDV.length_eq (get_downview p1);\nlet x, _ = lowstar_cswap_normal_t bit p0 p1 () in\n()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n ke: Hacl.Bignum.Exponentiation.exp t ->\n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Hacl.Impl.RSAPSS.rsapss_verify_st t ke a modBits\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_verify_bn_st t ke modBits\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n [@inline_let] let bits = size (bits t) in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n\n let n = sub pkey 0ul nLen in\n let r2 = sub pkey nLen nLen in\n let e = sub pkey (nLen +! nLen) eLen in\n\n let mask = BN.bn_lt_mask nLen s n in\n let h = ST.get () in\n SB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\n\n let res =\n if BB.unsafe_bool_of_limb mask then begin\n Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n\n if bn_lt_pow2 modBits m_def then true\n else false end\n else false in\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_to_msg_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n saltLen:size_t\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h ->\n live h msg /\\ live h m /\\ disjoint m msg /\\\n\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_bn_to_msg a (v modBits) (v saltLen) (v msgLen) (as_seq h0 msg) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_bn_to_msg_st t a modBits\n\nlet rsapss_verify_bn_to_msg #t a modBits saltLen msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n let em = create emLen (u8 0) in\n\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits == v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let m1 = sub m 0ul mLen in\n BN.bn_to_bytes_be emLen m1 em;\n let res = RP.pss_verify a saltLen msgLen msg emBits em in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_compute_msg_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> m:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h pkey /\\ live h m /\\\n disjoint m sgnt /\\ disjoint m pkey /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m) h0 h1 /\\\n (r, as_seq h1 m) == LS.rsapss_verify_compute_msg (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_verify_compute_msg:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_verify_compute_msg_st t ke modBits\n\nlet rsapss_verify_compute_msg #t ke modBits eBits pkey sgnt m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n let k = blocks modBits 8ul in\n\n let s = create nLen (uint #t 0) in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_from_bytes_be k sgnt s;\n\n let b = rsapss_verify_bn #t ke modBits eBits pkey m s in\n pop_frame ();\n b\n\n\ninline_for_extraction noextract\nlet rsapss_verify_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> saltLen:size_t\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h msg /\\ live h sgnt /\\ live h pkey /\\\n disjoint msg sgnt /\\ disjoint msg pkey /\\\n\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey) /\\\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_ a (v modBits) (v eBits) (as_seq h0 pkey)\n (v saltLen) (as_seq h0 sgnt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_verify_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_st1 t ke a modBits\n\nlet rsapss_verify_ #t ke a modBits eBits pkey saltLen sgnt msgLen msg =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n let b = rsapss_verify_compute_msg ke modBits eBits pkey sgnt m in\n let res = if b then rsapss_verify_bn_to_msg a modBits saltLen msgLen msg m else false in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> saltLen:size_t\n -> sgntLen:size_t\n -> sgnt:lbuffer uint8 sgntLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h msg /\\ live h sgnt /\\ live h pkey /\\\n disjoint msg sgnt /\\ disjoint msg pkey /\\\n\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify a (v modBits) (v eBits) (as_seq h0 pkey)\n (v saltLen) (v sgntLen) (as_seq h0 sgnt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_verify:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_st t ke a modBits\n\nPartial implementation:\nlet rsapss_verify #t ke a modBits eBits pkey saltLen sgntLen sgnt msgLen msg =\n \n"
},
{
"role": "assistant",
"content": "let hLen = RM.hash_len a in\nMath.Lemmas.pow2_lt_compat 61 32;\nMath.Lemmas.pow2_lt_compat 125 32;\nassert (v msgLen <= max_size_t);\nassert (v hLen + 8 < max_size_t);\nlet b = saltLen <=. 0xfffffffful -! hLen -! 8ul && sgntLen =. blocks modBits 8ul in\nif b then rsapss_verify_ ke a modBits eBits pkey saltLen sgnt msgLen msg else false"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n t: Hacl.Bignum.Definitions.limb_t ->\n ke: Hacl.Bignum.Exponentiation.exp t ->\n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Lib.IntTypes.size_t\n -> Type0\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_verify_bn_st t ke modBits\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n [@inline_let] let bits = size (bits t) in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n\n let n = sub pkey 0ul nLen in\n let r2 = sub pkey nLen nLen in\n let e = sub pkey (nLen +! nLen) eLen in\n\n let mask = BN.bn_lt_mask nLen s n in\n let h = ST.get () in\n SB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\n\n let res =\n if BB.unsafe_bool_of_limb mask then begin\n Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n\n if bn_lt_pow2 modBits m_def then true\n else false end\n else false in\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_to_msg_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n saltLen:size_t\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h ->\n live h msg /\\ live h m /\\ disjoint m msg /\\\n\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_bn_to_msg a (v modBits) (v saltLen) (v msgLen) (as_seq h0 msg) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_bn_to_msg_st t a modBits\n\nlet rsapss_verify_bn_to_msg #t a modBits saltLen msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n let em = create emLen (u8 0) in\n\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits == v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let m1 = sub m 0ul mLen in\n BN.bn_to_bytes_be emLen m1 em;\n let res = RP.pss_verify a saltLen msgLen msg emBits em in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_compute_msg_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> m:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h pkey /\\ live h m /\\\n disjoint m sgnt /\\ disjoint m pkey /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m) h0 h1 /\\\n (r, as_seq h1 m) == LS.rsapss_verify_compute_msg (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_verify_compute_msg:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_verify_compute_msg_st t ke modBits\n\nlet rsapss_verify_compute_msg #t ke modBits eBits pkey sgnt m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n let k = blocks modBits 8ul in\n\n let s = create nLen (uint #t 0) in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_from_bytes_be k sgnt s;\n\n let b = rsapss_verify_bn #t ke modBits eBits pkey m s in\n pop_frame ();\n b\n\n\ninline_for_extraction noextract\nlet rsapss_verify_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> saltLen:size_t\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h msg /\\ live h sgnt /\\ live h pkey /\\\n disjoint msg sgnt /\\ disjoint msg pkey /\\\n\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey) /\\\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_ a (v modBits) (v eBits) (as_seq h0 pkey)\n (v saltLen) (as_seq h0 sgnt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_verify_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_st1 t ke a modBits\n\nlet rsapss_verify_ #t ke a modBits eBits pkey saltLen sgnt msgLen msg =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n let b = rsapss_verify_compute_msg ke modBits eBits pkey sgnt m in\n let res = if b then rsapss_verify_bn_to_msg a modBits saltLen msgLen msg m else false in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> saltLen:size_t\n -> sgntLen:size_t\n -> sgnt:lbuffer uint8 sgntLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h msg /\\ live h sgnt /\\ live h pkey /\\\n disjoint msg sgnt /\\ disjoint msg pkey /\\\n\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify a (v modBits) (v eBits) (as_seq h0 pkey)\n (v saltLen) (v sgntLen) (as_seq h0 sgnt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_verify:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_st t ke a modBits\n\nlet rsapss_verify #t ke a modBits eBits pkey saltLen sgntLen sgnt msgLen msg =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n assert (v msgLen <= max_size_t);\n assert (v hLen + 8 < max_size_t);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n sgntLen =. blocks modBits 8ul in\n\n if b then\n rsapss_verify_ ke a modBits eBits pkey saltLen sgnt msgLen msg\n else\n false\n\nPartial implementation:\nlet rsapss_skey_sign_st\n (t: limb_t)\n (ke: BE.exp t)\n (a: Hash.hash_alg{S.hash_is_supported a})\n (modBits: size_t)\n =\n \n"
},
{
"role": "assistant",
"content": "\n eBits: size_t ->\n dBits: size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)} ->\n nb: lbuffer uint8 (blocks modBits 8ul) ->\n eb: lbuffer uint8 (blocks eBits 8ul) ->\n db: lbuffer uint8 (blocks dBits 8ul) ->\n saltLen: size_t ->\n salt: lbuffer uint8 saltLen ->\n msgLen: size_t ->\n msg: lbuffer uint8 msgLen ->\n sgnt: lbuffer uint8 (blocks modBits 8ul)\n -> Stack bool\n (requires\n fun h ->\n blocks modBits (size (bits t)) == ke.BE.bn.BN.len /\\ live h salt /\\ live h msg /\\\n live h sgnt /\\ live h nb /\\ live h eb /\\ live h db /\\ disjoint sgnt salt /\\\n disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt nb /\\ disjoint sgnt eb /\\\n disjoint sgnt db /\\ disjoint salt msg)\n (ensures\n fun h0 b h1 ->\n modifies (loc sgnt) h0 h1 /\\\n (let sgnt_s =\n S.rsapss_skey_sign a (v modBits) (v eBits) (v dBits) (as_seq h0 nb) (as_seq h0 eb)\n (as_seq h0 db) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg)\n in\n if b then Some? sgnt_s /\\ as_seq h1 sgnt == Some?.v sgnt_s else None? sgnt_s))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: FStar.Pervasives.norm [\n FStar.Pervasives.iota;\n FStar.Pervasives.zeta;\n FStar.Pervasives.delta_attr [\"Vale.Arch.HeapTypes_s.__reduce__\"; \"FStar.BigOps.__reduce__\"];\n FStar.Pervasives.delta_only [\n \"Vale.Interop.Base.uu___is_TD_Buffer\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_ok\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_regs\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_flags\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_heap\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_stack\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_stackTaint\";\n \"Vale.X64.Machine_Semantics_s.__proj__Mkmachine_state__item__ms_trace\";\n \"FStar.FunctionalExtensionality.on_dom\"; \"FStar.FunctionalExtensionality.on\";\n \"FStar.List.Tot.Base.fold_right_gtot\"; \"FStar.List.Tot.Base.map_gtot\";\n \"FStar.List.Tot.Base.length\"; \"FStar.Pervasives.Native.fst\"; \"FStar.Pervasives.Native.snd\";\n \"FStar.Pervasives.Native.__proj__Mktuple2__item___1\";\n \"FStar.Pervasives.Native.__proj__Mktuple2__item___2\"\n ];\n FStar.Pervasives.primops;\n FStar.Pervasives.simplify\n ]\n Vale.Inline.X64.Fadd_inline.lowstar_Fsub_t\n<:\nType0\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that fsub_lemma' has the required type *)\nlet fsub_lemma = as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'\n\nlet code_Fsub = FH.va_code_Fsub ()\n\n(* Here's the type expected for the fsub wrapper *)\n[@__reduce__]\nlet lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\n(* And here's the fsub wrapper itself *)\nlet lowstar_Fsub : lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\nPartial implementation:\nlet lowstar_Fsub_normal_t:normal lowstar_Fsub_t =\n \n"
},
{
"role": "assistant",
"content": "as_normal_t #lowstar_Fsub_t lowstar_Fsub"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: ty: Pulse.Syntax.Base.term -> t: Pulse.Syntax.Base.term -> FStar.Stubs.Reflection.Types.term\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\nPartial implementation:\nlet mk_arrow ty t =\n \n"
},
{
"role": "assistant",
"content": "RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n ke: Hacl.Bignum.Exponentiation.exp t ->\n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Hacl.Impl.RSAPSS.rsapss_sign_st t ke a modBits\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nPartial implementation:\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n \n"
},
{
"role": "assistant",
"content": "let hLen = RM.hash_len a in\nMath.Lemmas.pow2_lt_compat 61 32;\nMath.Lemmas.pow2_lt_compat 125 32;\nlet b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul && saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul\nin\nif b then rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt else false"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: ty: Pulse.Syntax.Base.term -> t: Pulse.Syntax.Base.term -> FStar.Stubs.Reflection.Types.term\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\nPartial implementation:\nlet mk_abs ty t =\n \n"
},
{
"role": "assistant",
"content": "let open RT in mk_abs (elab_term ty) T.Q_Explicit (elab_term t)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Prims.list Prims.string\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that fsub_lemma' has the required type *)\nlet fsub_lemma = as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'\n\nlet code_Fsub = FH.va_code_Fsub ()\n\n(* Here's the type expected for the fsub wrapper *)\n[@__reduce__]\nlet lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\n(* And here's the fsub wrapper itself *)\nlet lowstar_Fsub : lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\nlet lowstar_Fsub_normal_t : normal lowstar_Fsub_t\n = as_normal_t #lowstar_Fsub_t lowstar_Fsub\n\nlet fsub out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_Fsub_normal_t out f1 f2 () in\n ()\n\nPartial implementation:\nlet fsub_comments:list string =\n \n"
},
{
"role": "assistant",
"content": "[\"Computes the field substraction of two field elements\"]"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: g: Pulse.Typing.Env.env -> f: (_: Prims.unit -> FStar.Tactics.Effect.Tac Prims.string)\n -> FStar.Tactics.Effect.Tac Prims.unit\nEffect: FStar.Tactics.Effect.Tac\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nPartial implementation:\nlet debug (g: env) (f: (unit -> T.Tac string)) : T.Tac unit =\n \n"
},
{
"role": "assistant",
"content": "if RU.debug_at_level (fstar_env g) \"pulse.checker\" then T.print (f ())"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: n: Prims.nat -> Prims.string\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that fsub_lemma' has the required type *)\nlet fsub_lemma = as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'\n\nlet code_Fsub = FH.va_code_Fsub ()\n\n(* Here's the type expected for the fsub wrapper *)\n[@__reduce__]\nlet lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\n(* And here's the fsub wrapper itself *)\nlet lowstar_Fsub : lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\nlet lowstar_Fsub_normal_t : normal lowstar_Fsub_t\n = as_normal_t #lowstar_Fsub_t lowstar_Fsub\n\nlet fsub out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_Fsub_normal_t out f1 f2 () in\n ()\n\nlet fsub_comments : list string = [\"Computes the field substraction of two field elements\"]\n\nPartial implementation:\nlet fsub_names (n: nat) =\n \n"
},
{
"role": "assistant",
"content": "match n with\n| 0 -> \"out\"\n| 1 -> \"f1\"\n| 2 -> \"f2\"\n| _ -> \"\""
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: x: a -> Vale.Interop.Base.normal a\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\n\nPartial implementation:\nlet as_normal_t (#a: Type) (x: a) : normal a =\n \n"
},
{
"role": "assistant",
"content": "x"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: g: Pulse.Typing.Env.env -> p: Pulse.Syntax.Base.term\n -> Pulse.Typing.vprop_equiv g (Pulse.Syntax.Base.tm_star p Pulse.Syntax.Base.tm_emp) p\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nPartial implementation:\nlet ve_unit_r g (p: term) : vprop_equiv g (tm_star p tm_emp) p =\n \n"
},
{
"role": "assistant",
"content": "VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: r: Steel.GhostPCMReference.ref a p -> v: a -> v0: a -> v1: a\n -> Steel.Effect.Atomic.SteelGhost Prims.unit\nEffect: Steel.Effect.Atomic.SteelGhost\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\nmodule Steel.GhostPCMReference\n(* A ghost variant of Steel.PCMReference *)\nopen FStar.PCM\nopen FStar.Ghost\n\nopen Steel.Memory\nopen Steel.Effect.Atomic\nopen Steel.Effect\nmodule Mem = Steel.Memory\nmodule P = Steel.PCMReference\n\nlet ref (a:Type) (p:pcm a) = erased (Steel.Memory.ref a p)\n\n/// Its selector is non-informative (it is unit)\n[@@__reduce__]\nlet pts_to (#a:Type u#1) (#pcm:pcm a) (r:ref a pcm) ([@@@smt_fallback]v:a)\n = to_vprop (Steel.Memory.pts_to r v)\n\nlet alloc (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (x:a)\n : SteelGhost\n (ref a pcm) o\n (emp)\n (fun r -> pts_to r x)\n (requires fun _ -> pcm.refine x)\n (ensures fun _ _ _ -> True)\n = rewrite_slprop emp (to_vprop Mem.emp) (fun _ -> reveal_emp ());\n FStar.PCM.compatible_refl pcm x;\n let r = as_atomic_action_ghost (alloc_action o x) in\n r\n\nlet read (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (#v0:a)\n (r:ref a pcm)\n : SteelGhost a o\n (pts_to r v0)\n (fun _ -> pts_to r v0)\n (requires fun _ -> True)\n (ensures fun _ v _ -> compatible pcm v0 v)\n = let v = as_atomic_action_ghost (sel_action o r v0) in\n v\n\nlet write (#o:inames)\n (#a:Type)\n (#pcm:pcm a)\n (r:ref a pcm)\n (v0:a)\n (v1:a)\n : SteelGhost unit o\n (pts_to r v0)\n (fun _ -> pts_to r v1)\n (requires fun _ -> frame_preserving pcm v0 v1 /\\ pcm.refine v1)\n (ensures fun _ _ _ -> True)\n = as_atomic_action_ghost (upd_action o r v0 v1)\n\nlet upd_gen (#o:inames)\n (#a:Type)\n (#p:pcm a)\n (r:ref a p)\n (x y:a)\n (f:frame_preserving_upd p x y)\n : SteelGhostT unit o\n (pts_to r x)\n (fun _ -> pts_to r y)\n = as_atomic_action_ghost (Steel.Memory.upd_gen o r x y f)\n\nPartial implementation:\nlet share (#o: inames) (#a: Type) (#p: pcm a) (r: ref a p) (v v0 v1: a)\n : SteelGhost unit\n o\n (pts_to r v)\n (fun _ -> (pts_to r v0) `star` (pts_to r v1))\n (requires fun _ -> composable p v0 v1 /\\ v == op p v0 v1)\n (ensures fun _ _ _ -> True) =\n \n"
},
{
"role": "assistant",
"content": "P.split r v v0 v1"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: x: Vale.Interop.Base.normal a -> a\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\nPartial implementation:\nlet as_t (#a: Type) (x: normal a) : a =\n \n"
},
{
"role": "assistant",
"content": "x"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n ctxt_typing: Pulse.Typing.tot_typing g ctxt Pulse.Syntax.Base.tm_vprop ->\n d: Pulse.Typing.vprop_equiv g p ctxt\n -> Pulse.Typing.tot_typing g p Pulse.Syntax.Base.tm_vprop\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq\n\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv\n\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))\n\nlet simplify_lemma (c:comp_st) (c':comp_st) (post_hint:option post_hint_t)\n : Lemma\n (requires\n comp_post_matches_hint c post_hint /\\\n effect_annot_of_comp c == effect_annot_of_comp c' /\\\n comp_res c' == comp_res c /\\\n comp_u c' == comp_u c /\\\n comp_post c' == tm_star (comp_post c) tm_emp)\n (ensures comp_post_matches_hint (comp_st_with_post c' (comp_post c)) post_hint /\\\n comp_pre (comp_st_with_post c' (comp_post c)) == comp_pre c')\n = ()\n\nPartial implementation:\nlet vprop_equiv_typing_bk\n (#g: env)\n (#ctxt: _)\n (ctxt_typing: tot_typing g ctxt tm_vprop)\n (#p: _)\n (d: vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop =\n \n"
},
{
"role": "assistant",
"content": "let _, bk = vprop_equiv_typing d in\nbk ctxt_typing"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n ctxt_typing: Pulse.Typing.tot_typing g ctxt Pulse.Syntax.Base.tm_vprop ->\n d: Pulse.Typing.vprop_equiv g ctxt p\n -> Pulse.Typing.tot_typing g p Pulse.Syntax.Base.tm_vprop\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq\n\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv\n\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))\n\nlet simplify_lemma (c:comp_st) (c':comp_st) (post_hint:option post_hint_t)\n : Lemma\n (requires\n comp_post_matches_hint c post_hint /\\\n effect_annot_of_comp c == effect_annot_of_comp c' /\\\n comp_res c' == comp_res c /\\\n comp_u c' == comp_u c /\\\n comp_post c' == tm_star (comp_post c) tm_emp)\n (ensures comp_post_matches_hint (comp_st_with_post c' (comp_post c)) post_hint /\\\n comp_pre (comp_st_with_post c' (comp_post c)) == comp_pre c')\n = ()\n\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing\n\nlet comp_with_pre (c:comp_st) (pre:term) =\n match c with\n | C_ST st -> C_ST { st with pre }\n | C_STGhost st -> C_STGhost { st with pre }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with pre}\n\n\nlet st_equiv_pre (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (pre:term)\n (veq: vprop_equiv g (comp_pre c) pre)\n : st_typing g t (comp_with_pre c pre)\n = if eq_tm pre (comp_pre c) then d\n else\n let c' = comp_with_pre c pre in\n let (| u_of, pre_typing, x, post_typing |) =\n Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) veq (VE_Refl _ _)\n in\n t_equiv d st_equiv\n\n\n#push-options \"--z3rlimit_factor 4 --ifuel 2 --fuel 0\"\nlet k_elab_equiv_continuation (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt #ctxt1 #ctxt2:term)\n (k:continuation_elaborator g1 ctxt g2 ctxt1)\n (d:vprop_equiv g2 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt g2 ctxt2 =\n fun post_hint res ->\n let (| st, c, st_d |) = res in\n let st_d : st_typing g2 st c = st_d in\n assert (comp_pre c == ctxt2);\n let st_d' : st_typing g2 st (comp_with_pre c ctxt1) = st_equiv_pre st_d _ (VE_Sym _ _ _ d) in\n k post_hint (| st, _, st_d' |)\n#pop-options\n\nPartial implementation:\nlet vprop_equiv_typing_fwd\n (#g: env)\n (#ctxt: _)\n (ctxt_typing: tot_typing g ctxt tm_vprop)\n (#p: _)\n (d: vprop_equiv g ctxt p)\n : tot_typing g p tm_vprop =\n \n"
},
{
"role": "assistant",
"content": "let fwd, _ = vprop_equiv_typing d in\nfwd ctxt_typing"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.Interop.X64.arity_ok 3 Vale.Interop.Base.td\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\nPartial implementation:\nlet dom:IX64.arity_ok 3 td =\n \n"
},
{
"role": "assistant",
"content": "let y = [t64_mod; t64_no_mod; tuint64] in\nassert_norm (List.length y = 3);\ny"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: r: Vale.X64.Machine_s.reg_64 -> Prims.bool\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nPartial implementation:\nlet add1_regs_modified: MS.reg_64 -> bool =\n \n"
},
{
"role": "assistant",
"content": "fun (r: MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true else false"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n k: Pulse.Checker.Base.continuation_elaborator g1 ctxt1 g2 ctxt2 ->\n d1: Pulse.Typing.vprop_equiv g1 ctxt1 ctxt1' ->\n d2: Pulse.Typing.vprop_equiv g2 ctxt2 ctxt2'\n -> Pulse.Checker.Base.continuation_elaborator g1 ctxt1' g2 ctxt2'\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq\n\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv\n\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))\n\nlet simplify_lemma (c:comp_st) (c':comp_st) (post_hint:option post_hint_t)\n : Lemma\n (requires\n comp_post_matches_hint c post_hint /\\\n effect_annot_of_comp c == effect_annot_of_comp c' /\\\n comp_res c' == comp_res c /\\\n comp_u c' == comp_u c /\\\n comp_post c' == tm_star (comp_post c) tm_emp)\n (ensures comp_post_matches_hint (comp_st_with_post c' (comp_post c)) post_hint /\\\n comp_pre (comp_st_with_post c' (comp_post c)) == comp_pre c')\n = ()\n\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing\n\nlet comp_with_pre (c:comp_st) (pre:term) =\n match c with\n | C_ST st -> C_ST { st with pre }\n | C_STGhost st -> C_STGhost { st with pre }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with pre}\n\n\nlet st_equiv_pre (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (pre:term)\n (veq: vprop_equiv g (comp_pre c) pre)\n : st_typing g t (comp_with_pre c pre)\n = if eq_tm pre (comp_pre c) then d\n else\n let c' = comp_with_pre c pre in\n let (| u_of, pre_typing, x, post_typing |) =\n Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) veq (VE_Refl _ _)\n in\n t_equiv d st_equiv\n\n\n#push-options \"--z3rlimit_factor 4 --ifuel 2 --fuel 0\"\nlet k_elab_equiv_continuation (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt #ctxt1 #ctxt2:term)\n (k:continuation_elaborator g1 ctxt g2 ctxt1)\n (d:vprop_equiv g2 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt g2 ctxt2 =\n fun post_hint res ->\n let (| st, c, st_d |) = res in\n let st_d : st_typing g2 st c = st_d in\n assert (comp_pre c == ctxt2);\n let st_d' : st_typing g2 st (comp_with_pre c ctxt1) = st_equiv_pre st_d _ (VE_Sym _ _ _ d) in\n k post_hint (| st, _, st_d' |)\n#pop-options\n\nlet vprop_equiv_typing_fwd (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g ctxt p)\n : tot_typing g p tm_vprop \n = let fwd, _ = vprop_equiv_typing d in\n fwd ctxt_typing\n\n#push-options \"--z3rlimit_factor 4 --ifuel 1 --fuel 0\"\nlet k_elab_equiv_prefix\n (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt1 #ctxt2 #ctxt:term)\n (k:continuation_elaborator g1 ctxt1 g2 ctxt)\n (d:vprop_equiv g1 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt2 g2 ctxt =\n fun post_hint res ->\n let framing_token : frame_for_req_in_ctxt g1 ctxt2 ctxt1 = \n let d = VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Trans _ _ _ _ (VE_Unit _ _) d) in\n (| tm_emp, emp_typing, d |)\n in\n let res = k post_hint res in\n let (| st, c, st_d |) = res in\n assert (comp_pre c == ctxt1);\n (| _, _, st_equiv_pre st_d _ d |)\n #pop-options\n\nPartial implementation:\nlet k_elab_equiv\n (#g1: env)\n (#g2: env{g2 `env_extends` g1})\n (#ctxt1 #ctxt1' #ctxt2 #ctxt2': term)\n (k: continuation_elaborator g1 ctxt1 g2 ctxt2)\n (d1: vprop_equiv g1 ctxt1 ctxt1')\n (d2: vprop_equiv g2 ctxt2 ctxt2')\n : continuation_elaborator g1 ctxt1' g2 ctxt2' =\n \n"
},
{
"role": "assistant",
"content": "let k:continuation_elaborator g1 ctxt1 g2 ctxt2' = k_elab_equiv_continuation k d2 in\nlet k:continuation_elaborator g1 ctxt1' g2 ctxt2' = k_elab_equiv_prefix k d1 in\nk"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_post Vale.Inline.X64.Fadd_inline.dom\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\nPartial implementation:\nlet add1_post:VSig.vale_post dom =\n \n"
},
{
"role": "assistant",
"content": "fun\n (c: V.va_code)\n (out: b64)\n (f1: b64)\n (f2: uint64)\n (va_s0: V.va_state)\n (va_s1: V.va_state)\n (f: V.va_fuel)\n ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Hacl.Impl.RSAPSS.rsapss_verify_bn_to_msg_st t a modBits\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_verify_bn_st t ke modBits\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n [@inline_let] let bits = size (bits t) in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n\n let n = sub pkey 0ul nLen in\n let r2 = sub pkey nLen nLen in\n let e = sub pkey (nLen +! nLen) eLen in\n\n let mask = BN.bn_lt_mask nLen s n in\n let h = ST.get () in\n SB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\n\n let res =\n if BB.unsafe_bool_of_limb mask then begin\n Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n\n if bn_lt_pow2 modBits m_def then true\n else false end\n else false in\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_to_msg_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n saltLen:size_t\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h ->\n live h msg /\\ live h m /\\ disjoint m msg /\\\n\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_bn_to_msg a (v modBits) (v saltLen) (v msgLen) (as_seq h0 msg) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_bn_to_msg_st t a modBits\n\nPartial implementation:\nlet rsapss_verify_bn_to_msg #t a modBits saltLen msgLen msg m =\n \n"
},
{
"role": "assistant",
"content": "push_frame ();\n[@@ inline_let ]let bits:size_pos = bits t in\n[@@ inline_let ]let numb:size_pos = numbytes t in\nlet nLen = blocks modBits (size bits) in\nlet emBits = modBits -! 1ul in\nlet emLen = blocks emBits 8ul in\n[@@ inline_let ]let mLen = blocks emLen (size numb) in\nlet em = create emLen (u8 0) in\nLS.blocks_bits_lemma t (v emBits);\nLS.blocks_numb_lemma t (v emBits);\nassert (SD.blocks (v emBits) bits == v mLen);\nassert (numb * v mLen <= max_size_t);\nassert (v mLen <= v nLen);\nlet m1 = sub m 0ul mLen in\nBN.bn_to_bytes_be emLen m1 em;\nlet res = RP.pss_verify a saltLen msgLen msg emBits em in\npop_frame ();\nres"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Type0\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n\nPartial implementation:\nlet lowstar_add1_t =\n \n"
},
{
"role": "assistant",
"content": "assert_norm (List.length dom + List.length ([] <: list arg) <= 3);\nIX64.as_lowstar_sig_t_weak 3 arg_reg add1_regs_modified add1_xmms_modified code_add1 dom [] _ _\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_pre Vale.Inline.X64.Fadd_inline.dom\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n\nPartial implementation:\nlet add1_pre:VSig.vale_pre dom =\n \n"
},
{
"role": "assistant",
"content": "fun (c: V.va_code) (out: b64) (f1: b64) (f2: uint64) (va_s0: V.va_state) ->\n FU.va_req_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: p: Steel.Effect.Common.vprop\n -> FStar.Pervasives.Lemma\n (ensures Steel.Effect.Common.equiv (Steel.Effect.Common.star p Steel.Effect.Common.emp) p)\nEffect: FStar.Pervasives.Lemma\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.ST.Effect\nfriend Steel.Effect\nopen Steel.Memory\nopen FStar.Ghost\nmodule Mem = Steel.Memory\nmodule T = FStar.Tactics\ninclude Steel.Effect.Common\nopen Steel.Effect\n#set-options \"--warn_error -330\" //turn off the experimental feature warning\n#set-options \"--ide_id_info_off\"\n\nlet repr a framed pre post req ens : Type u#2 =\n Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)\n\nPartial implementation:\nlet equiv_star_emp_r (p: vprop) : Lemma ((p `star` emp) `equiv` p) =\n \n"
},
{
"role": "assistant",
"content": "cm_identity p;\nassert ((emp `star` p) `equiv` p);\nstar_commutative p emp;\nequiv_trans (p `star` emp) (emp `star` p) p"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n g: Pulse.Typing.Env.env ->\n i: Pulse.Syntax.Base.term ->\n _: Pulse.Typing.tot_typing g i Pulse.Syntax.Base.tm_inames\n -> Pulse.Typing.prop_validity g (Pulse.Typing.tm_inames_subset Pulse.Syntax.Base.tm_emp_inames i)\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq\n\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv\n\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))\n\nlet simplify_lemma (c:comp_st) (c':comp_st) (post_hint:option post_hint_t)\n : Lemma\n (requires\n comp_post_matches_hint c post_hint /\\\n effect_annot_of_comp c == effect_annot_of_comp c' /\\\n comp_res c' == comp_res c /\\\n comp_u c' == comp_u c /\\\n comp_post c' == tm_star (comp_post c) tm_emp)\n (ensures comp_post_matches_hint (comp_st_with_post c' (comp_post c)) post_hint /\\\n comp_pre (comp_st_with_post c' (comp_post c)) == comp_pre c')\n = ()\n\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing\n\nlet comp_with_pre (c:comp_st) (pre:term) =\n match c with\n | C_ST st -> C_ST { st with pre }\n | C_STGhost st -> C_STGhost { st with pre }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with pre}\n\n\nlet st_equiv_pre (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (pre:term)\n (veq: vprop_equiv g (comp_pre c) pre)\n : st_typing g t (comp_with_pre c pre)\n = if eq_tm pre (comp_pre c) then d\n else\n let c' = comp_with_pre c pre in\n let (| u_of, pre_typing, x, post_typing |) =\n Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) veq (VE_Refl _ _)\n in\n t_equiv d st_equiv\n\n\n#push-options \"--z3rlimit_factor 4 --ifuel 2 --fuel 0\"\nlet k_elab_equiv_continuation (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt #ctxt1 #ctxt2:term)\n (k:continuation_elaborator g1 ctxt g2 ctxt1)\n (d:vprop_equiv g2 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt g2 ctxt2 =\n fun post_hint res ->\n let (| st, c, st_d |) = res in\n let st_d : st_typing g2 st c = st_d in\n assert (comp_pre c == ctxt2);\n let st_d' : st_typing g2 st (comp_with_pre c ctxt1) = st_equiv_pre st_d _ (VE_Sym _ _ _ d) in\n k post_hint (| st, _, st_d' |)\n#pop-options\n\nlet vprop_equiv_typing_fwd (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g ctxt p)\n : tot_typing g p tm_vprop \n = let fwd, _ = vprop_equiv_typing d in\n fwd ctxt_typing\n\n#push-options \"--z3rlimit_factor 4 --ifuel 1 --fuel 0\"\nlet k_elab_equiv_prefix\n (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt1 #ctxt2 #ctxt:term)\n (k:continuation_elaborator g1 ctxt1 g2 ctxt)\n (d:vprop_equiv g1 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt2 g2 ctxt =\n fun post_hint res ->\n let framing_token : frame_for_req_in_ctxt g1 ctxt2 ctxt1 = \n let d = VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Trans _ _ _ _ (VE_Unit _ _) d) in\n (| tm_emp, emp_typing, d |)\n in\n let res = k post_hint res in\n let (| st, c, st_d |) = res in\n assert (comp_pre c == ctxt1);\n (| _, _, st_equiv_pre st_d _ d |)\n #pop-options\n\nlet k_elab_equiv\n (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt1 #ctxt1' #ctxt2 #ctxt2':term) \n (k:continuation_elaborator g1 ctxt1 g2 ctxt2)\n (d1:vprop_equiv g1 ctxt1 ctxt1')\n (d2:vprop_equiv g2 ctxt2 ctxt2')\n : continuation_elaborator g1 ctxt1' g2 ctxt2' =\n \n let k : continuation_elaborator g1 ctxt1 g2 ctxt2' =\n k_elab_equiv_continuation k d2 in\n let k : continuation_elaborator g1 ctxt1' g2 ctxt2' =\n k_elab_equiv_prefix k d1 in\n k\n\n#push-options \"--query_stats --fuel 2 --ifuel 2 --split_queries no --z3rlimit_factor 20\"\nopen Pulse.PP\nlet continuation_elaborator_with_bind (#g:env) (ctxt:term)\n (#c1:comp{stateful_comp c1})\n (#e1:st_term)\n (e1_typing:st_typing g e1 c1)\n (ctxt_pre1_typing:tot_typing g (tm_star ctxt (comp_pre c1)) tm_vprop)\n (x:nvar { None? (lookup g (snd x)) })\n : T.Tac (continuation_elaborator\n g\n (tm_star ctxt (comp_pre c1))\n (push_binding g (snd x) (fst x) (comp_res c1))\n (tm_star (open_term (comp_post c1) (snd x)) ctxt)) =\n\n let pre1 = comp_pre c1 in\n let res1 = comp_res c1 in\n let post1 = comp_post c1 in\n let ctxt_typing = star_typing_inversion_l ctxt_pre1_typing in\n // let p_prop = Metatheory.pure_typing_inversion pure_typing in\n let v_eq = VE_Comm g ctxt pre1 in\n let framing_token : frame_for_req_in_ctxt g (tm_star ctxt pre1) pre1 = \n (| ctxt, ctxt_typing, VE_Comm g pre1 ctxt |)\n in\n let (| c1, e1_typing |) =\n apply_frame ctxt_pre1_typing e1_typing framing_token in\n let (| u_of_1, pre_typing, _, _ |) =\n Metatheory.(st_comp_typing_inversion (fst <| comp_typing_inversion (st_typing_correctness e1_typing))) in\n let b = res1 in\n let ppname, x = x in\n let g' = push_binding g x ppname b in\n \n let post1_opened = open_term_nv post1 (v_as_nv x) in\n let k : continuation_elaborator g (tm_star ctxt pre1) g' (tm_star post1_opened ctxt) =\n fun post_hint res ->\n let (| e2, c2, e2_typing |) = res in\n assert (comp_post_matches_hint c2 post_hint);\n let e2_typing : st_typing g' e2 c2 = e2_typing in\n let e2_closed = close_st_term e2 x in\n assume (open_st_term e2_closed x == e2);\n assert (comp_pre c1 == (tm_star ctxt pre1));\n assert (comp_post c1 == tm_star post1 ctxt);\n assert (comp_pre c2 == tm_star post1_opened ctxt);\n assert (open_term (comp_post c1) x == tm_star post1_opened (open_term ctxt x));\n // ctxt is well-typed, hence ln\n assume (open_term ctxt x == ctxt);\n assert (open_term (comp_post c1) x == comp_pre c2);\n // we closed e2 with x\n assume (~ (x `Set.mem` freevars_st e2_closed));\n if x `Set.mem` freevars (comp_post c2)\n then fail g' None \"Impossible: freevar clash when constructing continuation elaborator for bind, please file a bug-report\"\n else (\n let t_typing, post_typing =\n Pulse.Typing.Combinators.bind_res_and_post_typing g c2 x post_hint in\n let g = push_context g \"mk_bind\" e1.range in\n // info_doc g None\n // [prefix 4 1 (doc_of_string \"mk_bind e1 = \") (doc_of_string (Pulse.Syntax.Printer.st_term_to_string e1));\n // prefix 4 1 (doc_of_string \"mk_bind c1 = \") (pp #comp c1);\n // prefix 4 1 (doc_of_string \"mk_bind e2 = \") (doc_of_string (Pulse.Syntax.Printer.st_term_to_string e2));\n // prefix 4 1 (doc_of_string \"mk_bind c2 = \") (pp #comp c2)]\n // ;\n let (| e, c, e_typing |) =\n Pulse.Typing.Combinators.mk_bind\n g (tm_star ctxt pre1) \n e1 e2_closed c1 c2 (ppname, x) e1_typing\n u_of_1 \n e2_typing\n t_typing\n post_typing\n (Some? post_hint)\n in\n (| e, c, e_typing |)\n )\n in\n k\n#pop-options\n\nmodule LN = Pulse.Typing.LN\n#push-options \"--z3rlimit_factor 4 --fuel 1 --ifuel 1\"\n\n\nlet st_comp_typing_with_post_hint \n (#g:env) (#ctxt:_)\n (ctxt_typing:tot_typing g ctxt tm_vprop)\n (post_hint:post_hint_opt g { Some? post_hint })\n (c:comp_st { comp_pre c == ctxt /\\ comp_post_matches_hint c post_hint })\n: st_comp_typing g (st_comp_of_comp c)\n= let st = st_comp_of_comp c in\n let Some ph = post_hint in\n let post_typing_src\n : tot_typing (push_binding ph.g ph.x ppname_default ph.ret_ty)\n (open_term ph.post ph.x) tm_vprop\n = ph.post_typing_src\n in\n let x = fresh g in\n assume (fresh_wrt x g (freevars ph.post));\n assume (None? (lookup g ph.x));\n let post_typing_src\n : tot_typing (push_binding ph.g x ppname_default ph.ret_ty)\n (open_term ph.post x) tm_vprop\n = if x = ph.x\n then post_typing_src\n else \n let open Pulse.Typing.Metatheory.Base in\n let tt :\n tot_typing\n (push_binding ph.g x ppname_default ph.ret_ty)\n (subst_term (open_term ph.post ph.x) (renaming ph.x x))\n (subst_term tm_vprop (renaming ph.x x)) =\n tot_typing_renaming1 ph.g ph.x ph.ret_ty (open_term ph.post ph.x) tm_vprop post_typing_src x\n in\n assert (subst_term tm_vprop (renaming ph.x x) == tm_vprop);\n assume (subst_term (open_term ph.post ph.x) (renaming ph.x x) ==\n open_term ph.post x);\n tt\n in\n let post_typing_src\n : tot_typing (push_binding g x ppname_default ph.ret_ty)\n (open_term ph.post x) tm_vprop\n = //weakening: TODO\n RU.magic ()\n in\n let ty_typing : universe_of ph.g st.res st.u = ph.ty_typing in\n let ty_typing : universe_of g st.res st.u =\n Pulse.Typing.Metatheory.tot_typing_weakening_standard ph.g ty_typing g\n in\n assert (st.res == ph.ret_ty);\n assert (st.post == ph.post);\n STC g st x ty_typing ctxt_typing post_typing_src\n\nlet continuation_elaborator_with_bind_fn (#g:env) (#ctxt:term)\n (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#e1:st_term)\n (#c1:comp { C_Tot? c1 })\n (b:binder{b.binder_ty == comp_res c1})\n (e1_typing:st_typing g e1 c1)\n (x:nvar { None? (lookup g (snd x)) })\n: T.Tac (continuation_elaborator\n g ctxt\n (push_binding g (snd x) ppname_default (comp_res c1)) ctxt)\n= let t1 = comp_res c1 in\n assert ((push_binding g (snd x) (fst x) t1) `env_extends` g);\n fun post_hint (| e2, c2, d2 |) ->\n if None? post_hint then T.fail \"bind_fn: expects the post_hint to be set\";\n let ppname, x = x in\n let e2_closed = close_st_term e2 x in\n assume (open_st_term (close_st_term e2 x) x == e2);\n let e = wr c2 (Tm_Bind {binder=b; head=e1; body=e2_closed}) in\n let (| u, c1_typing |) = Pulse.Typing.Metatheory.Base.st_typing_correctness_ctot e1_typing in\n let c2_typing : comp_typing g c2 (universe_of_comp c2) =\n match c2 with\n | C_ST st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n CT_ST _ _ stc\n \n | C_STAtomic i obs st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n let i_typing = CP.core_check_term g i T.E_Total tm_inames in\n CT_STAtomic _ _ obs _ i_typing stc\n\n | C_STGhost st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n CT_STGhost _ _ stc\n in\n let d : st_typing g e c2 =\n T_BindFn g e1 e2_closed c1 c2 b x e1_typing u c1_typing d2 c2_typing\n in\n (| e, c2, d |)\n\nlet rec check_equiv_emp (g:env) (vp:term)\n : option (vprop_equiv g vp tm_emp)\n = match vp.t with\n | Tm_Emp -> Some (VE_Refl _ _)\n | Tm_Star vp1 vp2 ->\n (match check_equiv_emp g vp1, check_equiv_emp g vp2 with\n | Some d1, Some d2 ->\n let d3 : vprop_equiv g (tm_star vp1 vp2) (tm_star tm_emp tm_emp)\n = VE_Ctxt _ _ _ _ _ d1 d2 in\n let d4 : vprop_equiv g (tm_star tm_emp tm_emp) tm_emp =\n VE_Unit _ _ in\n Some (VE_Trans _ _ _ _ d3 d4)\n | _, _ -> None)\n | _ -> None\n\nPartial implementation:\nlet emp_inames_included (g: env) (i: term) (_: tot_typing g i tm_inames)\n : prop_validity g (tm_inames_subset tm_emp_inames i) =\n \n"
},
{
"role": "assistant",
"content": "RU.magic ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n a: Type ->\n framed: Prims.bool ->\n pre: Steel.Effect.Common.pre_t ->\n post: Steel.Effect.Common.post_t a ->\n req: Steel.Effect.Common.req_t pre ->\n req': Steel.Effect.Common.req_t pre ->\n ens: Steel.Effect.Common.ens_t pre a post ->\n ens': Steel.Effect.Common.ens_t pre a post ->\n f: Steel.Effect.repr a framed pre post req ens ->\n _:\n Prims.squash (forall (h0: Steel.Effect.Common.hmem pre).\n req' (Steel.Effect.Common.mk_rmem pre h0) ==> req (Steel.Effect.Common.mk_rmem pre h0)) ->\n _:\n Prims.squash (forall (h0: Steel.Effect.Common.hmem pre)\n (x: a)\n (h1: Steel.Effect.Common.hmem (post x)).\n ens (Steel.Effect.Common.mk_rmem pre h0) x (Steel.Effect.Common.mk_rmem (post x) h1) ==>\n ens' (Steel.Effect.Common.mk_rmem pre h0) x (Steel.Effect.Common.mk_rmem (post x) h1))\n -> Steel.Effect.repr a framed pre post req' ens'\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.ST.Effect\nfriend Steel.Effect\nopen Steel.Memory\nopen FStar.Ghost\nmodule Mem = Steel.Memory\nmodule T = FStar.Tactics\ninclude Steel.Effect.Common\nopen Steel.Effect\n#set-options \"--warn_error -330\" //turn off the experimental feature warning\n#set-options \"--ide_id_info_off\"\n\nlet repr a framed pre post req ens : Type u#2 =\n Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)\n\nlet equiv_star_emp_r (p:vprop)\n : Lemma ((p `star` emp) `equiv` p)\n = cm_identity p;\n assert ((emp `star` p) `equiv` p);\n star_commutative p emp;\n equiv_trans (p `star` emp) (emp `star` p) p\n\nPartial implementation:\nlet weaken_repr\n a\n framed\n (pre: pre_t)\n (post: post_t a)\n (req: req_t pre)\n (req': req_t pre)\n (ens: ens_t pre a post)\n (ens': ens_t pre a post)\n (f: Steel.Effect.repr a framed pre post req ens)\n (_: squash (forall (h0: hmem pre). req' (mk_rmem _ h0) ==> req (mk_rmem _ h0)))\n (_:\n squash (forall (h0: hmem pre) x (h1: hmem (post x)).\n ens (mk_rmem _ h0) x (mk_rmem _ h1) ==> ens' (mk_rmem _ h0) x (mk_rmem _ h1)))\n : Tot (Steel.Effect.repr a framed pre post req' ens') =\n \n"
},
{
"role": "assistant",
"content": "let focus_rmem_refl (r: vprop) (h: rmem r)\n : Lemma (ensures focus_rmem #r h r == h) [SMTPat (focus_rmem #r h r)] =\n focus_rmem_refl r h\nin\nlet equiv_trans (x y z: vprop)\n : Lemma (requires equiv x y /\\ equiv y z)\n (ensures equiv x z)\n [SMTPat (equiv x z); SMTPat (equiv x y)] =\n equiv_trans x y z\nin\nlet cbs (p: vprop)\n : Lemma (p `can_be_split` (p `star` emp)) [SMTPat (p `can_be_split` (p `star` emp))] =\n star_commutative p emp;\n cm_identity p;\n equiv_sym (p `star` emp) p;\n equiv_can_be_split p (p `star` emp)\nin\nlet epost () : Lemma (equiv_forall post (fun x -> star (post x) emp)) =\n introduce forall x . (post x) `equiv` ((post x) `star` emp)\n with (equiv_star_emp_r (post x);\n equiv_sym ((post x) `star` emp) (post x));\n equiv_forall_elim post (fun x -> star (post x) emp)\nin\nepost ();\nSteel.Effect.subcomp_opaque a #framed #framed #pre #post #req #ens #pre #post #req' #ens' #emp #True\n #() #() #() f"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: a: Type -> x: a\n -> Steel.ST.Effect.repr a\n true\n (Steel.Effect.Common.return_pre (p x))\n p\n Prims.l_True\n (fun v -> v == x)\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.ST.Effect\nfriend Steel.Effect\nopen Steel.Memory\nopen FStar.Ghost\nmodule Mem = Steel.Memory\nmodule T = FStar.Tactics\ninclude Steel.Effect.Common\nopen Steel.Effect\n#set-options \"--warn_error -330\" //turn off the experimental feature warning\n#set-options \"--ide_id_info_off\"\n\nlet repr a framed pre post req ens : Type u#2 =\n Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)\n\nlet equiv_star_emp_r (p:vprop)\n : Lemma ((p `star` emp) `equiv` p)\n = cm_identity p;\n assert ((emp `star` p) `equiv` p);\n star_commutative p emp;\n equiv_trans (p `star` emp) (emp `star` p) p\n\nlet weaken_repr a framed\n (pre:pre_t)\n (post:post_t a)\n (req req':req_t pre)\n (ens ens':ens_t pre a post)\n (f:Steel.Effect.repr a framed pre post req ens)\n (_:squash (forall (h0:hmem pre).\n req' (mk_rmem _ h0) ==>\n req (mk_rmem _ h0)))\n (_:squash (forall (h0:hmem pre) x (h1:hmem (post x)).\n ens (mk_rmem _ h0)\n x\n (mk_rmem _ h1) ==>\n ens' (mk_rmem _ h0) x (mk_rmem _ h1)))\n : Tot (Steel.Effect.repr a framed pre post req' ens')\n = let focus_rmem_refl (r:vprop) (h:rmem r)\n : Lemma (ensures focus_rmem #r h r == h)\n [SMTPat (focus_rmem #r h r)]\n = focus_rmem_refl r h\n in\n let equiv_trans (x y z:vprop) : Lemma\n (requires equiv x y /\\ equiv y z)\n (ensures equiv x z)\n [SMTPat (equiv x z);\n SMTPat (equiv x y)]\n = equiv_trans x y z\n in\n let cbs (p:vprop)\n : Lemma (p `can_be_split` (p `star` emp))\n [SMTPat (p `can_be_split` (p `star` emp))]\n = star_commutative p emp;\n cm_identity p;\n equiv_sym (p `star` emp) p;\n equiv_can_be_split p (p `star` emp)\n in\n let epost ()\n : Lemma (equiv_forall post (fun x -> star (post x) emp))\n = introduce forall x. post x `equiv` (post x `star` emp)\n with (\n equiv_star_emp_r (post x);\n equiv_sym (post x `star` emp) (post x)\n );\n equiv_forall_elim post (fun x -> star (post x) emp)\n in\n epost ();\n Steel.Effect.subcomp_opaque a #framed #framed\n #pre #post\n #req #ens\n #pre #post\n #req' #ens'\n #emp\n #True\n #()\n #()\n #()\n f\n\nPartial implementation:\nlet return_ (a: Type) (x: a) (#[@@@ framing_implicit]p: (a -> vprop))\n : Tot (repr a true (return_pre (p x)) p True (fun v -> v == x)) =\n \n"
},
{
"role": "assistant",
"content": "let k:Steel.Effect.repr a true (p x) p (fun _ -> True) (return_ens a x p) =\n Steel.Effect.return_ a x #p\nin\nweaken_repr _ _ _ _ _ _ _ _ k () ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: i: Vale.Interop.X64.reg_nat 3 -> Vale.X64.Machine_s.reg_64\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nPartial implementation:\nlet of_arg (i: IX64.reg_nat 3) : MS.reg_64 =\n \n"
},
{
"role": "assistant",
"content": "match i with\n| 0 -> MS.rRdi\n| 1 -> MS.rRsi\n| 2 -> MS.rRdx"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.Inline.X64.Fadd_inline.lowstar_add1_t\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nPartial implementation:\nlet lowstar_add1:lowstar_add1_t =\n \n"
},
{
"role": "assistant",
"content": "assert_norm (List.length dom + List.length ([] <: list arg) <= 3);\nIX64.wrap_weak 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: _: Prims.unit -> FStar.All.ML Prims.int\nEffect: FStar.All.ML\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nPartial implementation:\nlet add1_code_inline () : FStar.All.ML int =\n \n"
},
{
"role": "assistant",
"content": "PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg\n add1_regs_modified add1_comments"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: v:\nVale.Interop.X64.arg_reg_relation' 3\n { forall (r: Vale.X64.Machine_s.reg_64). {:pattern Rel?.of_reg v r}\n Some? (Rel?.of_reg v r) ==> Rel?.of_arg v (Some?.v (Rel?.of_reg v r)) = r }\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nPartial implementation:\nlet arg_reg:IX64.arg_reg_relation 3 =\n \n"
},
{
"role": "assistant",
"content": "IX64.Rel of_reg of_arg"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n d: Pulse.Typing.typing g e eff t0 ->\n eq:\n FStar.Ghost.erased (FStar.Reflection.Typing.related (Pulse.Typing.elab_env g)\n (Pulse.Elaborate.Pure.elab_term t0)\n FStar.Reflection.Typing.R_Eq\n (Pulse.Elaborate.Pure.elab_term t1))\n -> Pulse.Typing.typing g e eff t1\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq\n\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv\n\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))\n\nlet simplify_lemma (c:comp_st) (c':comp_st) (post_hint:option post_hint_t)\n : Lemma\n (requires\n comp_post_matches_hint c post_hint /\\\n effect_annot_of_comp c == effect_annot_of_comp c' /\\\n comp_res c' == comp_res c /\\\n comp_u c' == comp_u c /\\\n comp_post c' == tm_star (comp_post c) tm_emp)\n (ensures comp_post_matches_hint (comp_st_with_post c' (comp_post c)) post_hint /\\\n comp_pre (comp_st_with_post c' (comp_post c)) == comp_pre c')\n = ()\n\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing\n\nlet comp_with_pre (c:comp_st) (pre:term) =\n match c with\n | C_ST st -> C_ST { st with pre }\n | C_STGhost st -> C_STGhost { st with pre }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with pre}\n\n\nlet st_equiv_pre (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (pre:term)\n (veq: vprop_equiv g (comp_pre c) pre)\n : st_typing g t (comp_with_pre c pre)\n = if eq_tm pre (comp_pre c) then d\n else\n let c' = comp_with_pre c pre in\n let (| u_of, pre_typing, x, post_typing |) =\n Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) veq (VE_Refl _ _)\n in\n t_equiv d st_equiv\n\n\n#push-options \"--z3rlimit_factor 4 --ifuel 2 --fuel 0\"\nlet k_elab_equiv_continuation (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt #ctxt1 #ctxt2:term)\n (k:continuation_elaborator g1 ctxt g2 ctxt1)\n (d:vprop_equiv g2 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt g2 ctxt2 =\n fun post_hint res ->\n let (| st, c, st_d |) = res in\n let st_d : st_typing g2 st c = st_d in\n assert (comp_pre c == ctxt2);\n let st_d' : st_typing g2 st (comp_with_pre c ctxt1) = st_equiv_pre st_d _ (VE_Sym _ _ _ d) in\n k post_hint (| st, _, st_d' |)\n#pop-options\n\nlet vprop_equiv_typing_fwd (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g ctxt p)\n : tot_typing g p tm_vprop \n = let fwd, _ = vprop_equiv_typing d in\n fwd ctxt_typing\n\n#push-options \"--z3rlimit_factor 4 --ifuel 1 --fuel 0\"\nlet k_elab_equiv_prefix\n (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt1 #ctxt2 #ctxt:term)\n (k:continuation_elaborator g1 ctxt1 g2 ctxt)\n (d:vprop_equiv g1 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt2 g2 ctxt =\n fun post_hint res ->\n let framing_token : frame_for_req_in_ctxt g1 ctxt2 ctxt1 = \n let d = VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Trans _ _ _ _ (VE_Unit _ _) d) in\n (| tm_emp, emp_typing, d |)\n in\n let res = k post_hint res in\n let (| st, c, st_d |) = res in\n assert (comp_pre c == ctxt1);\n (| _, _, st_equiv_pre st_d _ d |)\n #pop-options\n\nlet k_elab_equiv\n (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt1 #ctxt1' #ctxt2 #ctxt2':term) \n (k:continuation_elaborator g1 ctxt1 g2 ctxt2)\n (d1:vprop_equiv g1 ctxt1 ctxt1')\n (d2:vprop_equiv g2 ctxt2 ctxt2')\n : continuation_elaborator g1 ctxt1' g2 ctxt2' =\n \n let k : continuation_elaborator g1 ctxt1 g2 ctxt2' =\n k_elab_equiv_continuation k d2 in\n let k : continuation_elaborator g1 ctxt1' g2 ctxt2' =\n k_elab_equiv_prefix k d1 in\n k\n\n#push-options \"--query_stats --fuel 2 --ifuel 2 --split_queries no --z3rlimit_factor 20\"\nopen Pulse.PP\nlet continuation_elaborator_with_bind (#g:env) (ctxt:term)\n (#c1:comp{stateful_comp c1})\n (#e1:st_term)\n (e1_typing:st_typing g e1 c1)\n (ctxt_pre1_typing:tot_typing g (tm_star ctxt (comp_pre c1)) tm_vprop)\n (x:nvar { None? (lookup g (snd x)) })\n : T.Tac (continuation_elaborator\n g\n (tm_star ctxt (comp_pre c1))\n (push_binding g (snd x) (fst x) (comp_res c1))\n (tm_star (open_term (comp_post c1) (snd x)) ctxt)) =\n\n let pre1 = comp_pre c1 in\n let res1 = comp_res c1 in\n let post1 = comp_post c1 in\n let ctxt_typing = star_typing_inversion_l ctxt_pre1_typing in\n // let p_prop = Metatheory.pure_typing_inversion pure_typing in\n let v_eq = VE_Comm g ctxt pre1 in\n let framing_token : frame_for_req_in_ctxt g (tm_star ctxt pre1) pre1 = \n (| ctxt, ctxt_typing, VE_Comm g pre1 ctxt |)\n in\n let (| c1, e1_typing |) =\n apply_frame ctxt_pre1_typing e1_typing framing_token in\n let (| u_of_1, pre_typing, _, _ |) =\n Metatheory.(st_comp_typing_inversion (fst <| comp_typing_inversion (st_typing_correctness e1_typing))) in\n let b = res1 in\n let ppname, x = x in\n let g' = push_binding g x ppname b in\n \n let post1_opened = open_term_nv post1 (v_as_nv x) in\n let k : continuation_elaborator g (tm_star ctxt pre1) g' (tm_star post1_opened ctxt) =\n fun post_hint res ->\n let (| e2, c2, e2_typing |) = res in\n assert (comp_post_matches_hint c2 post_hint);\n let e2_typing : st_typing g' e2 c2 = e2_typing in\n let e2_closed = close_st_term e2 x in\n assume (open_st_term e2_closed x == e2);\n assert (comp_pre c1 == (tm_star ctxt pre1));\n assert (comp_post c1 == tm_star post1 ctxt);\n assert (comp_pre c2 == tm_star post1_opened ctxt);\n assert (open_term (comp_post c1) x == tm_star post1_opened (open_term ctxt x));\n // ctxt is well-typed, hence ln\n assume (open_term ctxt x == ctxt);\n assert (open_term (comp_post c1) x == comp_pre c2);\n // we closed e2 with x\n assume (~ (x `Set.mem` freevars_st e2_closed));\n if x `Set.mem` freevars (comp_post c2)\n then fail g' None \"Impossible: freevar clash when constructing continuation elaborator for bind, please file a bug-report\"\n else (\n let t_typing, post_typing =\n Pulse.Typing.Combinators.bind_res_and_post_typing g c2 x post_hint in\n let g = push_context g \"mk_bind\" e1.range in\n // info_doc g None\n // [prefix 4 1 (doc_of_string \"mk_bind e1 = \") (doc_of_string (Pulse.Syntax.Printer.st_term_to_string e1));\n // prefix 4 1 (doc_of_string \"mk_bind c1 = \") (pp #comp c1);\n // prefix 4 1 (doc_of_string \"mk_bind e2 = \") (doc_of_string (Pulse.Syntax.Printer.st_term_to_string e2));\n // prefix 4 1 (doc_of_string \"mk_bind c2 = \") (pp #comp c2)]\n // ;\n let (| e, c, e_typing |) =\n Pulse.Typing.Combinators.mk_bind\n g (tm_star ctxt pre1) \n e1 e2_closed c1 c2 (ppname, x) e1_typing\n u_of_1 \n e2_typing\n t_typing\n post_typing\n (Some? post_hint)\n in\n (| e, c, e_typing |)\n )\n in\n k\n#pop-options\n\nmodule LN = Pulse.Typing.LN\n#push-options \"--z3rlimit_factor 4 --fuel 1 --ifuel 1\"\n\n\nlet st_comp_typing_with_post_hint \n (#g:env) (#ctxt:_)\n (ctxt_typing:tot_typing g ctxt tm_vprop)\n (post_hint:post_hint_opt g { Some? post_hint })\n (c:comp_st { comp_pre c == ctxt /\\ comp_post_matches_hint c post_hint })\n: st_comp_typing g (st_comp_of_comp c)\n= let st = st_comp_of_comp c in\n let Some ph = post_hint in\n let post_typing_src\n : tot_typing (push_binding ph.g ph.x ppname_default ph.ret_ty)\n (open_term ph.post ph.x) tm_vprop\n = ph.post_typing_src\n in\n let x = fresh g in\n assume (fresh_wrt x g (freevars ph.post));\n assume (None? (lookup g ph.x));\n let post_typing_src\n : tot_typing (push_binding ph.g x ppname_default ph.ret_ty)\n (open_term ph.post x) tm_vprop\n = if x = ph.x\n then post_typing_src\n else \n let open Pulse.Typing.Metatheory.Base in\n let tt :\n tot_typing\n (push_binding ph.g x ppname_default ph.ret_ty)\n (subst_term (open_term ph.post ph.x) (renaming ph.x x))\n (subst_term tm_vprop (renaming ph.x x)) =\n tot_typing_renaming1 ph.g ph.x ph.ret_ty (open_term ph.post ph.x) tm_vprop post_typing_src x\n in\n assert (subst_term tm_vprop (renaming ph.x x) == tm_vprop);\n assume (subst_term (open_term ph.post ph.x) (renaming ph.x x) ==\n open_term ph.post x);\n tt\n in\n let post_typing_src\n : tot_typing (push_binding g x ppname_default ph.ret_ty)\n (open_term ph.post x) tm_vprop\n = //weakening: TODO\n RU.magic ()\n in\n let ty_typing : universe_of ph.g st.res st.u = ph.ty_typing in\n let ty_typing : universe_of g st.res st.u =\n Pulse.Typing.Metatheory.tot_typing_weakening_standard ph.g ty_typing g\n in\n assert (st.res == ph.ret_ty);\n assert (st.post == ph.post);\n STC g st x ty_typing ctxt_typing post_typing_src\n\nlet continuation_elaborator_with_bind_fn (#g:env) (#ctxt:term)\n (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#e1:st_term)\n (#c1:comp { C_Tot? c1 })\n (b:binder{b.binder_ty == comp_res c1})\n (e1_typing:st_typing g e1 c1)\n (x:nvar { None? (lookup g (snd x)) })\n: T.Tac (continuation_elaborator\n g ctxt\n (push_binding g (snd x) ppname_default (comp_res c1)) ctxt)\n= let t1 = comp_res c1 in\n assert ((push_binding g (snd x) (fst x) t1) `env_extends` g);\n fun post_hint (| e2, c2, d2 |) ->\n if None? post_hint then T.fail \"bind_fn: expects the post_hint to be set\";\n let ppname, x = x in\n let e2_closed = close_st_term e2 x in\n assume (open_st_term (close_st_term e2 x) x == e2);\n let e = wr c2 (Tm_Bind {binder=b; head=e1; body=e2_closed}) in\n let (| u, c1_typing |) = Pulse.Typing.Metatheory.Base.st_typing_correctness_ctot e1_typing in\n let c2_typing : comp_typing g c2 (universe_of_comp c2) =\n match c2 with\n | C_ST st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n CT_ST _ _ stc\n \n | C_STAtomic i obs st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n let i_typing = CP.core_check_term g i T.E_Total tm_inames in\n CT_STAtomic _ _ obs _ i_typing stc\n\n | C_STGhost st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n CT_STGhost _ _ stc\n in\n let d : st_typing g e c2 =\n T_BindFn g e1 e2_closed c1 c2 b x e1_typing u c1_typing d2 c2_typing\n in\n (| e, c2, d |)\n\nlet rec check_equiv_emp (g:env) (vp:term)\n : option (vprop_equiv g vp tm_emp)\n = match vp.t with\n | Tm_Emp -> Some (VE_Refl _ _)\n | Tm_Star vp1 vp2 ->\n (match check_equiv_emp g vp1, check_equiv_emp g vp2 with\n | Some d1, Some d2 ->\n let d3 : vprop_equiv g (tm_star vp1 vp2) (tm_star tm_emp tm_emp)\n = VE_Ctxt _ _ _ _ _ d1 d2 in\n let d4 : vprop_equiv g (tm_star tm_emp tm_emp) tm_emp =\n VE_Unit _ _ in\n Some (VE_Trans _ _ _ _ d3 d4)\n | _, _ -> None)\n | _ -> None\n\n\n\nlet emp_inames_included (g:env) (i:term) (_:tot_typing g i tm_inames)\n: prop_validity g (tm_inames_subset tm_emp_inames i)\n= RU.magic()\n\nlet return_in_ctxt (g:env) (y:var) (y_ppname:ppname) (u:universe) (ty:term) (ctxt:vprop)\n (ty_typing:universe_of g ty u)\n (post_hint0:post_hint_opt g { Some? post_hint0 /\\ checker_res_matches_post_hint g post_hint0 y ty ctxt})\n: Pure (st_typing_in_ctxt g ctxt post_hint0)\n (requires lookup g y == Some ty)\n (ensures fun _ -> True)\n= let Some post_hint = post_hint0 in\n let x = fresh g in\n assume (~ (x `Set.mem` freevars post_hint.post));\n let ctag =\n match post_hint.effect_annot with\n | EffectAnnotAtomic _ -> STT_Atomic\n | EffectAnnotGhost -> STT_Ghost\n | _ -> STT\n in\n let y_tm = tm_var {nm_index=y;nm_ppname=y_ppname} in\n let d = T_Return g ctag false u ty y_tm post_hint.post x ty_typing\n (RU.magic ()) // that null_var y is well typed at ty in g, we know since lookup g y == Some ty\n (RU.magic ()) // typing of (open post x) in (g, x) ... post_hint is well-typed, so should get\n in\n let t = wtag (Some ctag) (Tm_Return {expected_type=tm_unknown;insert_eq=false;term=y_tm}) in\n let c = comp_return ctag false u ty y_tm post_hint.post x in\n let d : st_typing g t c = d in\n assume (comp_u c == post_hint.u); // this u should follow from equality of t\n match c, post_hint.effect_annot with\n | C_STAtomic _ obs _, EffectAnnotAtomic { opens } ->\n assert (comp_inames c == tm_emp_inames);\n let pht = post_hint_typing g post_hint x in\n let validity = emp_inames_included g opens pht.effect_annot_typing in\n let d = T_Sub _ _ _ _ d (STS_AtomicInvs _ (st_comp_of_comp c) tm_emp_inames opens obs obs validity) in\n (| _, _, d |)\n | _ -> \n (| _, _, d |)\n\nlet match_comp_res_with_post_hint (#g:env) (#t:st_term) (#c:comp_st)\n (d:st_typing g t c)\n (post_hint:post_hint_opt g)\n : T.Tac (t':st_term &\n c':comp_st &\n st_typing g t' c') =\n\n match post_hint with\n | None -> (| t, c, d |)\n | Some { ret_ty } ->\n let cres = comp_res c in\n if eq_tm cres ret_ty\n then (| t, c, d |)\n else match Pulse.Checker.Pure.check_equiv g cres ret_ty with\n | None ->\n fail g (Some t.range)\n (Printf.sprintf \"Could not prove equiv for computed type %s and expected type %s\"\n (P.term_to_string cres)\n (P.term_to_string ret_ty))\n | Some tok ->\n let d_equiv\n : RT.equiv _ (elab_term cres) (elab_term ret_ty) =\n RT.Rel_eq_token _ _ _ (FStar.Squash.return_squash tok) in\n \n let c' = with_st_comp c {(st_comp_of_comp c) with res = ret_ty } in\n let (| cres_typing, cpre_typing, x, cpost_typing |) =\n st_comp_typing_inversion (fst <| comp_typing_inversion (st_typing_correctness d)) in\n\n let d_stequiv : st_equiv g c c' =\n ST_VPropEquiv _ c c' _ cpre_typing cres_typing cpost_typing d_equiv (VE_Refl _ _) (VE_Refl _ _)\n in\n\n (| t, c', T_Equiv _ _ _ _ d d_stequiv |)\n\nlet apply_checker_result_k (#g:env) (#ctxt:vprop) (#post_hint:post_hint_for_env g)\n (r:checker_result_t g ctxt (Some post_hint))\n (res_ppname:ppname)\n : T.Tac (st_typing_in_ctxt g ctxt (Some post_hint)) =\n\n // TODO: FIXME add to checker result type?\n let (| y, g1, (| u_ty, ty_y, d_ty_y |), (| pre', _ |), k |) = r in\n\n let (| u_ty_y, d_ty_y |) = Pulse.Checker.Pure.check_universe g1 ty_y in\n\n let d : st_typing_in_ctxt g1 pre' (Some post_hint) =\n return_in_ctxt g1 y res_ppname u_ty_y ty_y pre' d_ty_y (Some post_hint) in\n\n k (Some post_hint) d\n\n#push-options \"--z3rlimit_factor 4 --fuel 0 --ifuel 1 --query_stats\"\nlet checker_result_for_st_typing (#g:env) (#ctxt:vprop) (#post_hint:post_hint_opt g)\n (d:st_typing_in_ctxt g ctxt post_hint)\n (ppname:ppname)\n : T.Tac (checker_result_t g ctxt post_hint) =\n\n let (| t, c, d |) = d in\n \n let x = fresh g in\n\n let g' = push_binding g x ppname (comp_res c) in\n let ctxt' = open_term_nv (comp_post c) (ppname, x) in\n let k\n : continuation_elaborator\n g (tm_star tm_emp (comp_pre c))\n g' (tm_star ctxt' tm_emp) =\n continuation_elaborator_with_bind tm_emp d (RU.magic ()) (ppname, x) in\n let k\n : continuation_elaborator g (comp_pre c) g' ctxt' =\n k_elab_equiv k (RU.magic ()) (RU.magic ()) in\n\n let _ : squash (checker_res_matches_post_hint g post_hint x (comp_res c) ctxt') =\n match post_hint with\n | None -> ()\n | Some post_hint -> () in\n\n assert (g' `env_extends` g);\n\n let comp_res_typing, _, f =\n Metatheory.(st_comp_typing_inversion_cofinite (fst <| comp_typing_inversion (st_typing_correctness d))) in\n\n // RU.magic is the typing of comp_res in g'\n // weaken comp_res_typing\n\n assume (~ (x `Set.mem` freevars (comp_post c)));\n let tt : universe_of _ _ _ = RU.magic () in\n (| x, g', (| comp_u c, comp_res c, tt |), (| ctxt', f x |), k |)\n#pop-options\n\nmodule R = FStar.Reflection.V2\n\nlet readback_comp_res_as_comp (c:T.comp) : option comp =\n match c with\n | T.C_Total t -> (\n match readback_comp t with\n | None -> None\n | Some c -> Some c\n )\n | _ -> None\n\nlet rec is_stateful_arrow (g:env) (c:option comp) (args:list T.argv) (out:list T.argv)\n : T.Tac (option (list T.argv & T.argv))\n = let open R in\n match c with\n | None -> None\n | Some (C_ST _)\n | Some (C_STGhost _)\n | Some (C_STAtomic _ _ _) -> (\n match args, out with\n | [], hd::tl -> Some (List.rev tl, hd)\n | _ -> None //leftover or not enough args\n )\n\n | Some (C_Tot c_res) -> (\n if not (Tm_FStar? c_res.t)\n then None\n else (\n let Tm_FStar c_res = c_res.t in\n let ht = T.inspect c_res in\n match ht with\n | T.Tv_Arrow b c -> (\n match args with\n | [] -> ( //no more args; check that only implicits remain, ending in an stateful comp \n let bs, c = T.collect_arr_ln_bs c_res in\n if List.Tot.for_all (fun b -> R.Q_Implicit? (R.inspect_binder b).qual) bs\n then is_stateful_arrow g (readback_comp_res_as_comp (R.inspect_comp c)) [] out\n else None //too few args \n )\n\n | (arg, qual)::args' -> ( //check that this arg qual matches the binder and recurse accordingly\n match b.qual, qual with\n | T.Q_Meta _, T.Q_Implicit\n | T.Q_Implicit, T.Q_Implicit \n | T.Q_Explicit, T.Q_Explicit -> //consume this argument\n is_stateful_arrow g (readback_comp_res_as_comp c) args' ((arg, qual)::out)\n\n | T.Q_Meta _, T.Q_Explicit\n | T.Q_Implicit, T.Q_Explicit -> \n //don't consume this argument\n is_stateful_arrow g (readback_comp_res_as_comp c) args out\n\n | _ -> None //incompatible qualifiers; bail\n )\n )\n | _ ->\n let c_res' = RU.whnf_lax (elab_env g) c_res in\n let ht = T.inspect c_res' in\n if T.Tv_Arrow? ht\n then (\n assume (not_tv_unknown c_res');\n let c_res' = tm_fstar c_res' (T.range_of_term c_res') in\n is_stateful_arrow g (Some (C_Tot c_res')) args out\n )\n else None\n )\n )\n\nmodule RU = Pulse.RuntimeUtils \nlet is_stateful_application (g:env) (e:term) \n : T.Tac (option st_term)\n = match e.t with\n | Tm_FStar host_term -> (\n let head, args = T.collect_app_ln host_term in\n assume (not_tv_unknown head);\n match RU.lax_check_term_with_unknown_universes (elab_env g) head with\n | None -> None\n | Some ht -> \n assume (not_tv_unknown ht);\n let head_t = tm_fstar ht (T.range_of_term ht) in\n match is_stateful_arrow g (Some (C_Tot head_t)) args [] with \n | None -> None\n | Some (applied_args, (last_arg, aqual))->\n let head = T.mk_app head applied_args in\n assume (not_tv_unknown head);\n let head = tm_fstar head (T.range_of_term head) in\n assume (not_tv_unknown last_arg);\n let last_arg = tm_fstar last_arg (T.range_of_term last_arg) in\n let qual = \n match aqual with\n | T.Q_Implicit -> Some Implicit\n | _ -> None\n in\n let st_app = Tm_STApp { head; arg=last_arg; arg_qual=qual} in\n let st_app = { term = st_app; range=e.range; effect_tag=default_effect_hint } in\n Some st_app\n )\n | _ -> None\n\nPartial implementation:\nlet apply_conversion\n (#g: env)\n (#e: term)\n (#eff: _)\n (#t0: term)\n (d: typing g e eff t0)\n (#t1: term)\n (eq: Ghost.erased (RT.related (elab_env g) (elab_term t0) RT.R_Eq (elab_term t1)))\n : typing g e eff t1 =\n \n"
},
{
"role": "assistant",
"content": "let d:RT.typing (elab_env g) (elab_term e) (eff, (elab_term t0)) = d._0 in\nlet r:RT.related (elab_env g) (elab_term t0) RT.R_Eq (elab_term t1) = eq in\nlet r = RT.Rel_equiv _ _ _ RT.R_Sub r in\nlet s:RT.sub_comp (elab_env g) (eff, (elab_term t0)) (eff, elab_term t1) =\n RT.Relc_typ _ _ _ _ _ r\nin\nE (RT.T_Sub _ _ _ _ d s)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: r: Vale.X64.Machine_s.reg_64 -> Prims.bool\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nPartial implementation:\nlet fadd_regs_modified: MS.reg_64 -> bool =\n \n"
},
{
"role": "assistant",
"content": "fun (r: MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11\n then true\n else false"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n a: Type ->\n b: Type ->\n f: (_: FStar.Pervasives.eqtype_as_type Prims.unit -> Prims.PURE a) ->\n g: (x: a -> Steel.ST.Effect.repr b framed pre post (req x) (ens x))\n -> Steel.ST.Effect.repr b\n framed\n pre\n post\n (Steel.ST.Effect.bind_pure_st_req wp req)\n (Steel.ST.Effect.bind_pure_st_ens wp ens)\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.ST.Effect\nfriend Steel.Effect\nopen Steel.Memory\nopen FStar.Ghost\nmodule Mem = Steel.Memory\nmodule T = FStar.Tactics\ninclude Steel.Effect.Common\nopen Steel.Effect\n#set-options \"--warn_error -330\" //turn off the experimental feature warning\n#set-options \"--ide_id_info_off\"\n\nlet repr a framed pre post req ens : Type u#2 =\n Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)\n\nlet equiv_star_emp_r (p:vprop)\n : Lemma ((p `star` emp) `equiv` p)\n = cm_identity p;\n assert ((emp `star` p) `equiv` p);\n star_commutative p emp;\n equiv_trans (p `star` emp) (emp `star` p) p\n\nlet weaken_repr a framed\n (pre:pre_t)\n (post:post_t a)\n (req req':req_t pre)\n (ens ens':ens_t pre a post)\n (f:Steel.Effect.repr a framed pre post req ens)\n (_:squash (forall (h0:hmem pre).\n req' (mk_rmem _ h0) ==>\n req (mk_rmem _ h0)))\n (_:squash (forall (h0:hmem pre) x (h1:hmem (post x)).\n ens (mk_rmem _ h0)\n x\n (mk_rmem _ h1) ==>\n ens' (mk_rmem _ h0) x (mk_rmem _ h1)))\n : Tot (Steel.Effect.repr a framed pre post req' ens')\n = let focus_rmem_refl (r:vprop) (h:rmem r)\n : Lemma (ensures focus_rmem #r h r == h)\n [SMTPat (focus_rmem #r h r)]\n = focus_rmem_refl r h\n in\n let equiv_trans (x y z:vprop) : Lemma\n (requires equiv x y /\\ equiv y z)\n (ensures equiv x z)\n [SMTPat (equiv x z);\n SMTPat (equiv x y)]\n = equiv_trans x y z\n in\n let cbs (p:vprop)\n : Lemma (p `can_be_split` (p `star` emp))\n [SMTPat (p `can_be_split` (p `star` emp))]\n = star_commutative p emp;\n cm_identity p;\n equiv_sym (p `star` emp) p;\n equiv_can_be_split p (p `star` emp)\n in\n let epost ()\n : Lemma (equiv_forall post (fun x -> star (post x) emp))\n = introduce forall x. post x `equiv` (post x `star` emp)\n with (\n equiv_star_emp_r (post x);\n equiv_sym (post x `star` emp) (post x)\n );\n equiv_forall_elim post (fun x -> star (post x) emp)\n in\n epost ();\n Steel.Effect.subcomp_opaque a #framed #framed\n #pre #post\n #req #ens\n #pre #post\n #req' #ens'\n #emp\n #True\n #()\n #()\n #()\n f\n\n\nlet return_ (a:Type)\n (x:a)\n (#[@@@ framing_implicit] p:a -> vprop)\n : Tot (repr a true (return_pre (p x)) p True (fun v -> v == x))\n = let k : Steel.Effect.repr a true\n (p x)\n p\n (fun _ -> True)\n (return_ens a x p)\n = Steel.Effect.return_ a x #p\n in\n weaken_repr _ _ _ _ _ _ _ _ k () ()\n\nlet bind (a:Type) (b:Type)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t)\n (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:Type0)\n (#[@@@ framing_implicit] ens_f:a -> Type0)\n (#[@@@ framing_implicit] pre_g:a -> pre_t)\n (#[@@@ framing_implicit] post_g:a -> post_t b)\n (#[@@@ framing_implicit] req_g:(a -> Type0))\n (#[@@@ framing_implicit] ens_g:(a -> b -> Type0))\n (#[@@@ framing_implicit] frame_f:vprop)\n (#[@@@ framing_implicit] frame_g:a -> vprop)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] _x1: squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit] _x2: squash (maybe_emp_dep framed_g frame_g))\n (#[@@@ framing_implicit] pr:a -> prop)\n (#[@@@ framing_implicit] p1:squash\n (can_be_split_forall_dep pr\n (fun x -> post_f x `star` frame_f)\n (fun x -> pre_g x `star` frame_g x)))\n (#[@@@ framing_implicit] p2:squash\n (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))\n (f:repr a framed_f pre_f post_f req_f ens_f)\n (g:(x:a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))\n = let c = Steel.Effect.bind a b #framed_f #framed_g\n #pre_f\n #post_f\n #(fun _ -> req_f)\n #(fun _ x _ -> ens_f x)\n #pre_g\n #post_g\n #(fun x _ -> req_g x)\n #(fun x _ y _ -> ens_g x y)\n #frame_f\n #frame_g\n #post\n #_x1\n #_x2\n #pr\n #p1\n #p2\n f g\n in\n weaken_repr _ _ _ _ _ _ _ _ c () ()\n\nlet subcomp (a:Type)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t)\n (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:Type0)\n (#[@@@ framing_implicit] ens_f:a -> Type0)\n (#[@@@ framing_implicit] pre_g:pre_t)\n (#[@@@ framing_implicit] post_g:post_t a)\n (#[@@@ framing_implicit] req_g:Type0)\n (#[@@@ framing_implicit] ens_g:a -> Type0)\n (#[@@@ framing_implicit] frame:vprop)\n (#[@@@ framing_implicit] _x1 : squash (maybe_emp framed_f frame))\n (#[@@@ framing_implicit] p1:squash (\n can_be_split pre_g (pre_f `star` frame)))\n (#[@@@ framing_implicit] p2:squash (\n equiv_forall post_g (fun x -> post_f x `star` frame)))\n (f:repr a framed_f pre_f post_f req_f ens_f)\n : Pure (repr a framed_g pre_g post_g req_g ens_g)\n (requires\n req_g ==> (req_f /\\ (forall x. ens_f x ==> ens_g x)))\n (ensures fun _ -> True)\n = weaken_repr _ _ _ _ _ _ _ _\n (Steel.Effect.subcomp\n a\n #framed_f\n #framed_g\n #pre_f\n #post_f\n #(fun _ -> req_f)\n #(fun _ x _ -> ens_f x)\n #pre_g\n #post_g\n #(fun _ -> req_g)\n #(fun _ x _ -> ens_g x)\n #frame\n #_x1\n #True\n #p1\n #p2\n f)\n () ()\n\nPartial implementation:\nlet bind_pure_st_\n (a b: Type)\n (#[@@@ framing_implicit]wp: pure_wp a)\n (#framed: eqtype_as_type bool)\n (#[@@@ framing_implicit]pre: pre_t)\n (#[@@@ framing_implicit]post: post_t b)\n (#[@@@ framing_implicit]req: (a -> Type0))\n (#[@@@ framing_implicit]ens: (a -> b -> Type0))\n (f: (eqtype_as_type unit -> PURE a wp))\n (g: (x: a -> repr b framed pre post (req x) (ens x)))\n : repr b framed pre post (bind_pure_st_req wp req) (bind_pure_st_ens wp ens) =\n \n"
},
{
"role": "assistant",
"content": "let c:Steel.Effect.repr b\n framed\n pre\n post\n (bind_pure_steel__req wp (fun x _ -> req x))\n (bind_pure_steel__ens wp (fun x _ y _ -> ens x y)) =\n (Steel.Effect.bind_pure_steel_ a b #wp #framed #pre #post #(fun x _ -> req x)\n #(fun x _ y _ -> ens x y) f g)\nin\nFStar.Monotonic.Pure.elim_pure_wp_monotonicity #a wp;\nweaken_repr _ _ _ _ _ _ _ _ c () ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.Interop.X64.arity_ok_stdcall Vale.Interop.Base.td\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\nPartial implementation:\nlet fadd_dom:IX64.arity_ok_stdcall td =\n \n"
},
{
"role": "assistant",
"content": "let y = [t64_mod; t64_no_mod; t64_no_mod] in\nassert_norm (List.length y = 3);\ny"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: ke: Hacl.Bignum.Exponentiation.exp t -> modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Hacl.Impl.RSAPSS.rsapss_verify_bn_st t ke modBits\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\n\nPartial implementation:\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n \n"
},
{
"role": "assistant",
"content": "[@@ inline_let ]let bits = size (bits t) in\nlet nLen = blocks modBits bits in\nlet eLen = blocks eBits bits in\nlet n = sub pkey 0ul nLen in\nlet r2 = sub pkey nLen nLen in\nlet e = sub pkey (nLen +! nLen) eLen in\nlet mask = BN.bn_lt_mask nLen s n in\nlet h = ST.get () in\nSB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\nlet res =\n if BB.unsafe_bool_of_limb mask\n then\n (Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen)\n (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen)\n (as_seq h0 n)\n (as_seq h0 r2)\n (as_seq h1 s)\n (v eBits)\n (as_seq h0 e));\n if bn_lt_pow2 modBits m_def then true else false)\n else false\nin\nres"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_sig Vale.Inline.X64.Fadd_inline.add1_regs_modified\n Vale.Inline.X64.Fadd_inline.add1_xmms_modified\n Vale.Inline.X64.Fadd_inline.add1_pre\n Vale.Inline.X64.Fadd_inline.add1_post\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\nPartial implementation:\nlet add1_lemma =\n \n"
},
{
"role": "assistant",
"content": "as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n a: Type ->\n b: Type ->\n f: Steel.ST.Effect.repr a framed_f pre_f post_f req_f ens_f ->\n g: (x: a -> Steel.ST.Effect.repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x))\n -> Steel.ST.Effect.repr b\n true\n (Steel.Effect.Common.star pre_f frame_f)\n post\n (Steel.ST.Effect.bind_req a req_f ens_f pr req_g)\n (Steel.ST.Effect.bind_ens a b ens_f ens_g)\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.ST.Effect\nfriend Steel.Effect\nopen Steel.Memory\nopen FStar.Ghost\nmodule Mem = Steel.Memory\nmodule T = FStar.Tactics\ninclude Steel.Effect.Common\nopen Steel.Effect\n#set-options \"--warn_error -330\" //turn off the experimental feature warning\n#set-options \"--ide_id_info_off\"\n\nlet repr a framed pre post req ens : Type u#2 =\n Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)\n\nlet equiv_star_emp_r (p:vprop)\n : Lemma ((p `star` emp) `equiv` p)\n = cm_identity p;\n assert ((emp `star` p) `equiv` p);\n star_commutative p emp;\n equiv_trans (p `star` emp) (emp `star` p) p\n\nlet weaken_repr a framed\n (pre:pre_t)\n (post:post_t a)\n (req req':req_t pre)\n (ens ens':ens_t pre a post)\n (f:Steel.Effect.repr a framed pre post req ens)\n (_:squash (forall (h0:hmem pre).\n req' (mk_rmem _ h0) ==>\n req (mk_rmem _ h0)))\n (_:squash (forall (h0:hmem pre) x (h1:hmem (post x)).\n ens (mk_rmem _ h0)\n x\n (mk_rmem _ h1) ==>\n ens' (mk_rmem _ h0) x (mk_rmem _ h1)))\n : Tot (Steel.Effect.repr a framed pre post req' ens')\n = let focus_rmem_refl (r:vprop) (h:rmem r)\n : Lemma (ensures focus_rmem #r h r == h)\n [SMTPat (focus_rmem #r h r)]\n = focus_rmem_refl r h\n in\n let equiv_trans (x y z:vprop) : Lemma\n (requires equiv x y /\\ equiv y z)\n (ensures equiv x z)\n [SMTPat (equiv x z);\n SMTPat (equiv x y)]\n = equiv_trans x y z\n in\n let cbs (p:vprop)\n : Lemma (p `can_be_split` (p `star` emp))\n [SMTPat (p `can_be_split` (p `star` emp))]\n = star_commutative p emp;\n cm_identity p;\n equiv_sym (p `star` emp) p;\n equiv_can_be_split p (p `star` emp)\n in\n let epost ()\n : Lemma (equiv_forall post (fun x -> star (post x) emp))\n = introduce forall x. post x `equiv` (post x `star` emp)\n with (\n equiv_star_emp_r (post x);\n equiv_sym (post x `star` emp) (post x)\n );\n equiv_forall_elim post (fun x -> star (post x) emp)\n in\n epost ();\n Steel.Effect.subcomp_opaque a #framed #framed\n #pre #post\n #req #ens\n #pre #post\n #req' #ens'\n #emp\n #True\n #()\n #()\n #()\n f\n\n\nlet return_ (a:Type)\n (x:a)\n (#[@@@ framing_implicit] p:a -> vprop)\n : Tot (repr a true (return_pre (p x)) p True (fun v -> v == x))\n = let k : Steel.Effect.repr a true\n (p x)\n p\n (fun _ -> True)\n (return_ens a x p)\n = Steel.Effect.return_ a x #p\n in\n weaken_repr _ _ _ _ _ _ _ _ k () ()\n\nPartial implementation:\nlet bind\n (a b: Type)\n (#framed_f #framed_g: eqtype_as_type bool)\n (#[@@@ framing_implicit]pre_f: pre_t)\n (#[@@@ framing_implicit]post_f: post_t a)\n (#[@@@ framing_implicit]req_f: Type0)\n (#[@@@ framing_implicit]ens_f: (a -> Type0))\n (#[@@@ framing_implicit]pre_g: (a -> pre_t))\n (#[@@@ framing_implicit]post_g: (a -> post_t b))\n (#[@@@ framing_implicit]req_g: (a -> Type0))\n (#[@@@ framing_implicit]ens_g: (a -> b -> Type0))\n (#[@@@ framing_implicit]frame_f: vprop)\n (#[@@@ framing_implicit]frame_g: (a -> vprop))\n (#[@@@ framing_implicit]post: post_t b)\n (#[@@@ framing_implicit]_x1: squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit]_x2: squash (maybe_emp_dep framed_g frame_g))\n (#[@@@ framing_implicit]pr: (a -> prop))\n (#[@@@ framing_implicit]p1:\n squash (can_be_split_forall_dep pr\n (fun x -> (post_f x) `star` frame_f)\n (fun x -> (pre_g x) `star` (frame_g x))))\n (#[@@@ framing_implicit]p2:\n squash (can_be_split_post (fun x y -> (post_g x y) `star` (frame_g x)) post))\n (f: repr a framed_f pre_f post_f req_f ens_f)\n (g: (x: a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))\n =\n \n"
},
{
"role": "assistant",
"content": "let c =\n Steel.Effect.bind a b #framed_f #framed_g #pre_f #post_f #(fun _ -> req_f) #(fun _ x _ -> ens_f x)\n #pre_g #post_g #(fun x _ -> req_g x) #(fun x _ y _ -> ens_g x y) #frame_f #frame_g #post #_x1\n #_x2 #pr #p1 #p2 f g\nin\nweaken_repr _ _ _ _ _ _ _ _ c () ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: alg: Vale.AES.AES_common_s.algorithm -> Vale.X64.Decls.va_code\nEffect: Prims.Tot\n\nContext:\nmodule Vale.AES.X64.GCMdecryptOpt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_s\nopen Vale.AES.GCTR_s\nopen Vale.AES.GCTR\nopen Vale.AES.GCM\nopen Vale.AES.GHash_s\nopen Vale.AES.GHash\nopen Vale.AES.GCM_s\nopen Vale.AES.X64.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers\nopen Vale.AES.X64.GHash\nopen Vale.AES.X64.GCTR\nopen Vale.X64.Machine_s\nopen Vale.X64.Memory\nopen Vale.X64.Stack_i\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsStack\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.AES.X64.GF128_Mul\nopen Vale.X64.Stack\nopen Vale.X64.CPU_Features_s\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.X64.AESopt\nopen Vale.AES.X64.AESGCM\nopen Vale.AES.X64.AESopt2\nopen Vale.Lib.Meta\nopen Vale.AES.X64.GCMencryptOpt\nopen Vale.AES.OptPublic\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 20 --max_ifuel 0\"\n//-- Gcm_extra_bytes\n\nval va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code\n\nPartial implementation:\nlet va_code_Gcm_extra_bytes alg =\n \n"
},
{
"role": "assistant",
"content": "(va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 5)\n (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax)\n 0\n Secret)\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 0))\n (va_CCons (va_code_Ghash_extra_bytes ())\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11))\n (va_CCons (va_code_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9))\n (va_CCons (va_code_AESEncryptBlock alg)\n (va_CCons (va_code_Pxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 0))\n (va_CCons (va_code_Store128_buffer (va_op_heaplet_mem_heaplet 5)\n (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 10)\n 0\n Secret)\n (va_CNil ()))))))))))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: a: Type -> f: Steel.ST.Effect.repr a framed_f pre_f post_f req_f ens_f\n -> Prims.Pure (Steel.ST.Effect.repr a framed_g pre_g post_g req_g ens_g)\nEffect: Prims.Pure\n\nContext:\n(*\n Copyright 2020 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Steel.ST.Effect\nfriend Steel.Effect\nopen Steel.Memory\nopen FStar.Ghost\nmodule Mem = Steel.Memory\nmodule T = FStar.Tactics\ninclude Steel.Effect.Common\nopen Steel.Effect\n#set-options \"--warn_error -330\" //turn off the experimental feature warning\n#set-options \"--ide_id_info_off\"\n\nlet repr a framed pre post req ens : Type u#2 =\n Steel.Effect.repr a framed pre post (fun _ -> req) (fun _ v _ -> ens v)\n\nlet equiv_star_emp_r (p:vprop)\n : Lemma ((p `star` emp) `equiv` p)\n = cm_identity p;\n assert ((emp `star` p) `equiv` p);\n star_commutative p emp;\n equiv_trans (p `star` emp) (emp `star` p) p\n\nlet weaken_repr a framed\n (pre:pre_t)\n (post:post_t a)\n (req req':req_t pre)\n (ens ens':ens_t pre a post)\n (f:Steel.Effect.repr a framed pre post req ens)\n (_:squash (forall (h0:hmem pre).\n req' (mk_rmem _ h0) ==>\n req (mk_rmem _ h0)))\n (_:squash (forall (h0:hmem pre) x (h1:hmem (post x)).\n ens (mk_rmem _ h0)\n x\n (mk_rmem _ h1) ==>\n ens' (mk_rmem _ h0) x (mk_rmem _ h1)))\n : Tot (Steel.Effect.repr a framed pre post req' ens')\n = let focus_rmem_refl (r:vprop) (h:rmem r)\n : Lemma (ensures focus_rmem #r h r == h)\n [SMTPat (focus_rmem #r h r)]\n = focus_rmem_refl r h\n in\n let equiv_trans (x y z:vprop) : Lemma\n (requires equiv x y /\\ equiv y z)\n (ensures equiv x z)\n [SMTPat (equiv x z);\n SMTPat (equiv x y)]\n = equiv_trans x y z\n in\n let cbs (p:vprop)\n : Lemma (p `can_be_split` (p `star` emp))\n [SMTPat (p `can_be_split` (p `star` emp))]\n = star_commutative p emp;\n cm_identity p;\n equiv_sym (p `star` emp) p;\n equiv_can_be_split p (p `star` emp)\n in\n let epost ()\n : Lemma (equiv_forall post (fun x -> star (post x) emp))\n = introduce forall x. post x `equiv` (post x `star` emp)\n with (\n equiv_star_emp_r (post x);\n equiv_sym (post x `star` emp) (post x)\n );\n equiv_forall_elim post (fun x -> star (post x) emp)\n in\n epost ();\n Steel.Effect.subcomp_opaque a #framed #framed\n #pre #post\n #req #ens\n #pre #post\n #req' #ens'\n #emp\n #True\n #()\n #()\n #()\n f\n\n\nlet return_ (a:Type)\n (x:a)\n (#[@@@ framing_implicit] p:a -> vprop)\n : Tot (repr a true (return_pre (p x)) p True (fun v -> v == x))\n = let k : Steel.Effect.repr a true\n (p x)\n p\n (fun _ -> True)\n (return_ens a x p)\n = Steel.Effect.return_ a x #p\n in\n weaken_repr _ _ _ _ _ _ _ _ k () ()\n\nlet bind (a:Type) (b:Type)\n (#framed_f:eqtype_as_type bool)\n (#framed_g:eqtype_as_type bool)\n (#[@@@ framing_implicit] pre_f:pre_t)\n (#[@@@ framing_implicit] post_f:post_t a)\n (#[@@@ framing_implicit] req_f:Type0)\n (#[@@@ framing_implicit] ens_f:a -> Type0)\n (#[@@@ framing_implicit] pre_g:a -> pre_t)\n (#[@@@ framing_implicit] post_g:a -> post_t b)\n (#[@@@ framing_implicit] req_g:(a -> Type0))\n (#[@@@ framing_implicit] ens_g:(a -> b -> Type0))\n (#[@@@ framing_implicit] frame_f:vprop)\n (#[@@@ framing_implicit] frame_g:a -> vprop)\n (#[@@@ framing_implicit] post:post_t b)\n (#[@@@ framing_implicit] _x1: squash (maybe_emp framed_f frame_f))\n (#[@@@ framing_implicit] _x2: squash (maybe_emp_dep framed_g frame_g))\n (#[@@@ framing_implicit] pr:a -> prop)\n (#[@@@ framing_implicit] p1:squash\n (can_be_split_forall_dep pr\n (fun x -> post_f x `star` frame_f)\n (fun x -> pre_g x `star` frame_g x)))\n (#[@@@ framing_implicit] p2:squash\n (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post))\n (f:repr a framed_f pre_f post_f req_f ens_f)\n (g:(x:a -> repr b framed_g (pre_g x) (post_g x) (req_g x) (ens_g x)))\n = let c = Steel.Effect.bind a b #framed_f #framed_g\n #pre_f\n #post_f\n #(fun _ -> req_f)\n #(fun _ x _ -> ens_f x)\n #pre_g\n #post_g\n #(fun x _ -> req_g x)\n #(fun x _ y _ -> ens_g x y)\n #frame_f\n #frame_g\n #post\n #_x1\n #_x2\n #pr\n #p1\n #p2\n f g\n in\n weaken_repr _ _ _ _ _ _ _ _ c () ()\n\nPartial implementation:\nlet subcomp\n (a: Type)\n (#framed_f #framed_g: eqtype_as_type bool)\n (#[@@@ framing_implicit]pre_f: pre_t)\n (#[@@@ framing_implicit]post_f: post_t a)\n (#[@@@ framing_implicit]req_f: Type0)\n (#[@@@ framing_implicit]ens_f: (a -> Type0))\n (#[@@@ framing_implicit]pre_g: pre_t)\n (#[@@@ framing_implicit]post_g: post_t a)\n (#[@@@ framing_implicit]req_g: Type0)\n (#[@@@ framing_implicit]ens_g: (a -> Type0))\n (#[@@@ framing_implicit]frame: vprop)\n (#[@@@ framing_implicit]_x1: squash (maybe_emp framed_f frame))\n (#[@@@ framing_implicit]p1: squash (can_be_split pre_g (pre_f `star` frame)))\n (#[@@@ framing_implicit]p2: squash (equiv_forall post_g (fun x -> (post_f x) `star` frame)))\n (f: repr a framed_f pre_f post_f req_f ens_f)\n : Pure (repr a framed_g pre_g post_g req_g ens_g)\n (requires req_g ==> (req_f /\\ (forall x. ens_f x ==> ens_g x)))\n (ensures fun _ -> True) =\n \n"
},
{
"role": "assistant",
"content": "weaken_repr _ _ _ _ _ _ _ _\n (Steel.Effect.subcomp a #framed_f #framed_g #pre_f #post_f #(fun _ -> req_f)\n #(fun _ x _ -> ens_f x) #pre_g #post_g #(fun _ -> req_g) #(fun _ x _ -> ens_g x) #frame #_x1\n #True #p1 #p2 f) () ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: r: Vale.X64.Machine_s.reg_64 -> Prims.bool\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nPartial implementation:\nlet fsub_regs_modified: MS.reg_64 -> bool =\n \n"
},
{
"role": "assistant",
"content": "fun (r: MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true else false"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Type0\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n\nPartial implementation:\nlet lowstar_fadd_t =\n \n"
},
{
"role": "assistant",
"content": "assert_norm (List.length fadd_dom + List.length ([] <: list arg) <= 3);\nIX64.as_lowstar_sig_t_weak 3 arg_reg fadd_regs_modified fadd_xmms_modified code_Fadd fadd_dom [] _ _\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: alg: Vale.AES.AES_common_s.algorithm -> Vale.X64.Decls.va_pbool\nEffect: Prims.Tot\n\nContext:\nmodule Vale.AES.X64.GCMdecryptOpt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_s\nopen Vale.AES.GCTR_s\nopen Vale.AES.GCTR\nopen Vale.AES.GCM\nopen Vale.AES.GHash_s\nopen Vale.AES.GHash\nopen Vale.AES.GCM_s\nopen Vale.AES.X64.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers\nopen Vale.AES.X64.GHash\nopen Vale.AES.X64.GCTR\nopen Vale.X64.Machine_s\nopen Vale.X64.Memory\nopen Vale.X64.Stack_i\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsStack\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.AES.X64.GF128_Mul\nopen Vale.X64.Stack\nopen Vale.X64.CPU_Features_s\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.X64.AESopt\nopen Vale.AES.X64.AESGCM\nopen Vale.AES.X64.AESopt2\nopen Vale.Lib.Meta\nopen Vale.AES.X64.GCMencryptOpt\nopen Vale.AES.OptPublic\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 20 --max_ifuel 0\"\n//-- Gcm_extra_bytes\n\nval va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_extra_bytes alg =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 0)) (va_CCons (va_code_Ghash_extra_bytes ()) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_CCons (va_code_Pshufb (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 9)) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_Pxor\n (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_CNil ()))))))))))\n\nval va_codegen_success_Gcm_extra_bytes : alg:algorithm -> Tot va_pbool\n\nPartial implementation:\nlet va_codegen_success_Gcm_extra_bytes alg =\n \n"
},
{
"role": "assistant",
"content": "(va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 5)\n (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax)\n 0\n Secret)\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 0))\n (va_pbool_and (va_codegen_success_Ghash_extra_bytes ())\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11))\n (va_pbool_and (va_codegen_success_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9))\n (va_pbool_and (va_codegen_success_AESEncryptBlock alg)\n (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 0))\n (va_pbool_and (va_codegen_success_Store128_buffer (va_op_heaplet_mem_heaplet\n 5)\n (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 10)\n 0\n Secret)\n (va_ttrue ())))))))))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.Interop.X64.arity_ok_stdcall Vale.Interop.Base.td\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\nPartial implementation:\nlet fsub_dom:IX64.arity_ok_stdcall td =\n \n"
},
{
"role": "assistant",
"content": "let y = [t64_mod; t64_no_mod; t64_no_mod] in\nassert_norm (List.length y = 3);\ny"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: w1: ID5.wp a -> w2: (_: a -> ID5.wp b) -> ID5.wp b\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule DM4F_layered5\n\n(* Same as DM4F, but layered over a layered PURE without monotonicity *)\nopen ID5\nopen DM4F_Utils\n\nPartial implementation:\nlet pure_bind_wp (#a #b: Type) (w1: ID5.wp a) (w2: (a -> ID5.wp b)) : ID5.wp b =\n \n"
},
{
"role": "assistant",
"content": "ID5.bind_wp w1 w2"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: w: DM4F_layered5.wp0 st a -> Type0\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule DM4F_layered5\n\n(* Same as DM4F, but layered over a layered PURE without monotonicity *)\nopen ID5\nopen DM4F_Utils\n\nunfold\nlet pure_bind_wp (#a #b : Type) (w1 : ID5.wp a) (w2 : a -> ID5.wp b) : ID5.wp b =\n ID5.bind_wp w1 w2\n\n(* Simulating state effect in DM4F, hopefully doable by a tactic. *)\n\ntype post_t st a = a -> st -> Type0\n\ntype wp0 (st:Type u#0) (a:Type u#ua) : Type u#(max 1 ua) =\n st -> post_t st a -> Type0\n\nPartial implementation:\nlet st_monotonic #st #a (w: wp0 st a) : Type0 =\n \n"
},
{
"role": "assistant",
"content": "forall s0 p1 p2. (forall x s1. p1 x s1 ==> p2 x s1) ==> w s0 p1 ==> w s0 p2"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Type0\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that fsub_lemma' has the required type *)\nlet fsub_lemma = as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'\n\nlet code_Fsub = FH.va_code_Fsub ()\n\n(* Here's the type expected for the fsub wrapper *)\n\nPartial implementation:\nlet lowstar_Fsub_t =\n \n"
},
{
"role": "assistant",
"content": "assert_norm (List.length fsub_dom + List.length ([] <: list arg) <= 3);\nIX64.as_lowstar_sig_t_weak 3 arg_reg fsub_regs_modified fsub_xmms_modified code_Fsub fsub_dom [] _ _\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_sig Vale.Inline.X64.Fadd_inline.fadd_regs_modified\n Vale.Inline.X64.Fadd_inline.fadd_xmms_modified\n Vale.Inline.X64.Fadd_inline.fadd_pre\n Vale.Inline.X64.Fadd_inline.fadd_post\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\nPartial implementation:\nlet fadd_lemma =\n \n"
},
{
"role": "assistant",
"content": "as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: alg: Vale.AES.AES_common_s.algorithm -> Vale.X64.Decls.va_code\nEffect: Prims.Tot\n\nContext:\nmodule Vale.AES.X64.GCMdecryptOpt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_s\nopen Vale.AES.GCTR_s\nopen Vale.AES.GCTR\nopen Vale.AES.GCM\nopen Vale.AES.GHash_s\nopen Vale.AES.GHash\nopen Vale.AES.GCM_s\nopen Vale.AES.X64.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers\nopen Vale.AES.X64.GHash\nopen Vale.AES.X64.GCTR\nopen Vale.X64.Machine_s\nopen Vale.X64.Memory\nopen Vale.X64.Stack_i\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsStack\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.AES.X64.GF128_Mul\nopen Vale.X64.Stack\nopen Vale.X64.CPU_Features_s\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.X64.AESopt\nopen Vale.AES.X64.AESGCM\nopen Vale.AES.X64.AESopt2\nopen Vale.Lib.Meta\nopen Vale.AES.X64.GCMencryptOpt\nopen Vale.AES.OptPublic\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 20 --max_ifuel 0\"\n//-- Gcm_extra_bytes\n\nval va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_extra_bytes alg =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 0)) (va_CCons (va_code_Ghash_extra_bytes ()) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_CCons (va_code_Pshufb (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 9)) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_Pxor\n (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_CNil ()))))))))))\n\nval va_codegen_success_Gcm_extra_bytes : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_extra_bytes alg =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Ghash_extra_bytes ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_pbool_and\n (va_codegen_success_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (va_pbool_and\n (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_ttrue ())))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRax) 0 Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_xmm 0 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_LE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) (FStar.Seq.Base.create #quad32 1 hash_input)) (let (snap:(FStar.Seq.Base.seq\n Vale.X64.Decls.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 11 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 204 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 10) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 207 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_reveal ()) (va_QEmpty (()))))))))))))))\n\n\nval va_lemma_Gcm_extra_bytes : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n inout_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 -> completed_quads:(seq quad32) ->\n h_LE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_extra_bytes alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (len:(va_int_range 1 1)) = 1 in sse_enabled /\\ Vale.X64.Decls.buffers_disjoint128 keys_b\n inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b inout_b /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax va_s0) inout_b\n len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) /\\ va_state_eq va_sM\n (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10 va_sM (va_update_xmm 8\n va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5 va_sM (va_update_xmm 4\n va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_xmm 0\n va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM (va_update_ok va_sM\n (va_update_mem va_sM va_s0))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_extra_bytes va_b0 va_s0 alg inout_b key round_keys keys_b hkeys_b total_bytes\n old_hash completed_quads h_LE =\n let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8;\n va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm\n 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem] in\n let va_qc = va_qcode_Gcm_extra_bytes va_mods alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_extra_bytes alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 121 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (len:(va_int_range 1 1)) = 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 174 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.X64.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 177 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.AES.GCTR.gctr_partial alg len (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0)) /\\ label\n va_range1\n \"***** POSTCONDITION NOT MET AT line 180 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 181 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 182 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let padded_bytes = Vale.AES.GCTR_s.pad_to_128_bits input_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 183 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_quads = Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 186 column 59 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (l_and (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0)\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_sM) == Vale.AES.GHash.ghash_incremental\n h_LE old_hash input_quads)))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ (let (len:(va_int_range 1 1)) = 1 in sse_enabled /\\\n Vale.X64.Decls.buffers_disjoint128 keys_b inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b\n inout_b /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax\n va_s0) inout_b len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_mem:vale_heap) (va_x_rcx:nat64) (va_x_r11:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32)\n (va_x_xmm2:quad32) (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32)\n (va_x_xmm7:quad32) (va_x_xmm8:quad32) (va_x_xmm10:quad32) (va_x_heap5:vale_heap)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_mem_heaplet 5\n va_x_heap5 (va_upd_xmm 10 va_x_xmm10 (va_upd_xmm 8 va_x_xmm8 (va_upd_xmm 7 va_x_xmm7\n (va_upd_xmm 6 va_x_xmm6 (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3\n (va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR11\n va_x_r11 (va_upd_reg64 rRcx va_x_rcx (va_upd_mem va_x_mem va_s0)))))))))))))) in va_get_ok\n va_sM /\\ (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_extra_bytes : alg:algorithm -> inout_b:buffer128 -> key:(seq nat32) ->\n round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> total_bytes:nat ->\n old_hash:quad32 -> completed_quads:(seq quad32) -> h_LE:quad32 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_extra_bytes alg) ([va_Mod_flags;\n va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5;\n va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11;\n va_Mod_reg64 rRcx; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_extra_bytes (va_code_Gcm_extra_bytes alg) va_s0 alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_LE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10\n va_sM (va_update_xmm 8 va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5\n va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1\n va_sM (va_update_xmm 0 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit (va_code_Gcm_extra_bytes alg)) =\n (va_QProc (va_code_Gcm_extra_bytes alg) ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10;\n va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm\n 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem])\n (va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE) (va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE))\n//--\n//-- Gcm_blocks128\n\nval va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code\n\nPartial implementation:\nlet va_code_Gcm_blocks128 alg =\n \n"
},
{
"role": "assistant",
"content": "(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax))\n (va_CCons (va_code_Ghash_buffer ())\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRbx))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdx)\n (va_op_opr64_reg64 rR12))\n (va_CCons (va_code_Gctr_blocks128 alg) (va_CNil ())))))))))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.Inline.X64.Fadd_inline.lowstar_fadd_t\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nPartial implementation:\nlet lowstar_fadd:lowstar_fadd_t =\n \n"
},
{
"role": "assistant",
"content": "assert_norm (List.length fadd_dom + List.length ([] <: list arg) <= 3);\nIX64.wrap_weak 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n code: Vale.X64.Decls.va_code ->\n _win: Prims.bool ->\n out: Vale.Inline.X64.Fadd_inline.b64 ->\n f1: Vale.Inline.X64.Fadd_inline.b64 ->\n f2: Vale.Inline.X64.Fadd_inline.uint64 ->\n va_s0: Vale.X64.Decls.va_state\n -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)\nEffect: Prims.Ghost\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\nPartial implementation:\nlet add1_lemma' (code: V.va_code) (_win: bool) (out f1: b64) (f2: uint64) (va_s0: V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires add1_pre code out f1 f2 va_s0)\n (ensures\n (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\ ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out)) ME.loc_none)\n (VS.vs_get_vale_heap va_s0)\n (VS.vs_get_vale_heap va_s1))) =\n \n"
},
{
"role": "assistant",
"content": "let va_s1, f =\n FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\nin\nVale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\nVale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n(va_s1, f)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.Inline.X64.Fadd_inline.lowstar_Fsub_t\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that fsub_lemma' has the required type *)\nlet fsub_lemma = as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'\n\nlet code_Fsub = FH.va_code_Fsub ()\n\n(* Here's the type expected for the fsub wrapper *)\n[@__reduce__]\nlet lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\nPartial implementation:\nlet lowstar_Fsub:lowstar_Fsub_t =\n \n"
},
{
"role": "assistant",
"content": "assert_norm (List.length fsub_dom + List.length ([] <: list arg) <= 3);\nIX64.wrap_weak 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: alg: Vale.AES.AES_common_s.algorithm -> offset: Prims.int -> Vale.X64.Decls.va_pbool\nEffect: Prims.Tot\n\nContext:\nmodule Vale.AES.X64.GCMdecryptOpt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_s\nopen Vale.AES.GCTR_s\nopen Vale.AES.GCTR\nopen Vale.AES.GCM\nopen Vale.AES.GHash_s\nopen Vale.AES.GHash\nopen Vale.AES.GCM_s\nopen Vale.AES.X64.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers\nopen Vale.AES.X64.GHash\nopen Vale.AES.X64.GCTR\nopen Vale.X64.Machine_s\nopen Vale.X64.Memory\nopen Vale.X64.Stack_i\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsStack\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.AES.X64.GF128_Mul\nopen Vale.X64.Stack\nopen Vale.X64.CPU_Features_s\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.X64.AESopt\nopen Vale.AES.X64.AESGCM\nopen Vale.AES.X64.AESopt2\nopen Vale.Lib.Meta\nopen Vale.AES.X64.GCMencryptOpt\nopen Vale.AES.OptPublic\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 20 --max_ifuel 0\"\n//-- Gcm_extra_bytes\n\nval va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_extra_bytes alg =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 0)) (va_CCons (va_code_Ghash_extra_bytes ()) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_CCons (va_code_Pshufb (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 9)) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_Pxor\n (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_CNil ()))))))))))\n\nval va_codegen_success_Gcm_extra_bytes : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_extra_bytes alg =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Ghash_extra_bytes ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_pbool_and\n (va_codegen_success_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (va_pbool_and\n (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_ttrue ())))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRax) 0 Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_xmm 0 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_LE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) (FStar.Seq.Base.create #quad32 1 hash_input)) (let (snap:(FStar.Seq.Base.seq\n Vale.X64.Decls.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 11 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 204 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 10) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 207 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_reveal ()) (va_QEmpty (()))))))))))))))\n\n\nval va_lemma_Gcm_extra_bytes : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n inout_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 -> completed_quads:(seq quad32) ->\n h_LE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_extra_bytes alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (len:(va_int_range 1 1)) = 1 in sse_enabled /\\ Vale.X64.Decls.buffers_disjoint128 keys_b\n inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b inout_b /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax va_s0) inout_b\n len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) /\\ va_state_eq va_sM\n (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10 va_sM (va_update_xmm 8\n va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5 va_sM (va_update_xmm 4\n va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_xmm 0\n va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM (va_update_ok va_sM\n (va_update_mem va_sM va_s0))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_extra_bytes va_b0 va_s0 alg inout_b key round_keys keys_b hkeys_b total_bytes\n old_hash completed_quads h_LE =\n let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8;\n va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm\n 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem] in\n let va_qc = va_qcode_Gcm_extra_bytes va_mods alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_extra_bytes alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 121 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (len:(va_int_range 1 1)) = 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 174 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.X64.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 177 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.AES.GCTR.gctr_partial alg len (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0)) /\\ label\n va_range1\n \"***** POSTCONDITION NOT MET AT line 180 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 181 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 182 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let padded_bytes = Vale.AES.GCTR_s.pad_to_128_bits input_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 183 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_quads = Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 186 column 59 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (l_and (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0)\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_sM) == Vale.AES.GHash.ghash_incremental\n h_LE old_hash input_quads)))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ (let (len:(va_int_range 1 1)) = 1 in sse_enabled /\\\n Vale.X64.Decls.buffers_disjoint128 keys_b inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b\n inout_b /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax\n va_s0) inout_b len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_mem:vale_heap) (va_x_rcx:nat64) (va_x_r11:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32)\n (va_x_xmm2:quad32) (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32)\n (va_x_xmm7:quad32) (va_x_xmm8:quad32) (va_x_xmm10:quad32) (va_x_heap5:vale_heap)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_mem_heaplet 5\n va_x_heap5 (va_upd_xmm 10 va_x_xmm10 (va_upd_xmm 8 va_x_xmm8 (va_upd_xmm 7 va_x_xmm7\n (va_upd_xmm 6 va_x_xmm6 (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3\n (va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR11\n va_x_r11 (va_upd_reg64 rRcx va_x_rcx (va_upd_mem va_x_mem va_s0)))))))))))))) in va_get_ok\n va_sM /\\ (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_extra_bytes : alg:algorithm -> inout_b:buffer128 -> key:(seq nat32) ->\n round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> total_bytes:nat ->\n old_hash:quad32 -> completed_quads:(seq quad32) -> h_LE:quad32 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_extra_bytes alg) ([va_Mod_flags;\n va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5;\n va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11;\n va_Mod_reg64 rRcx; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_extra_bytes (va_code_Gcm_extra_bytes alg) va_s0 alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_LE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10\n va_sM (va_update_xmm 8 va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5\n va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1\n va_sM (va_update_xmm 0 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit (va_code_Gcm_extra_bytes alg)) =\n (va_QProc (va_code_Gcm_extra_bytes alg) ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10;\n va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm\n 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem])\n (va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE) (va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE))\n//--\n//-- Gcm_blocks128\n\nval va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_CCons\n (va_code_Ghash_buffer ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi)\n (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdx)\n (va_op_opr64_reg64 rR12)) (va_CCons (va_code_Gctr_blocks128 alg) (va_CNil ())))))))))\n\nval va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Ghash_buffer ()) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR12)) (va_pbool_and\n (va_codegen_success_Gctr_blocks128 alg) (va_ttrue ()))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_blocks128 (va_mods:va_mods_t) (alg:algorithm) (in_b:buffer128) (out_b:buffer128)\n (key:(seq nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_LE:quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b in_b h_LE (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_old_s))) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR12)) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b) (va_QEmpty (()))))))))))\n\n\nval va_lemma_Gcm_blocks128 : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> in_b:buffer128 ->\n out_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> h_LE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_blocks128 alg) va_s0 /\\ va_get_ok va_s0 /\\\n (sse_enabled /\\ Vale.X64.Decls.buffers_disjoint128 keys_b out_b /\\\n Vale.X64.Decls.buffers_disjoint128 hkeys_b out_b /\\ (Vale.X64.Decls.buffers_disjoint128 in_b\n out_b \\/ in_b == out_b) /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0)\n (va_get_reg64 rRax va_s0) in_b (va_get_reg64 rRdx va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) out_b\n (va_get_reg64 rRdx va_s0) (va_get_mem_layout va_s0) Secret /\\ va_get_reg64 rRax va_s0 + 16\n `op_Multiply` va_get_reg64 rRdx va_s0 < pow2_64 /\\ va_get_reg64 rRdi va_s0 + 16 `op_Multiply`\n va_get_reg64 rRdx va_s0 < pow2_64 /\\ l_and (Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 in_b == Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 out_b)\n (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg64 rRdx\n va_s0 == Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b /\\ va_get_xmm 9 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\\n va_get_reg64 rRdx va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg64 rR8\n va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\ pclmulqdq_enabled /\\\n Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)\n (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (Vale.X64.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR.gctr_partial alg (va_get_reg64 rRdx va_s0) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b) (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) key\n (va_get_xmm 11 va_s0) /\\ va_get_xmm 11 va_sM == Vale.AES.GCTR.inc32lite (va_get_xmm 11 va_s0)\n (va_get_reg64 rRdx va_s0) /\\ (va_get_reg64 rRdx va_s0 == 0 ==> l_and (va_get_xmm 8 va_sM ==\n va_get_xmm 8 va_s0) (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg64 rRdx va_s0 > 0 ==>\n l_and (va_get_reg64 rRdx va_s0 <= FStar.Seq.Base.length #Vale.X64.Decls.quad32\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==> FStar.Seq.Base.length\n #Vale.X64.Decls.quad32 (FStar.Seq.Base.slice #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b) 0 (va_get_reg64 rRdx va_s0)) > 0)\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_sM) == Vale.AES.GHash.ghash_incremental\n h_LE (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s0)) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b)))) /\\ va_state_eq va_sM (va_update_flags va_sM\n (va_update_mem_heaplet 1 va_sM (va_update_xmm 10 va_sM (va_update_xmm 11 va_sM (va_update_xmm 8\n va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5 va_sM (va_update_xmm 4\n va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_xmm 0\n va_sM (va_update_reg64 rR12 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rR10 va_sM\n (va_update_reg64 rR11 va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRbx va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_blocks128 va_b0 va_s0 alg in_b out_b key round_keys keys_b hkeys_b h_LE =\n let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_mem_heaplet 1; va_Mod_xmm 10; va_Mod_xmm 11;\n va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm\n 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR12; va_Mod_reg64 rRdx; va_Mod_reg64 rR10;\n va_Mod_reg64 rR11; va_Mod_reg64 rRdi; va_Mod_reg64 rRbx; va_Mod_ok; va_Mod_mem] in\n let va_qc = va_qcode_Gcm_blocks128 va_mods alg in_b out_b key round_keys keys_b hkeys_b h_LE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_blocks128 alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 210 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_ok va_sM) /\\ (label va_range1\n \"***** POSTCONDITION NOT MET AT line 255 column 53 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.X64.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 261 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.AES.GCTR.gctr_partial alg (va_get_reg64 rRdx va_s0) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b) (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) key\n (va_get_xmm 11 va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 262 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_xmm 11 va_sM == Vale.AES.GCTR.inc32lite (va_get_xmm 11 va_s0) (va_get_reg64 rRdx\n va_s0)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 265 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_reg64 rRdx va_s0 == 0 ==> l_and (va_get_xmm 8 va_sM == va_get_xmm 8 va_s0)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b == Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) out_b)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 267 column 131 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_reg64 rRdx va_s0 > 0 ==> l_and (va_get_reg64 rRdx va_s0 <= FStar.Seq.Base.length\n #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==>\n FStar.Seq.Base.length #Vale.X64.Decls.quad32 (FStar.Seq.Base.slice #Vale.X64.Decls.quad32\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) 0 (va_get_reg64 rRdx va_s0)) > 0)\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_sM) == Vale.AES.GHash.ghash_incremental\n h_LE (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s0)) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 1; va_Mod_xmm 10; va_Mod_xmm 11; va_Mod_xmm\n 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2;\n va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR12; va_Mod_reg64 rRdx; va_Mod_reg64 rR10;\n va_Mod_reg64 rR11; va_Mod_reg64 rRdi; va_Mod_reg64 rRbx; va_Mod_ok; va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_LE:quad32) (va_s0:va_state)\n (va_k:(va_state -> unit -> Type0)) : Type0 =\n (va_get_ok va_s0 /\\ (sse_enabled /\\ Vale.X64.Decls.buffers_disjoint128 keys_b out_b /\\\n Vale.X64.Decls.buffers_disjoint128 hkeys_b out_b /\\ (Vale.X64.Decls.buffers_disjoint128 in_b\n out_b \\/ in_b == out_b) /\\ Vale.X64.Decls.validSrcAddrs128 (va_get_mem_heaplet 1 va_s0)\n (va_get_reg64 rRax va_s0) in_b (va_get_reg64 rRdx va_s0) (va_get_mem_layout va_s0) Secret /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) out_b\n (va_get_reg64 rRdx va_s0) (va_get_mem_layout va_s0) Secret /\\ va_get_reg64 rRax va_s0 + 16\n `op_Multiply` va_get_reg64 rRdx va_s0 < pow2_64 /\\ va_get_reg64 rRdi va_s0 + 16 `op_Multiply`\n va_get_reg64 rRdx va_s0 < pow2_64 /\\ l_and (Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 in_b == Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 out_b)\n (Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b < pow2_32) /\\ va_get_reg64 rRdx\n va_s0 == Vale.X64.Decls.buffer_length #Vale.X64.Memory.vuint128 in_b /\\ va_get_xmm 9 va_s0 ==\n Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\\n va_get_reg64 rRdx va_s0 < pow2_32 /\\ aes_reqs alg key round_keys keys_b (va_get_reg64 rR8\n va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\ pclmulqdq_enabled /\\\n Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0 va_s0) hkeys_b)\n (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret) /\\ (forall (va_x_mem:vale_heap) (va_x_rbx:nat64) (va_x_rdi:nat64) (va_x_r11:nat64)\n (va_x_r10:nat64) (va_x_rdx:nat64) (va_x_r12:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32)\n (va_x_xmm2:quad32) (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32)\n (va_x_xmm7:quad32) (va_x_xmm8:quad32) (va_x_xmm11:quad32) (va_x_xmm10:quad32)\n (va_x_heap1:vale_heap) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl\n (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_xmm 10 va_x_xmm10 (va_upd_xmm 11 va_x_xmm11\n (va_upd_xmm 8 va_x_xmm8 (va_upd_xmm 7 va_x_xmm7 (va_upd_xmm 6 va_x_xmm6 (va_upd_xmm 5 va_x_xmm5\n (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3 (va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 1 va_x_xmm1\n (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64\n rR10 va_x_r10 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRbx\n va_x_rbx (va_upd_mem va_x_mem va_s0))))))))))))))))))) in va_get_ok va_sM /\\\n (Vale.X64.Decls.modifies_buffer128 out_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1\n va_sM) /\\ Vale.AES.GCTR.gctr_partial alg (va_get_reg64 rRdx va_s0) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b) (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b) key\n (va_get_xmm 11 va_s0) /\\ va_get_xmm 11 va_sM == Vale.AES.GCTR.inc32lite (va_get_xmm 11 va_s0)\n (va_get_reg64 rRdx va_s0) /\\ (va_get_reg64 rRdx va_s0 == 0 ==> l_and (va_get_xmm 8 va_sM ==\n va_get_xmm 8 va_s0) (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_sM) out_b ==\n Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) out_b)) /\\ (va_get_reg64 rRdx va_s0 > 0 ==>\n l_and (va_get_reg64 rRdx va_s0 <= FStar.Seq.Base.length #Vale.X64.Decls.quad32\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 1 va_s0) in_b) ==> FStar.Seq.Base.length\n #Vale.X64.Decls.quad32 (FStar.Seq.Base.slice #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b) 0 (va_get_reg64 rRdx va_s0)) > 0)\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_sM) == Vale.AES.GHash.ghash_incremental\n h_LE (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_s0)) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 1 va_s0) in_b)))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_blocks128 : alg:algorithm -> in_b:buffer128 -> out_b:buffer128 -> key:(seq\n nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> h_LE:quad32 ->\n va_s0:va_state -> va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b\n h_LE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_blocks128 alg) ([va_Mod_flags;\n va_Mod_mem_heaplet 1; va_Mod_xmm 10; va_Mod_xmm 11; va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6;\n va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_xmm 0;\n va_Mod_reg64 rR12; va_Mod_reg64 rRdx; va_Mod_reg64 rR10; va_Mod_reg64 rR11; va_Mod_reg64 rRdi;\n va_Mod_reg64 rRbx; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_LE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_blocks128 (va_code_Gcm_blocks128 alg) va_s0 alg in_b out_b key\n round_keys keys_b hkeys_b h_LE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_mem_heaplet 1 va_sM (va_update_xmm 10\n va_sM (va_update_xmm 11 va_sM (va_update_xmm 8 va_sM (va_update_xmm 7 va_sM (va_update_xmm 6\n va_sM (va_update_xmm 5 va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM (va_update_xmm 2\n va_sM (va_update_xmm 1 va_sM (va_update_xmm 0 va_sM (va_update_reg64 rR12 va_sM\n (va_update_reg64 rRdx va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR11 va_sM\n (va_update_reg64 rRdi va_sM (va_update_reg64 rRbx va_sM (va_update_ok va_sM (va_update_mem\n va_sM va_s0))))))))))))))))))))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 1; va_Mod_xmm 10; va_Mod_xmm 11; va_Mod_xmm\n 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2;\n va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR12; va_Mod_reg64 rRdx; va_Mod_reg64 rR10;\n va_Mod_reg64 rR11; va_Mod_reg64 rRdi; va_Mod_reg64 rRbx; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_blocks128 (alg:algorithm) (in_b:buffer128) (out_b:buffer128) (key:(seq nat32))\n (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (h_LE:quad32) : (va_quickCode\n unit (va_code_Gcm_blocks128 alg)) =\n (va_QProc (va_code_Gcm_blocks128 alg) ([va_Mod_flags; va_Mod_mem_heaplet 1; va_Mod_xmm 10;\n va_Mod_xmm 11; va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm\n 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR12; va_Mod_reg64 rRdx; va_Mod_reg64\n rR10; va_Mod_reg64 rR11; va_Mod_reg64 rRdi; va_Mod_reg64 rRbx; va_Mod_mem])\n (va_wp_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_LE)\n (va_wpProof_Gcm_blocks128 alg in_b out_b key round_keys keys_b hkeys_b h_LE))\n//--\n//-- Gcm_blocks\n#push-options \"--z3rlimit 1000\"\n\nval va_code_Gcm_blocks : alg:algorithm -> offset:int -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks alg offset =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rRcx))\n (va_CCons (va_code_AddLea64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rR9) (va_const_opr64\n 32)) (va_CCons (va_code_Load64_stack (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRsp)\n (offset + 0)) (va_CCons (va_code_Gcm_blocks_auth ()) (va_CCons (va_code_Load64_stack\n (va_op_dst_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRsp) (offset + 8)) (va_CCons\n (va_code_Load64_stack (va_op_dst_opr64_reg64 rRsi) (va_op_reg_opr64_reg64 rRsp) (offset + 16))\n (va_CCons (va_code_Load64_stack (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRsp)\n (offset + 24)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR13))\n (va_CCons (va_code_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 2) (va_op_xmm_xmm 1) (va_op_reg_opr64_reg64\n rR8) 0 Public) (va_CCons (va_code_Store128_buffer (va_op_heaplet_mem_heaplet 3)\n (va_op_reg_opr64_reg64 rRbp) (va_op_xmm_xmm 1) 0 Secret) (va_CCons (va_code_Load_one_lsb\n (va_op_xmm_xmm 10)) (va_CCons (va_code_VPaddd (va_op_xmm_xmm 1) (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 10)) (va_CCons (va_code_AES_GCM_decrypt_6mult alg) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 11) (va_op_reg_opr64_reg64\n rRbp) 32 Secret) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx))\n (va_CCons (va_code_Load64_stack (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRsp)\n (offset + 32)) (va_CCons (va_code_Load64_stack (va_op_dst_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRsp) (offset + 40)) (va_CCons (va_code_Load64_stack\n (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRsp) (offset + 48)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons\n (va_code_InitPshufbMask (va_op_xmm_xmm 9) (va_op_reg_opr64_reg64 rR12)) (va_CCons\n (va_code_Pshufb (va_op_xmm_xmm 11) (va_op_xmm_xmm 9)) (va_CCons (va_code_Gcm_blocks128 alg)\n (va_CCons (va_code_Stack_lemma ()) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR14)\n (va_opr_code_Stack (va_op_reg64_reg64 rRsp) (offset + 24) Public)) (va_CCons (va_code_IMul64\n (va_op_dst_opr64_reg64 rR14) (va_const_opr64 16)) (va_CCons (va_code_Load64_stack\n (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRsp) (offset + 64)) (va_CCons (va_IfElse\n (va_cmp_gt (va_op_cmp_reg64 rR13) (va_op_cmp_reg64 rR14)) (va_Block (va_CCons\n (va_code_Load64_stack (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRsp) (offset + 56))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rR13)) (va_CCons\n (va_code_And64 (va_op_dst_opr64_reg64 rR10) (va_const_opr64 15)) (va_CCons\n (va_code_Gcm_extra_bytes alg) (va_CCons (va_Block (va_CNil ())) (va_CNil ()))))))) (va_Block\n (va_CNil ()))) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rR15))\n (va_CCons (va_code_Gcm_make_length_quad ()) (va_CCons (va_code_Ghash_register ()) (va_CCons\n (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 3) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRbp) 0 Secret) (va_CCons (va_code_Gctr_register alg) (va_CCons (va_Block (va_CNil ()))\n (va_CNil ()))))))))))))))))))))))))))))))))))))\n\nval va_codegen_success_Gcm_blocks : alg:algorithm -> offset:int -> Tot va_pbool\n\nPartial implementation:\nlet va_codegen_success_Gcm_blocks alg offset =\n \n"
},
{
"role": "assistant",
"content": "(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rRcx))\n (va_pbool_and (va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rR9)\n (va_op_opr64_reg64 rR9)\n (va_const_opr64 32))\n (va_pbool_and (va_codegen_success_Load64_stack (va_op_dst_opr64_reg64 rRbx)\n (va_op_reg_opr64_reg64 rRsp)\n (offset + 0))\n (va_pbool_and (va_codegen_success_Gcm_blocks_auth ())\n (va_pbool_and (va_codegen_success_Load64_stack (va_op_dst_opr64_reg64 rRdi)\n (va_op_reg_opr64_reg64 rRsp)\n (offset + 8))\n (va_pbool_and (va_codegen_success_Load64_stack (va_op_dst_opr64_reg64 rRsi)\n (va_op_reg_opr64_reg64 rRsp)\n (offset + 16))\n (va_pbool_and (va_codegen_success_Load64_stack (va_op_dst_opr64_reg64 rRdx)\n (va_op_reg_opr64_reg64 rRsp)\n (offset + 24))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)\n (va_op_opr64_reg64 rR13))\n (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 9))\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet\n 2)\n (va_op_xmm_xmm 1)\n (va_op_reg_opr64_reg64 rR8)\n 0\n Public)\n (va_pbool_and (va_codegen_success_Store128_buffer (va_op_heaplet_mem_heaplet\n 3)\n (va_op_reg_opr64_reg64 rRbp)\n (va_op_xmm_xmm 1)\n 0\n Secret)\n (va_pbool_and (va_codegen_success_Load_one_lsb (va_op_xmm_xmm\n 10))\n (va_pbool_and (va_codegen_success_VPaddd (va_op_xmm_xmm\n 1)\n (va_op_xmm_xmm 1)\n (va_op_xmm_xmm 10))\n (va_pbool_and (va_codegen_success_AES_GCM_decrypt_6mult\n alg)\n (va_pbool_and (va_codegen_success_Load128_buffer\n (va_op_heaplet_mem_heaplet 3)\n (va_op_xmm_xmm 11)\n (va_op_reg_opr64_reg64 rRbp)\n 32\n Secret)\n (va_pbool_and (va_codegen_success_Mov64 (\n va_op_dst_opr64_reg64 rR8)\n (va_op_opr64_reg64 rRcx))\n (va_pbool_and (va_codegen_success_Load64_stack\n (va_op_dst_opr64_reg64 rRax)\n (va_op_reg_opr64_reg64 rRsp)\n (offset + 32))\n (va_pbool_and (va_codegen_success_Load64_stack\n (va_op_dst_opr64_reg64 rRdi\n )\n (va_op_reg_opr64_reg64 rRsp\n )\n (offset + 40))\n (va_pbool_and (va_codegen_success_Load64_stack\n (va_op_dst_opr64_reg64\n rRdx)\n (va_op_reg_opr64_reg64\n rRsp)\n (offset + 48))\n (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64\n rR14)\n (va_op_opr64_reg64\n rRdx))\n (va_pbool_and (va_codegen_success_InitPshufbMask\n (va_op_xmm_xmm\n 9)\n (va_op_reg_opr64_reg64\n rR12))\n (va_pbool_and (va_codegen_success_Pshufb\n (va_op_xmm_xmm\n 11)\n (va_op_xmm_xmm\n 9))\n (va_pbool_and\n (va_codegen_success_Gcm_blocks128\n alg)\n (va_pbool_and\n (va_codegen_success_Stack_lemma\n ()\n )\n (va_pbool_and\n (\n va_codegen_success_Add64\n (\n va_op_dst_opr64_reg64\n rR14\n\n )\n (\n va_opr_code_Stack\n (\n va_op_reg64_reg64\n rRsp\n\n )\n (\n offset +\n 24\n )\n Public\n\n )\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_IMul64\n (\n va_op_dst_opr64_reg64\n rR14\n\n )\n (\n va_const_opr64\n 16\n\n )\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_Load64_stack\n (\n va_op_dst_opr64_reg64\n rR13\n\n )\n (\n va_op_reg_opr64_reg64\n rRsp\n\n )\n (\n offset +\n 64\n )\n\n )\n (\n va_pbool_and\n (\n va_pbool_and\n (\n va_codegen_success_Load64_stack\n (\n va_op_dst_opr64_reg64\n rRax\n\n )\n (\n va_op_reg_opr64_reg64\n rRsp\n\n )\n (\n offset +\n 56\n )\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_Mov64\n (\n va_op_dst_opr64_reg64\n rR10\n\n )\n (\n va_op_opr64_reg64\n rR13\n\n )\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_And64\n (\n va_op_dst_opr64_reg64\n rR10\n\n )\n (\n va_const_opr64\n 15\n\n )\n\n )\n (\n va_codegen_success_Gcm_extra_bytes\n alg\n\n )\n\n )\n\n )\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_Mov64\n (\n va_op_dst_opr64_reg64\n rR11\n\n )\n (\n va_op_opr64_reg64\n rR15\n\n )\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_Gcm_make_length_quad\n ()\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_Ghash_register\n ()\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_Load128_buffer\n (\n va_op_heaplet_mem_heaplet\n 3\n\n )\n (\n va_op_xmm_xmm\n 0\n\n )\n (\n va_op_reg_opr64_reg64\n rRbp\n\n )\n 0\n Secret\n\n )\n (\n va_pbool_and\n (\n va_codegen_success_Gctr_register\n alg\n\n )\n (\n va_ttrue\n ()\n\n )\n\n )\n\n )\n\n )\n\n )\n\n )\n\n )\n\n )\n\n )\n ))\n ))))))))))))\n )))))))))))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: _: Prims.unit -> FStar.All.ML Prims.int\nEffect: FStar.All.ML\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nPartial implementation:\nlet fadd_code_inline () : FStar.All.ML int =\n \n"
},
{
"role": "assistant",
"content": "PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg\n fadd_regs_modified fadd_comments"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: alg: Vale.AES.AES_common_s.algorithm -> Vale.X64.Decls.va_pbool\nEffect: Prims.Tot\n\nContext:\nmodule Vale.AES.X64.GCMdecryptOpt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_s\nopen Vale.AES.GCTR_s\nopen Vale.AES.GCTR\nopen Vale.AES.GCM\nopen Vale.AES.GHash_s\nopen Vale.AES.GHash\nopen Vale.AES.GCM_s\nopen Vale.AES.X64.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers\nopen Vale.AES.X64.GHash\nopen Vale.AES.X64.GCTR\nopen Vale.X64.Machine_s\nopen Vale.X64.Memory\nopen Vale.X64.Stack_i\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsStack\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.AES.X64.GF128_Mul\nopen Vale.X64.Stack\nopen Vale.X64.CPU_Features_s\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.X64.AESopt\nopen Vale.AES.X64.AESGCM\nopen Vale.AES.X64.AESopt2\nopen Vale.Lib.Meta\nopen Vale.AES.X64.GCMencryptOpt\nopen Vale.AES.OptPublic\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 20 --max_ifuel 0\"\n//-- Gcm_extra_bytes\n\nval va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_extra_bytes alg =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 0)) (va_CCons (va_code_Ghash_extra_bytes ()) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_CCons (va_code_Pshufb (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 9)) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_Pxor\n (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_CNil ()))))))))))\n\nval va_codegen_success_Gcm_extra_bytes : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_extra_bytes alg =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Ghash_extra_bytes ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_pbool_and\n (va_codegen_success_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (va_pbool_and\n (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_ttrue ())))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRax) 0 Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_xmm 0 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_LE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) (FStar.Seq.Base.create #quad32 1 hash_input)) (let (snap:(FStar.Seq.Base.seq\n Vale.X64.Decls.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 11 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 204 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 10) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 207 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_reveal ()) (va_QEmpty (()))))))))))))))\n\n\nval va_lemma_Gcm_extra_bytes : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n inout_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 -> completed_quads:(seq quad32) ->\n h_LE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_extra_bytes alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (len:(va_int_range 1 1)) = 1 in sse_enabled /\\ Vale.X64.Decls.buffers_disjoint128 keys_b\n inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b inout_b /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax va_s0) inout_b\n len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) /\\ va_state_eq va_sM\n (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10 va_sM (va_update_xmm 8\n va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5 va_sM (va_update_xmm 4\n va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_xmm 0\n va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM (va_update_ok va_sM\n (va_update_mem va_sM va_s0))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_extra_bytes va_b0 va_s0 alg inout_b key round_keys keys_b hkeys_b total_bytes\n old_hash completed_quads h_LE =\n let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8;\n va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm\n 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem] in\n let va_qc = va_qcode_Gcm_extra_bytes va_mods alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_extra_bytes alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 121 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (len:(va_int_range 1 1)) = 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 174 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.X64.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 177 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.AES.GCTR.gctr_partial alg len (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0)) /\\ label\n va_range1\n \"***** POSTCONDITION NOT MET AT line 180 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 181 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 182 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let padded_bytes = Vale.AES.GCTR_s.pad_to_128_bits input_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 183 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_quads = Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 186 column 59 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (l_and (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0)\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_sM) == Vale.AES.GHash.ghash_incremental\n h_LE old_hash input_quads)))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ (let (len:(va_int_range 1 1)) = 1 in sse_enabled /\\\n Vale.X64.Decls.buffers_disjoint128 keys_b inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b\n inout_b /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax\n va_s0) inout_b len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_mem:vale_heap) (va_x_rcx:nat64) (va_x_r11:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32)\n (va_x_xmm2:quad32) (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32)\n (va_x_xmm7:quad32) (va_x_xmm8:quad32) (va_x_xmm10:quad32) (va_x_heap5:vale_heap)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_mem_heaplet 5\n va_x_heap5 (va_upd_xmm 10 va_x_xmm10 (va_upd_xmm 8 va_x_xmm8 (va_upd_xmm 7 va_x_xmm7\n (va_upd_xmm 6 va_x_xmm6 (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3\n (va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR11\n va_x_r11 (va_upd_reg64 rRcx va_x_rcx (va_upd_mem va_x_mem va_s0)))))))))))))) in va_get_ok\n va_sM /\\ (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_extra_bytes : alg:algorithm -> inout_b:buffer128 -> key:(seq nat32) ->\n round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> total_bytes:nat ->\n old_hash:quad32 -> completed_quads:(seq quad32) -> h_LE:quad32 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_extra_bytes alg) ([va_Mod_flags;\n va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5;\n va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11;\n va_Mod_reg64 rRcx; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_extra_bytes (va_code_Gcm_extra_bytes alg) va_s0 alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_LE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10\n va_sM (va_update_xmm 8 va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5\n va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1\n va_sM (va_update_xmm 0 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit (va_code_Gcm_extra_bytes alg)) =\n (va_QProc (va_code_Gcm_extra_bytes alg) ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10;\n va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm\n 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem])\n (va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE) (va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE))\n//--\n//-- Gcm_blocks128\n\nval va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_CCons\n (va_code_Ghash_buffer ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi)\n (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdx)\n (va_op_opr64_reg64 rR12)) (va_CCons (va_code_Gctr_blocks128 alg) (va_CNil ())))))))))\n\nval va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool\n\nPartial implementation:\nlet va_codegen_success_Gcm_blocks128 alg =\n \n"
},
{
"role": "assistant",
"content": "(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi)\n (va_op_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Ghash_buffer ())\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi)\n (va_op_opr64_reg64 rRbx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)\n (va_op_opr64_reg64 rR12))\n (va_pbool_and (va_codegen_success_Gctr_blocks128 alg) (va_ttrue ()))))))))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: w1: DM4F_layered5.wp st a -> w2: DM4F_layered5.wp st a -> Type0\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule DM4F_layered5\n\n(* Same as DM4F, but layered over a layered PURE without monotonicity *)\nopen ID5\nopen DM4F_Utils\n\nunfold\nlet pure_bind_wp (#a #b : Type) (w1 : ID5.wp a) (w2 : a -> ID5.wp b) : ID5.wp b =\n ID5.bind_wp w1 w2\n\n(* Simulating state effect in DM4F, hopefully doable by a tactic. *)\n\ntype post_t st a = a -> st -> Type0\n\ntype wp0 (st:Type u#0) (a:Type u#ua) : Type u#(max 1 ua) =\n st -> post_t st a -> Type0\n\nlet st_monotonic #st #a (w : wp0 st a) : Type0 =\n //forall s0 p1 p2. (forall r. p1 r ==> p2 r) ==> w s0 p1 ==> w s0 p2\n // ^ this version seems to be less SMT-friendly\n forall s0 p1 p2. (forall x s1. p1 x s1 ==> p2 x s1) ==> w s0 p1 ==> w s0 p2\n\ntype wp st a = w:(wp0 st a){st_monotonic w}\n\nopen FStar.Monotonic.Pure\n\ntype repr (a:Type u#ua) (st:Type0) (wp : wp u#ua st a) : Type u#(max 1 ua) =\n s0:st -> ID (a & st) (as_pure_wp (fun p -> wp s0 (curry p)))\n\nunfold\nlet return_wp (#a:Type) (#st:Type0) (x:a) : wp st a =\n fun s0 p -> p x s0\n\nlet return (a:Type) (x:a) (st:Type0) : repr a st (return_wp x) =\n fun s0 -> (x, s0)\n\nunfold\nlet bind_wp (#a:Type) (#b:Type) (#st:Type0)\n (w1 : wp st a) (w2 : a -> wp st b) : wp st b =\n fun s0 p -> w1 s0 (fun y s1 -> w2 y s1 p)\n\nlet bind (a:Type) (b:Type) (st:Type0)\n (wp_c : wp st a)\n (wp_f : a -> wp st b)\n (c : repr a st wp_c)\n (f : (x:a -> repr b st (wp_f x)))\n: repr b st (bind_wp wp_c wp_f)\n= fun s0 ->\n //let (y, s1) = c s0 in\n //f y s1\n // GM: argh! using the match above introduces noise in the VC, a true precondition\n // that becomes a pain since we don't have monotonicity nor even extensionality\n let r = c s0 in\n f (fst r) (snd r)\n\nlet ite_wp #a #st (b:bool) (w1 w2 : wp st a) : wp st a =\n fun s0 p -> (b ==> w1 s0 p) /\\ ((~b) ==> w2 s0 p)\n\nlet if_then_else\n (a:Type)\n (st:Type0)\n (wpf wpg : wp st a)\n (f : repr a st wpf)\n (g : repr a st wpg)\n (b : bool)\n : Type\n = repr a st (ite_wp b wpf wpg)\n\nPartial implementation:\nlet stronger (#a: Type) (#st: Type0) (w1 w2: wp st a) : Type0 =\n \n"
},
{
"role": "assistant",
"content": "forall s0 p. w1 s0 p ==> w2 s0 p"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: _: Prims.unit -> FStar.All.ML Prims.int\nEffect: FStar.All.ML\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that fsub_lemma' has the required type *)\nlet fsub_lemma = as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'\n\nlet code_Fsub = FH.va_code_Fsub ()\n\n(* Here's the type expected for the fsub wrapper *)\n[@__reduce__]\nlet lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\n(* And here's the fsub wrapper itself *)\nlet lowstar_Fsub : lowstar_Fsub_t =\n assert_norm (List.length fsub_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fsub_regs_modified\n fsub_xmms_modified\n code_Fsub\n fsub_dom\n (W.mk_prediction code_Fsub fsub_dom [] (fsub_lemma code_Fsub IA.win))\n\nlet lowstar_Fsub_normal_t : normal lowstar_Fsub_t\n = as_normal_t #lowstar_Fsub_t lowstar_Fsub\n\nlet fsub out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_Fsub_normal_t out f1 f2 () in\n ()\n\nlet fsub_comments : list string = [\"Computes the field substraction of two field elements\"]\n\nlet fsub_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nPartial implementation:\nlet fsub_code_inline () : FStar.All.ML int =\n \n"
},
{
"role": "assistant",
"content": "PR.print_inline \"fsub\" 0 None (List.length fsub_dom) fsub_dom fsub_names code_Fsub of_arg\n fsub_regs_modified fsub_comments"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n va_mods: Vale.X64.QuickCode.va_mods_t ->\n alg: Vale.AES.AES_common_s.algorithm ->\n in_b: Vale.X64.Memory.buffer128 ->\n out_b: Vale.X64.Memory.buffer128 ->\n key: FStar.Seq.Base.seq Vale.X64.Memory.nat32 ->\n round_keys: FStar.Seq.Base.seq Vale.X64.Decls.quad32 ->\n keys_b: Vale.X64.Memory.buffer128 ->\n hkeys_b: Vale.X64.Memory.buffer128 ->\n h_LE: Vale.X64.Decls.quad32\n -> Vale.X64.QuickCode.va_quickCode Prims.unit\n (Vale.AES.X64.GCMdecryptOpt.va_code_Gcm_blocks128 alg)\nEffect: Prims.Tot\n\nContext:\nmodule Vale.AES.X64.GCMdecryptOpt\nopen Vale.Def.Prop_s\nopen Vale.Def.Opaque_s\nopen FStar.Seq\nopen Vale.Def.Words_s\nopen Vale.Def.Words.Seq_s\nopen Vale.Def.Types_s\nopen Vale.Arch.Types\nopen Vale.Arch.HeapImpl\nopen Vale.AES.AES_s\nopen Vale.AES.GCTR_s\nopen Vale.AES.GCTR\nopen Vale.AES.GCM\nopen Vale.AES.GHash_s\nopen Vale.AES.GHash\nopen Vale.AES.GCM_s\nopen Vale.AES.X64.AES\nopen Vale.AES.GF128_s\nopen Vale.AES.GF128\nopen Vale.Poly1305.Math\nopen Vale.AES.GCM_helpers\nopen Vale.AES.X64.GHash\nopen Vale.AES.X64.GCTR\nopen Vale.X64.Machine_s\nopen Vale.X64.Memory\nopen Vale.X64.Stack_i\nopen Vale.X64.State\nopen Vale.X64.Decls\nopen Vale.X64.InsBasic\nopen Vale.X64.InsMem\nopen Vale.X64.InsVector\nopen Vale.X64.InsStack\nopen Vale.X64.InsAes\nopen Vale.X64.QuickCode\nopen Vale.X64.QuickCodes\nopen Vale.AES.X64.GF128_Mul\nopen Vale.X64.Stack\nopen Vale.X64.CPU_Features_s\nopen Vale.Math.Poly2.Bits_s\nopen Vale.AES.X64.AESopt\nopen Vale.AES.X64.AESGCM\nopen Vale.AES.X64.AESopt2\nopen Vale.Lib.Meta\nopen Vale.AES.X64.GCMencryptOpt\nopen Vale.AES.OptPublic\nopen Vale.Lib.Basic\n#reset-options \"--z3rlimit 20 --max_ifuel 0\"\n//-- Gcm_extra_bytes\n\nval va_code_Gcm_extra_bytes : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_extra_bytes alg =\n (va_Block (va_CCons (va_code_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_CCons (va_code_Mov128 (va_op_xmm_xmm 10)\n (va_op_xmm_xmm 0)) (va_CCons (va_code_Ghash_extra_bytes ()) (va_CCons (va_code_Mov128\n (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_CCons (va_code_Pshufb (va_op_xmm_xmm 0)\n (va_op_xmm_xmm 9)) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_Pxor\n (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_CCons (va_code_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_CNil ()))))))))))\n\nval va_codegen_success_Gcm_extra_bytes : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_extra_bytes alg =\n (va_pbool_and (va_codegen_success_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0)\n (va_op_reg_opr64_reg64 rRax) 0 Secret) (va_pbool_and (va_codegen_success_Mov128 (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Ghash_extra_bytes ()) (va_pbool_and\n (va_codegen_success_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_pbool_and\n (va_codegen_success_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (va_pbool_and\n (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_Pxor (va_op_xmm_xmm\n 10) (va_op_xmm_xmm 0)) (va_pbool_and (va_codegen_success_Store128_buffer\n (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax) (va_op_xmm_xmm 10) 0 Secret)\n (va_ttrue ())))))))))\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_qcode_Gcm_extra_bytes (va_mods:va_mods_t) (alg:algorithm) (inout_b:buffer128) (key:(seq\n nat32)) (round_keys:(seq quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat)\n (old_hash:quad32) (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit\n (va_code_Gcm_extra_bytes alg)) =\n (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (len:(va_int_range\n 1 1)) = 1 in va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 188 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Load128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_xmm_xmm 0) (va_op_reg_opr64_reg64\n rRax) 0 Secret inout_b 0) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 189 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (fun (va_s:va_state) _ -> let\n (hash_input:quad32) = va_get_xmm 0 va_s in va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 193 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_extra_bytes hkeys_b total_bytes old_hash h_LE completed_quads) (fun\n (va_s:va_state) _ -> va_qAssert va_range1\n \"***** PRECONDITION NOT MET AT line 194 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (FStar.Seq.Base.equal #Vale.X64.Decls.quad32 (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s)\n inout_b) (FStar.Seq.Base.create #quad32 1 hash_input)) (let (snap:(FStar.Seq.Base.seq\n Vale.X64.Decls.quad32)) = Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s) inout_b in va_QSeq\n va_range1\n \"***** PRECONDITION NOT MET AT line 198 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov128 (va_op_xmm_xmm 0) (va_op_xmm_xmm 11)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 199 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pshufb (va_op_xmm_xmm 0) (va_op_xmm_xmm 9)) (fun (va_s:va_state) _ -> va_QBind\n va_range1\n \"***** PRECONDITION NOT MET AT line 200 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_AESEncryptBlock alg (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 11 va_s)) key\n round_keys keys_b) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 201 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.AES_s.aes_encrypt_LE_reveal ()) (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 204 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Pxor (va_op_xmm_xmm 10) (va_op_xmm_xmm 0)) (va_QBind va_range1\n \"***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Store128_buffer (va_op_heaplet_mem_heaplet 5) (va_op_reg_opr64_reg64 rRax)\n (va_op_xmm_xmm 10) 0 Secret inout_b 0) (fun (va_s:va_state) _ -> va_qPURE va_range1\n \"***** PRECONDITION NOT MET AT line 207 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (fun (_:unit) -> Vale.AES.GCTR.gctr_partial_reveal ()) (va_QEmpty (()))))))))))))))\n\n\nval va_lemma_Gcm_extra_bytes : va_b0:va_code -> va_s0:va_state -> alg:algorithm ->\n inout_b:buffer128 -> key:(seq nat32) -> round_keys:(seq quad32) -> keys_b:buffer128 ->\n hkeys_b:buffer128 -> total_bytes:nat -> old_hash:quad32 -> completed_quads:(seq quad32) ->\n h_LE:quad32\n -> Ghost (va_state & va_fuel)\n (requires (va_require_total va_b0 (va_code_Gcm_extra_bytes alg) va_s0 /\\ va_get_ok va_s0 /\\ (let\n (len:(va_int_range 1 1)) = 1 in sse_enabled /\\ Vale.X64.Decls.buffers_disjoint128 keys_b\n inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b inout_b /\\\n Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax va_s0) inout_b\n len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes)))\n (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\\ va_get_ok va_sM /\\\n (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) /\\ va_state_eq va_sM\n (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10 va_sM (va_update_xmm 8\n va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5 va_sM (va_update_xmm 4\n va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1 va_sM (va_update_xmm 0\n va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM (va_update_ok va_sM\n (va_update_mem va_sM va_s0))))))))))))))))))\n[@\"opaque_to_smt\"]\nlet va_lemma_Gcm_extra_bytes va_b0 va_s0 alg inout_b key round_keys keys_b hkeys_b total_bytes\n old_hash completed_quads h_LE =\n let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8;\n va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm\n 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem] in\n let va_qc = va_qcode_Gcm_extra_bytes va_mods alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE in\n let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gcm_extra_bytes alg) va_qc va_s0 (fun\n va_s0 va_sM va_g -> let () = va_g in label va_range1\n \"***** POSTCONDITION NOT MET AT line 121 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_get_ok va_sM) /\\ (let (len:(va_int_range 1 1)) = 1 in label va_range1\n \"***** POSTCONDITION NOT MET AT line 174 column 55 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.X64.Decls.modifies_buffer128 inout_b (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5\n va_sM)) /\\ label va_range1\n \"***** POSTCONDITION NOT MET AT line 177 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (Vale.AES.GCTR.gctr_partial alg len (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b)\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0)) /\\ label\n va_range1\n \"***** POSTCONDITION NOT MET AT line 180 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let raw_quads = FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_s0) inout_b) in label va_range1\n \"***** POSTCONDITION NOT MET AT line 181 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 182 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let padded_bytes = Vale.AES.GCTR_s.pad_to_128_bits input_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 183 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (let input_quads = Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in label va_range1\n \"***** POSTCONDITION NOT MET AT line 186 column 59 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (l_and (FStar.Seq.Base.length #Vale.Def.Types_s.quad32 input_quads > 0)\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_sM) == Vale.AES.GHash.ghash_incremental\n h_LE old_hash input_quads)))))))) in\n assert_norm (va_qc.mods == va_mods);\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_ok; va_Mod_mem]) va_sM va_s0;\n (va_sM, va_fM)\n\n[@ va_qattr]\nlet va_wp_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) (va_s0:va_state) (va_k:(va_state -> unit -> Type0))\n : Type0 =\n (va_get_ok va_s0 /\\ (let (len:(va_int_range 1 1)) = 1 in sse_enabled /\\\n Vale.X64.Decls.buffers_disjoint128 keys_b inout_b /\\ Vale.X64.Decls.buffers_disjoint128 hkeys_b\n inout_b /\\ Vale.X64.Decls.validDstAddrs128 (va_get_mem_heaplet 5 va_s0) (va_get_reg64 rRax\n va_s0) inout_b len (va_get_mem_layout va_s0) Secret /\\ len == Vale.X64.Decls.buffer_length\n #Vale.X64.Memory.vuint128 inout_b /\\ va_get_xmm 9 va_s0 == Vale.Def.Words_s.Mkfour\n #Vale.Def.Types_s.nat32 202182159 134810123 67438087 66051 /\\ aes_reqs alg key round_keys\n keys_b (va_get_reg64 rR8 va_s0) (va_get_mem_heaplet 0 va_s0) (va_get_mem_layout va_s0) /\\\n pclmulqdq_enabled /\\ Vale.AES.GHash.hkeys_reqs_priv (Vale.X64.Decls.s128 (va_get_mem_heaplet 0\n va_s0) hkeys_b) (Vale.Def.Types_s.reverse_bytes_quad32 h_LE) /\\ Vale.X64.Decls.validSrcAddrs128\n (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rR9 va_s0 - 32) hkeys_b 8 (va_get_mem_layout va_s0)\n Secret /\\ va_get_xmm 8 va_s0 == Vale.Def.Types_s.reverse_bytes_quad32\n (Vale.AES.GHash.ghash_incremental0 h_LE old_hash completed_quads) /\\ FStar.Seq.Base.length\n #quad32 completed_quads == total_bytes `op_Division` 16 /\\ total_bytes < 16 `op_Multiply`\n FStar.Seq.Base.length #quad32 completed_quads + 16 /\\ va_get_reg64 rR10 va_s0 == total_bytes\n `op_Modulus` 16 /\\ total_bytes `op_Modulus` 16 =!= 0 /\\ (0 < total_bytes /\\ total_bytes < 16\n `op_Multiply` Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes) /\\ 16 `op_Multiply`\n (Vale.AES.GCM_helpers.bytes_to_quad_size total_bytes - 1) < total_bytes) /\\ (forall\n (va_x_mem:vale_heap) (va_x_rcx:nat64) (va_x_r11:nat64) (va_x_xmm0:quad32) (va_x_xmm1:quad32)\n (va_x_xmm2:quad32) (va_x_xmm3:quad32) (va_x_xmm4:quad32) (va_x_xmm5:quad32) (va_x_xmm6:quad32)\n (va_x_xmm7:quad32) (va_x_xmm8:quad32) (va_x_xmm10:quad32) (va_x_heap5:vale_heap)\n (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_mem_heaplet 5\n va_x_heap5 (va_upd_xmm 10 va_x_xmm10 (va_upd_xmm 8 va_x_xmm8 (va_upd_xmm 7 va_x_xmm7\n (va_upd_xmm 6 va_x_xmm6 (va_upd_xmm 5 va_x_xmm5 (va_upd_xmm 4 va_x_xmm4 (va_upd_xmm 3 va_x_xmm3\n (va_upd_xmm 2 va_x_xmm2 (va_upd_xmm 1 va_x_xmm1 (va_upd_xmm 0 va_x_xmm0 (va_upd_reg64 rR11\n va_x_r11 (va_upd_reg64 rRcx va_x_rcx (va_upd_mem va_x_mem va_s0)))))))))))))) in va_get_ok\n va_sM /\\ (let (len:(va_int_range 1 1)) = 1 in Vale.X64.Decls.modifies_buffer128 inout_b\n (va_get_mem_heaplet 5 va_s0) (va_get_mem_heaplet 5 va_sM) /\\ Vale.AES.GCTR.gctr_partial alg len\n (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0) inout_b) (Vale.X64.Decls.s128\n (va_get_mem_heaplet 5 va_sM) inout_b) key (va_get_xmm 11 va_s0) /\\ (let raw_quads =\n FStar.Seq.Base.append #quad32 completed_quads (Vale.X64.Decls.s128 (va_get_mem_heaplet 5 va_s0)\n inout_b) in let input_bytes = FStar.Seq.Base.slice #Vale.Def.Types_s.nat8\n (Vale.Def.Types_s.le_seq_quad32_to_bytes raw_quads) 0 total_bytes in let padded_bytes =\n Vale.AES.GCTR_s.pad_to_128_bits input_bytes in let input_quads =\n Vale.Def.Types_s.le_bytes_to_seq_quad32 padded_bytes in l_and (FStar.Seq.Base.length\n #Vale.Def.Types_s.quad32 input_quads > 0) (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8\n va_sM) == Vale.AES.GHash.ghash_incremental h_LE old_hash input_quads))) ==> va_k va_sM (())))\n\n\nval va_wpProof_Gcm_extra_bytes : alg:algorithm -> inout_b:buffer128 -> key:(seq nat32) ->\n round_keys:(seq quad32) -> keys_b:buffer128 -> hkeys_b:buffer128 -> total_bytes:nat ->\n old_hash:quad32 -> completed_quads:(seq quad32) -> h_LE:quad32 -> va_s0:va_state ->\n va_k:(va_state -> unit -> Type0)\n -> Ghost (va_state & va_fuel & unit)\n (requires (va_t_require va_s0 /\\ va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE va_s0 va_k))\n (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gcm_extra_bytes alg) ([va_Mod_flags;\n va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5;\n va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11;\n va_Mod_reg64 rRcx; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))\n[@\"opaque_to_smt\"]\nlet va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE va_s0 va_k =\n let (va_sM, va_f0) = va_lemma_Gcm_extra_bytes (va_code_Gcm_extra_bytes alg) va_s0 alg inout_b key\n round_keys keys_b hkeys_b total_bytes old_hash completed_quads h_LE in\n va_lemma_upd_update va_sM;\n assert (va_state_eq va_sM (va_update_flags va_sM (va_update_mem_heaplet 5 va_sM (va_update_xmm 10\n va_sM (va_update_xmm 8 va_sM (va_update_xmm 7 va_sM (va_update_xmm 6 va_sM (va_update_xmm 5\n va_sM (va_update_xmm 4 va_sM (va_update_xmm 3 va_sM (va_update_xmm 2 va_sM (va_update_xmm 1\n va_sM (va_update_xmm 0 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rRcx va_sM\n (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))));\n va_lemma_norm_mods ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10; va_Mod_xmm 8; va_Mod_xmm\n 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm 2; va_Mod_xmm 1;\n va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem]) va_sM va_s0;\n let va_g = () in\n (va_sM, va_f0, va_g)\n\n[@ \"opaque_to_smt\" va_qattr]\nlet va_quick_Gcm_extra_bytes (alg:algorithm) (inout_b:buffer128) (key:(seq nat32)) (round_keys:(seq\n quad32)) (keys_b:buffer128) (hkeys_b:buffer128) (total_bytes:nat) (old_hash:quad32)\n (completed_quads:(seq quad32)) (h_LE:quad32) : (va_quickCode unit (va_code_Gcm_extra_bytes alg)) =\n (va_QProc (va_code_Gcm_extra_bytes alg) ([va_Mod_flags; va_Mod_mem_heaplet 5; va_Mod_xmm 10;\n va_Mod_xmm 8; va_Mod_xmm 7; va_Mod_xmm 6; va_Mod_xmm 5; va_Mod_xmm 4; va_Mod_xmm 3; va_Mod_xmm\n 2; va_Mod_xmm 1; va_Mod_xmm 0; va_Mod_reg64 rR11; va_Mod_reg64 rRcx; va_Mod_mem])\n (va_wp_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b total_bytes old_hash\n completed_quads h_LE) (va_wpProof_Gcm_extra_bytes alg inout_b key round_keys keys_b hkeys_b\n total_bytes old_hash completed_quads h_LE))\n//--\n//-- Gcm_blocks128\n\nval va_code_Gcm_blocks128 : alg:algorithm -> Tot va_code\n[@ \"opaque_to_smt\" va_qattr]\nlet va_code_Gcm_blocks128 alg =\n (va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx)) (va_CCons\n (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_CCons\n (va_code_Ghash_buffer ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdi)\n (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRdx)\n (va_op_opr64_reg64 rR12)) (va_CCons (va_code_Gctr_blocks128 alg) (va_CNil ())))))))))\n\nval va_codegen_success_Gcm_blocks128 : alg:algorithm -> Tot va_pbool\n[@ \"opaque_to_smt\" va_qattr]\nlet va_codegen_success_Gcm_blocks128 alg =\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx))\n (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax))\n (va_pbool_and (va_codegen_success_Ghash_buffer ()) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64\n (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR12)) (va_pbool_and\n (va_codegen_success_Gctr_blocks128 alg) (va_ttrue ()))))))))\n\nPartial implementation:\nlet va_qcode_Gcm_blocks128\n (va_mods: va_mods_t)\n (alg: algorithm)\n (in_b out_b: buffer128)\n (key: (seq nat32))\n (round_keys: (seq quad32))\n (keys_b hkeys_b: buffer128)\n (h_LE: quad32)\n : (va_quickCode unit (va_code_Gcm_blocks128 alg)) =\n \n"
},
{
"role": "assistant",
"content": "(qblock va_mods\n (fun (va_s: va_state) ->\n let va_old_s:va_state = va_s in\n va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 274 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdi))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 275 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRdx))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 276 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 277 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Ghash_buffer hkeys_b\n in_b\n h_LE\n (Vale.Def.Types_s.reverse_bytes_quad32 (va_get_xmm 8 va_old_s)))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 278 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRbx))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 279 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR12))\n (va_QSeq va_range1\n \"***** PRECONDITION NOT MET AT line 280 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/x64/Vale.AES.X64.GCMdecryptOpt.vaf *****\"\n (va_quick_Gctr_blocks128 alg in_b out_b key round_keys keys_b)\n (va_QEmpty (()))))))))))"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Vale.AsLowStar.ValeSig.vale_sig Vale.Inline.X64.Fadd_inline.fsub_regs_modified\n Vale.Inline.X64.Fadd_inline.fsub_xmms_modified\n Vale.Inline.X64.Fadd_inline.fsub_pre\n Vale.Inline.X64.Fadd_inline.fsub_post\nEffect: Prims.Tot\n\nContext:\nmodule Vale.Inline.X64.Fadd_inline\n\nopen FStar.Mul\nopen FStar.HyperStack.ST\nmodule HS = FStar.HyperStack\nmodule B = LowStar.Buffer\nmodule DV = LowStar.BufferView.Down\nopen Vale.Def.Types_s\n\nopen Vale.Interop.Base\nmodule IX64 = Vale.Interop.X64\nmodule VSig = Vale.AsLowStar.ValeSig\nmodule LSig = Vale.AsLowStar.LowStarSig\nmodule ME = Vale.X64.Memory\nmodule V = Vale.X64.Decls\nmodule IA = Vale.Interop.Assumptions\nmodule W = Vale.AsLowStar.Wrapper\nopen Vale.X64.MemoryAdapters\nmodule VS = Vale.X64.State\nmodule MS = Vale.X64.Machine_s\nmodule PR = Vale.X64.Print_Inline_s\n\nmodule FU = Vale.Curve25519.X64.FastUtil\nmodule FH = Vale.Curve25519.X64.FastHybrid\nmodule FW = Vale.Curve25519.X64.FastWide\n\nlet uint64 = UInt64.t\n\n(* A little utility to trigger normalization in types *)\nlet as_t (#a:Type) (x:normal a) : a = x\nlet as_normal_t (#a:Type) (x:a) : normal a = x\n\n[@__reduce__]\nlet b64 = buf_t TUInt64 TUInt64\n[@__reduce__]\nlet t64_mod = TD_Buffer TUInt64 TUInt64 default_bq\n[@__reduce__]\nlet t64_no_mod = TD_Buffer TUInt64 TUInt64 ({modified=false; strict_disjointness=false; taint=MS.Secret})\n[@__reduce__]\nlet tuint64 = TD_Base TUInt64\n\n[@__reduce__]\nlet dom: IX64.arity_ok 3 td =\n let y = [t64_mod; t64_no_mod; tuint64] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet add1_pre : VSig.vale_pre dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state) ->\n FU.va_req_Fast_add1 c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2)\n\n[@__reduce__]\nlet add1_post : VSig.vale_post dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FU.va_ens_Fast_add1 c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet add1_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet add1_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet add1_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:uint64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n add1_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 add1_regs_modified add1_xmms_modified /\\\n add1_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FU.va_lemma_Fast_add1 code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (UInt64.v f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet add1_lemma = as_t #(VSig.vale_sig add1_regs_modified add1_xmms_modified add1_pre add1_post) add1_lemma'\n\nlet code_add1 = FU.va_code_Fast_add1 ()\n\nlet of_reg (r:MS.reg_64) : option (IX64.reg_nat 3) = match r with\n | 5 -> Some 0 // rdi\n | 4 -> Some 1 // rsi\n | 3 -> Some 2 // rdx\n | _ -> None\n\nlet of_arg (i:IX64.reg_nat 3) : MS.reg_64 = match i with\n | 0 -> MS.rRdi\n | 1 -> MS.rRsi\n | 2 -> MS.rRdx\n\nlet arg_reg : IX64.arg_reg_relation 3 = IX64.Rel of_reg of_arg\n\n(* Here's the type expected for the add1 wrapper *)\n[@__reduce__]\nlet lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\n(* And here's the add1 wrapper itself *)\nlet lowstar_add1 : lowstar_add1_t =\n assert_norm (List.length dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n add1_regs_modified\n add1_xmms_modified\n code_add1\n dom\n (W.mk_prediction code_add1 dom [] (add1_lemma code_add1 IA.win))\n\nlet lowstar_add1_normal_t : normal lowstar_add1_t\n = as_normal_t #lowstar_add1_t lowstar_add1\n\nopen Vale.AsLowStar.MemoryHelpers\n\nlet add_scalar out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n let (x, _) = lowstar_add1_normal_t out f1 f2 () in\n x\n\nlet add1_comments : list string =\n [\"Computes the addition of four-element f1 with value in f2\"; \"and returns the carry (if any)\"]\n\nlet add1_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet add1_code_inline () : FStar.All.ML int =\n PR.print_inline \"add_scalar\" 0 None (List.length dom) dom add1_names code_add1 of_arg add1_regs_modified add1_comments\n\n\n[@__reduce__]\nlet fadd_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fadd_pre : VSig.vale_pre fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fadd c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fadd_post : VSig.vale_post fadd_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fadd c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 50\"\n\nlet fadd_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rRdx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fadd_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fadd_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fadd_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fadd_regs_modified fadd_xmms_modified /\\\n fadd_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fadd code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\n(* Prove that add1_lemma' has the required type *)\nlet fadd_lemma = as_t #(VSig.vale_sig fadd_regs_modified fadd_xmms_modified fadd_pre fadd_post) fadd_lemma'\n\nlet code_Fadd = FH.va_code_Fadd ()\n\n(* Here's the type expected for the fadd wrapper *)\n[@__reduce__]\nlet lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.as_lowstar_sig_t_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n []\n _\n _\n // The boolean here doesn't matter\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\n(* And here's the fadd wrapper itself *)\nlet lowstar_fadd : lowstar_fadd_t =\n assert_norm (List.length fadd_dom + List.length ([]<:list arg) <= 3);\n IX64.wrap_weak\n 3\n arg_reg\n fadd_regs_modified\n fadd_xmms_modified\n code_Fadd\n fadd_dom\n (W.mk_prediction code_Fadd fadd_dom [] (fadd_lemma code_Fadd IA.win))\n\nlet lowstar_fadd_normal_t : normal lowstar_fadd_t\n = as_normal_t #lowstar_fadd_t lowstar_fadd\n\nlet fadd out f1 f2\n = DV.length_eq (get_downview out);\n DV.length_eq (get_downview f1);\n DV.length_eq (get_downview f2);\n let (x, _) = lowstar_fadd_normal_t out f1 f2 () in\n ()\n\nlet fadd_comments : list string = [\"Computes the field addition of two field elements\"]\n\nlet fadd_names (n:nat) =\n match n with\n | 0 -> \"out\"\n | 1 -> \"f1\"\n | 2 -> \"f2\"\n | _ -> \"\"\n\nlet fadd_code_inline () : FStar.All.ML int =\n PR.print_inline \"fadd\" 0 None (List.length fadd_dom) fadd_dom fadd_names code_Fadd of_arg fadd_regs_modified fadd_comments\n\n[@__reduce__]\nlet fsub_dom: IX64.arity_ok_stdcall td =\n let y = [t64_mod; t64_no_mod; t64_no_mod] in\n assert_norm (List.length y = 3);\n y\n\n(* Need to rearrange the order of arguments *)\n[@__reduce__]\nlet fsub_pre : VSig.vale_pre fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state) ->\n FH.va_req_Fsub c va_s0\n (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2)\n\n[@__reduce__]\nlet fsub_post : VSig.vale_post fsub_dom =\n fun (c:V.va_code)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n (va_s1:V.va_state)\n (f:V.va_fuel) ->\n FH.va_ens_Fsub c va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) va_s1 f\n\n#set-options \"--z3rlimit 200\"\n\nlet fsub_regs_modified: MS.reg_64 -> bool = fun (r:MS.reg_64) ->\n let open MS in\n if r = rRax || r = rRcx || r = rR8 || r = rR9 || r = rR10 || r = rR11 then true\n else false\n\nlet fsub_xmms_modified = fun _ -> false\n\n[@__reduce__]\nlet fsub_lemma'\n (code:V.va_code)\n (_win:bool)\n (out:b64)\n (f1:b64)\n (f2:b64)\n (va_s0:V.va_state)\n : Ghost (V.va_state & V.va_fuel)\n (requires\n fsub_pre code out f1 f2 va_s0)\n (ensures (fun (va_s1, f) ->\n V.eval_code code va_s0 f va_s1 /\\\n VSig.vale_calling_conventions va_s0 va_s1 fsub_regs_modified fsub_xmms_modified /\\\n fsub_post code out f1 f2 va_s0 va_s1 f /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer out) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f1) /\\\n ME.buffer_readable (VS.vs_get_vale_heap va_s1) (as_vale_buffer f2) /\\\n ME.buffer_writeable (as_vale_buffer out) /\\\n ME.buffer_writeable (as_vale_buffer f1) /\\\n ME.buffer_writeable (as_vale_buffer f2) /\\\n ME.modifies (ME.loc_union (ME.loc_buffer (as_vale_buffer out))\n ME.loc_none) (VS.vs_get_vale_heap va_s0) (VS.vs_get_vale_heap va_s1)\n )) =\n let va_s1, f = FH.va_lemma_Fsub code va_s0 (as_vale_buffer out) (as_vale_buffer f1) (as_vale_buffer f2) in\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 out;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f1;\n Vale.AsLowStar.MemoryHelpers.buffer_writeable_reveal ME.TUInt64 ME.TUInt64 f2;\n (va_s1, f)\n\nPartial implementation:\nlet fsub_lemma =\n \n"
},
{
"role": "assistant",
"content": "as_t #(VSig.vale_sig fsub_regs_modified fsub_xmms_modified fsub_pre fsub_post) fsub_lemma'"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: g: Pulse.Typing.Env.env -> e: Pulse.Syntax.Base.effect_annot\n -> FStar.Tactics.Effect.Tac (Pulse.Typing.effect_annot_typing g e)\nEffect: FStar.Tactics.Effect.Tac\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nPartial implementation:\nlet check_effect_annot (g: env) (e: effect_annot) : T.Tac (effect_annot_typing g e) =\n \n"
},
{
"role": "assistant",
"content": "match e with\n| EffectAnnotSTT | EffectAnnotGhost -> ()\n| EffectAnnotAtomic { opens = opens } -> CP.core_check_term g opens T.E_Total tm_inames"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Prims.eqtype\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2017 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(*\nA standard library for manipulation of value bytes.\n\nThis model is realized by Bytes.bytes in OCaml and by\nstruct {uintX_t size; char *bytes} (or similar) in C.\n\nThis file is essentially a specialized version of FStar.Seq,\nwith lemmas and refinements taylored for typical operations on\nbytes, and with support for machine integers and C-extractible versions\n(which Seq does not provide.)\n\n@summary Value bytes standard library\n*)\nmodule FStar.Bytes\n\nmodule S = FStar.Seq\nmodule U = FStar.UInt\nmodule U8 = FStar.UInt8\nmodule U16 = FStar.UInt16\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule Str = FStar.String\nmodule Chr = FStar.Char\n\nPartial implementation:\nlet u8 =\n \n"
},
{
"role": "assistant",
"content": "U8.t"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: ke: Hacl.Bignum.Exponentiation.exp t -> modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Hacl.Impl.RSAPSS.rsapss_verify_compute_msg_st t ke modBits\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n\n let em = create emLen (u8 0) in\n RP.pss_encode a saltLen salt msgLen msg emBits em;\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits = v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let h' = ST.get () in\n update_sub_f h' m 0ul mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\n pop_frame ()\n\n\ninline_for_extraction noextract\nlet rsapss_sign_compute_sgnt_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h skey /\\ live h m /\\\n disjoint sgnt skey /\\ disjoint m sgnt /\\ disjoint m skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_compute_sgnt (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_compute_sgnt:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_sign_compute_sgnt_st t ke modBits\n\nlet rsapss_sign_compute_sgnt #t ke modBits eBits dBits skey m sgnt =\n push_frame ();\n let h_init = ST.get () in\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let k = blocks modBits 8ul in\n let s = create nLen (uint #t 0) in\n let m' = create nLen (uint #t 0) in\n let eq_b = rsapss_sign_bn ke modBits eBits dBits skey m m' s in\n LS.blocks_bits_lemma t (v modBits);\n LS.blocks_numb_lemma t (v modBits);\n assert (SD.blocks (v k) numb == v nLen);\n assert (numb * v nLen <= max_size_t);\n BN.bn_to_bytes_be k s sgnt;\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st1 (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 eq_m h1 -> modifies (loc sgnt) h0 h1 /\\\n (eq_m, as_seq h1 sgnt) == LS.rsapss_sign_ a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st1 t ke a modBits\n\nlet rsapss_sign_ #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let m = create nLen (uint #t 0) in\n rsapss_sign_msg_to_bn a modBits saltLen salt msgLen msg m;\n let eq_b = rsapss_sign_compute_sgnt ke modBits eBits dBits skey m sgnt in\n pop_frame ();\n eq_b\n\n\ninline_for_extraction noextract\nlet rsapss_sign_st (t:limb_t) (ke:BE.exp t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> sgnt:lbuffer uint8 (blocks modBits 8ul) ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h salt /\\ live h msg /\\ live h sgnt /\\ live h skey /\\\n disjoint sgnt salt /\\ disjoint sgnt msg /\\ disjoint sgnt salt /\\ disjoint sgnt skey /\\\n disjoint salt msg /\\\n\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey))\n (ensures fun h0 b h1 -> modifies (loc sgnt) h0 h1 /\\\n (b, as_seq h1 sgnt) == LS.rsapss_sign a (v modBits) (v eBits) (v dBits)\n (as_seq h0 skey) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_sign:\n #t:limb_t\n -> ke:BE.exp t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_st t ke a modBits\n\nlet rsapss_sign #t ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt =\n let hLen = RM.hash_len a in\n Math.Lemmas.pow2_lt_compat 61 32;\n Math.Lemmas.pow2_lt_compat 125 32;\n //assert (max_size_t < Hash.max_input_length a);\n\n let b =\n saltLen <=. 0xfffffffful -! hLen -! 8ul &&\n saltLen +! hLen +! 2ul <=. blocks (modBits -! 1ul) 8ul in\n\n if b then\n rsapss_sign_ ke a modBits eBits dBits skey saltLen salt msgLen msg sgnt\n else\n false\n\n\n\ninline_for_extraction noextract\nval bn_lt_pow2:\n #t:limb_t\n -> modBits:size_t{1 < v modBits}\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h -> live h m)\n (ensures fun h0 r h1 -> h0 == h1 /\\\n r == LS.bn_lt_pow2 (v modBits) (as_seq h0 m))\n\nlet bn_lt_pow2 #t modBits m =\n if not ((modBits -! 1ul) %. 8ul =. 0ul) then true\n else begin\n let get_bit = BN.bn_get_ith_bit (blocks modBits (size (bits t))) m (modBits -! 1ul) in\n BB.unsafe_bool_of_limb0 get_bit end\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> m_def:lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h pkey /\\ live h m_def /\\ live h s /\\\n disjoint m_def pkey /\\ disjoint m_def s /\\ disjoint s pkey /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m_def) h0 h1 /\\\n (r, as_seq h1 m_def) == LS.rsapss_verify_bn (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 m_def) (as_seq h0 s))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_verify_bn_st t ke modBits\nlet rsapss_verify_bn #t ke modBits eBits pkey m_def s =\n [@inline_let] let bits = size (bits t) in\n let nLen = blocks modBits bits in\n let eLen = blocks eBits bits in\n\n let n = sub pkey 0ul nLen in\n let r2 = sub pkey nLen nLen in\n let e = sub pkey (nLen +! nLen) eLen in\n\n let mask = BN.bn_lt_mask nLen s n in\n let h = ST.get () in\n SB.bn_lt_mask_lemma (as_seq h s) (as_seq h n);\n\n let res =\n if BB.unsafe_bool_of_limb mask then begin\n Math.Lemmas.pow2_le_compat (v bits * v nLen) (v modBits);\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h n);\n\n let h0 = ST.get () in\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m_def;\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 m_def)\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n\n if bn_lt_pow2 modBits m_def then true\n else false end\n else false in\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_bn_to_msg_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n saltLen:size_t\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t (blocks modBits (size (bits t))) ->\n Stack bool\n (requires fun h ->\n live h msg /\\ live h m /\\ disjoint m msg /\\\n\n LS.rsapss_verify_pre a (v saltLen) (v msgLen) (as_seq h msg))\n (ensures fun h0 r h1 -> modifies0 h0 h1 /\\\n r == LS.rsapss_verify_bn_to_msg a (v modBits) (v saltLen) (v msgLen) (as_seq h0 msg) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_verify_bn_to_msg:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_verify_bn_to_msg_st t a modBits\n\nlet rsapss_verify_bn_to_msg #t a modBits saltLen msgLen msg m =\n push_frame ();\n [@inline_let] let bits : size_pos = bits t in\n [@inline_let] let numb : size_pos = numbytes t in\n let nLen = blocks modBits (size bits) in\n\n let emBits = modBits -! 1ul in\n let emLen = blocks emBits 8ul in\n [@inline_let] let mLen = blocks emLen (size numb) in\n let em = create emLen (u8 0) in\n\n LS.blocks_bits_lemma t (v emBits);\n LS.blocks_numb_lemma t (v emBits);\n assert (SD.blocks (v emBits) bits == v mLen);\n assert (numb * v mLen <= max_size_t);\n assert (v mLen <= v nLen);\n\n let m1 = sub m 0ul mLen in\n BN.bn_to_bytes_be emLen m1 em;\n let res = RP.pss_verify a saltLen msgLen msg emBits em in\n pop_frame ();\n res\n\n\ninline_for_extraction noextract\nlet rsapss_verify_compute_msg_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t{LS.pkey_len_pre t (v modBits) (v eBits)}\n -> pkey:lbignum t (2ul *! len +! blocks eBits (size (bits t)))\n -> sgnt:lbuffer uint8 (blocks modBits 8ul)\n -> m:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h sgnt /\\ live h pkey /\\ live h m /\\\n disjoint m sgnt /\\ disjoint m pkey /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_pkey_pre (v modBits) (v eBits) (as_seq h pkey))\n (ensures fun h0 r h1 -> modifies (loc m) h0 h1 /\\\n (r, as_seq h1 m) == LS.rsapss_verify_compute_msg (v modBits) (v eBits) (as_seq h0 pkey) (as_seq h0 sgnt))\n\n\ninline_for_extraction noextract\nval rsapss_verify_compute_msg:\n #t:limb_t\n -> ke:BE.exp t\n -> modBits:modBits_t t ->\n rsapss_verify_compute_msg_st t ke modBits\n\nPartial implementation:\nlet rsapss_verify_compute_msg #t ke modBits eBits pkey sgnt m =\n \n"
},
{
"role": "assistant",
"content": "push_frame ();\n[@@ inline_let ]let bits:size_pos = bits t in\n[@@ inline_let ]let numb:size_pos = numbytes t in\nlet nLen = blocks modBits (size bits) in\nlet k = blocks modBits 8ul in\nlet s = create nLen (uint #t 0) in\nLS.blocks_bits_lemma t (v modBits);\nLS.blocks_numb_lemma t (v modBits);\nassert (SD.blocks (v k) numb == v nLen);\nassert (numb * v nLen <= max_size_t);\nBN.bn_from_bytes_be k sgnt s;\nlet b = rsapss_verify_bn #t ke modBits eBits pkey m s in\npop_frame ();\nb"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: ct: Pulse.Typing.comp_typing_u g c\n -> Pulse.Typing.effect_annot_typing g (Pulse.Syntax.Base.effect_annot_of_comp c)\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\nPartial implementation:\nlet comp_typing_as_effect_annot_typing (#g: env) (#c: comp_st) (ct: comp_typing_u g c)\n : effect_annot_typing g (effect_annot_of_comp c) =\n \n"
},
{
"role": "assistant",
"content": "let _, iname_typing = Metatheory.comp_typing_inversion ct in\nmatch c with\n| C_ST _ -> ()\n| C_STGhost _ -> ()\n| C_STAtomic opens obs _ -> iname_typing"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: d: Pulse.Typing.st_typing g st c -> eq: Pulse.Typing.st_equiv g c c'\n -> Pulse.Typing.st_typing g st c'\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nPartial implementation:\nlet t_equiv #g #st #c (d: st_typing g st c) (#c': comp) (eq: st_equiv g c c') : st_typing g st c' =\n \n"
},
{
"role": "assistant",
"content": "match d with\n| T_Equiv _ _ _ _ d0 eq' ->\n (match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq'')\n| _ -> T_Equiv _ _ _ _ d eq"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: ke: Hacl.Bignum.Exponentiation.exp t -> modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Hacl.Impl.RSAPSS.rsapss_sign_bn_st t ke modBits\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\n\nPartial implementation:\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n \n"
},
{
"role": "assistant",
"content": "[@@ inline_let ]let bits:size_pos = bits t in\nlet nLen = blocks modBits (size bits) in\nlet eLen = blocks eBits (size bits) in\nlet dLen = blocks dBits (size bits) in\nlet n = sub skey 0ul nLen in\nlet r2 = sub skey nLen nLen in\nlet e = sub skey (nLen +! nLen) eLen in\nlet d = sub skey (nLen +! nLen +! eLen) dLen in\nMath.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\nlet h0 = ST.get () in\nSM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\nBE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\nBE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\nlet h1 = ST.get () in\nSD.bn_eval_inj (v nLen)\n (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen)\n (as_seq h0 n)\n (as_seq h0 r2)\n (as_seq h0 m)\n (v dBits)\n (as_seq h0 d));\nSD.bn_eval_inj (v nLen)\n (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen)\n (as_seq h0 n)\n (as_seq h0 r2)\n (as_seq h1 s)\n (v eBits)\n (as_seq h0 e));\nlet eq_m = BN.bn_eq_mask nLen m m' in\nmapT nLen s (logand eq_m) s;\nBB.unsafe_bool_of_limb eq_m"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: ct: Pulse.Typing.comp_typing_u g c -> Pulse.Typing.post_hint_for_env g\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n\nPartial implementation:\nlet post_hint_from_comp_typing #g #c ct =\n \n"
},
{
"role": "assistant",
"content": "let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\nlet (| ty_typing , pre_typing , x , post_typing |) =\n Metatheory.st_comp_typing_inversion st_comp_typing\nin\nlet effect_annot_typing = comp_typing_as_effect_annot_typing ct in\nlet p:post_hint_t =\n {\n g = g;\n effect_annot = _;\n effect_annot_typing = effect_annot_typing;\n ret_ty = comp_res c;\n u = comp_u c;\n ty_typing = ty_typing;\n post = comp_post c;\n x = x;\n post_typing_src = post_typing;\n post_typing = post_typing_as_abstraction post_typing\n }\nin\np"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Prims.eqtype\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2017 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(*\nA standard library for manipulation of value bytes.\n\nThis model is realized by Bytes.bytes in OCaml and by\nstruct {uintX_t size; char *bytes} (or similar) in C.\n\nThis file is essentially a specialized version of FStar.Seq,\nwith lemmas and refinements taylored for typical operations on\nbytes, and with support for machine integers and C-extractible versions\n(which Seq does not provide.)\n\n@summary Value bytes standard library\n*)\nmodule FStar.Bytes\n\nmodule S = FStar.Seq\nmodule U = FStar.UInt\nmodule U8 = FStar.UInt8\nmodule U16 = FStar.UInt16\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule Str = FStar.String\nmodule Chr = FStar.Char\n\nPartial implementation:\nlet u16 =\n \n"
},
{
"role": "assistant",
"content": "U16.t"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: l: FStar.UInt32.t -> Type0\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2017 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(*\nA standard library for manipulation of value bytes.\n\nThis model is realized by Bytes.bytes in OCaml and by\nstruct {uintX_t size; char *bytes} (or similar) in C.\n\nThis file is essentially a specialized version of FStar.Seq,\nwith lemmas and refinements taylored for typical operations on\nbytes, and with support for machine integers and C-extractible versions\n(which Seq does not provide.)\n\n@summary Value bytes standard library\n*)\nmodule FStar.Bytes\n\nmodule S = FStar.Seq\nmodule U = FStar.UInt\nmodule U8 = FStar.UInt8\nmodule U16 = FStar.UInt16\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule Str = FStar.String\nmodule Chr = FStar.Char\n\nunfold let u8 = U8.t\nunfold let u16 = U16.t\nunfold let u32 = U32.t\n\n(** Realized by uint8_t in C and int in OCaml (char does not have necessary operators...) *)\nunfold type byte = u8\n\n(** Realized in C by a pair of a length field and uint8_t* in C\n Realized in OCaml by a string *)\nval bytes : t:Type0{hasEq t}\nval len : bytes -> u32\n\nunfold let length b = FStar.UInt32.v (len b)\n\n(** representation for specs that need lemmas not defined here. *)\nval reveal:\n bytes\n -> GTot (S.seq byte)\n\nval length_reveal:\n x:bytes\n -> Lemma (ensures (S.length (reveal x) = length x))\n [SMTPatOr [[SMTPat (S.length (reveal x))];\n [SMTPat (len x)]]]\n\nval hide:\n s:S.seq byte{S.length s < pow2 32}\n -> GTot bytes\n\nval hide_reveal:\n x:bytes\n -> Lemma (ensures (hide (reveal x) = x))\n [SMTPat (reveal x)]\n\nval reveal_hide:\n x:S.seq byte{S.length x < pow2 32}\n -> Lemma (ensures (reveal (hide x) == x))\n [SMTPat (hide x)]\n\ntype lbytes (l:nat) = b:bytes{length b = l}\ntype kbytes (k:nat) = b:bytes{length b < pow2 k}\n\nPartial implementation:\nlet lbytes32 (l: UInt32.t) =\n \n"
},
{
"role": "assistant",
"content": "b: bytes{len b = l}"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n g: Pulse.Typing.Env.env ->\n ctxt: Prims.list Pulse.Syntax.Base.term ->\n goal: Prims.list Pulse.Syntax.Base.term\n -> FStar.Tactics.Effect.Tac Prims.string\nEffect: FStar.Tactics.Effect.Tac\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nPartial implementation:\nlet format_failed_goal (g: env) (ctxt goal: list term) =\n \n"
},
{
"role": "assistant",
"content": "let terms_to_strings (ts: list term) = T.map Pulse.Syntax.Printer.term_to_string ts in\nlet numbered_list ss =\n let _, s =\n T.fold_left (fun (i, acc) s -> (i + 1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss\n in\n String.concat \"\\n \" (List.rev s)\nin\nlet format_terms (ts: list term) = numbered_list (terms_to_strings ts) in\nPrintf.sprintf \"Failed to prove the following goals:\\n %s\\nThe remaining conjuncts in the separation logic context available for use are:\\n %s\\nThe typing context is:\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: b1: FStar.Bytes.bytes -> b2: FStar.Bytes.bytes -> Prims.Pure FStar.Bytes.bytes\nEffect: Prims.Pure\n\nContext:\n(*\n Copyright 2008-2017 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(*\nA standard library for manipulation of value bytes.\n\nThis model is realized by Bytes.bytes in OCaml and by\nstruct {uintX_t size; char *bytes} (or similar) in C.\n\nThis file is essentially a specialized version of FStar.Seq,\nwith lemmas and refinements taylored for typical operations on\nbytes, and with support for machine integers and C-extractible versions\n(which Seq does not provide.)\n\n@summary Value bytes standard library\n*)\nmodule FStar.Bytes\n\nmodule S = FStar.Seq\nmodule U = FStar.UInt\nmodule U8 = FStar.UInt8\nmodule U16 = FStar.UInt16\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule Str = FStar.String\nmodule Chr = FStar.Char\n\nunfold let u8 = U8.t\nunfold let u16 = U16.t\nunfold let u32 = U32.t\n\n(** Realized by uint8_t in C and int in OCaml (char does not have necessary operators...) *)\nunfold type byte = u8\n\n(** Realized in C by a pair of a length field and uint8_t* in C\n Realized in OCaml by a string *)\nval bytes : t:Type0{hasEq t}\nval len : bytes -> u32\n\nunfold let length b = FStar.UInt32.v (len b)\n\n(** representation for specs that need lemmas not defined here. *)\nval reveal:\n bytes\n -> GTot (S.seq byte)\n\nval length_reveal:\n x:bytes\n -> Lemma (ensures (S.length (reveal x) = length x))\n [SMTPatOr [[SMTPat (S.length (reveal x))];\n [SMTPat (len x)]]]\n\nval hide:\n s:S.seq byte{S.length s < pow2 32}\n -> GTot bytes\n\nval hide_reveal:\n x:bytes\n -> Lemma (ensures (hide (reveal x) = x))\n [SMTPat (reveal x)]\n\nval reveal_hide:\n x:S.seq byte{S.length x < pow2 32}\n -> Lemma (ensures (reveal (hide x) == x))\n [SMTPat (hide x)]\n\ntype lbytes (l:nat) = b:bytes{length b = l}\ntype kbytes (k:nat) = b:bytes{length b < pow2 k}\n\nlet lbytes32 (l:UInt32.t) = b:bytes{len b = l}\n\nval empty_bytes : lbytes 0\nval empty_unique:\n b:bytes\n -> Lemma (length b = 0 ==> b = empty_bytes)\n [SMTPat (len b)]\n\n(** If you statically know the length, it is OK to read at arbitrary indexes *)\nval get:\n b:bytes\n -> pos:u32{U32.v pos < length b}\n -> Pure byte\n (requires True)\n (ensures (fun y -> y == S.index (reveal b) (U32.v pos)))\n\nunfold let op_String_Access = get\n\nunfold let index (b:bytes) (i:nat{i < length b}) = get b (U32.uint_to_t i)\n\nlet equal b1 b2 =\n length b1 = length b2 /\\\n (forall (i:u32{U32.v i < length b1}).{:pattern (b1.[i]); (b2.[i])} b1.[i] == b2.[i])\n\nval extensionality:\n b1:bytes\n -> b2:bytes\n -> Lemma (requires (equal b1 b2))\n (ensures (b1 = b2))\n\n(** creating byte values **)\nval create:\n len:u32\n -> v:byte\n -> b:lbytes (U32.v len){forall (i:u32{U32.(i <^ len)}).{:pattern b.[i]} b.[i] == v}\n\nunfold\nlet create_ (n:nat{FStar.UInt.size n U32.n}) v = create (U32.uint_to_t n) v\n\nval init:\n len:u32\n -> f:(i:u32{U32.(i <^ len)} -> byte)\n -> b:lbytes (U32.v len){forall (i:u32{U32.(i <^ len)}).{:pattern b.[i]} b.[i] == f i}\n\n// this is a hack JROESCH\nval abyte (b:byte) : lbytes 1\n (* admit () create 1ul b *)\n\nval twobytes (b:byte*byte) : lbytes 2\n // init 2ul (fun i -> if i = 0ul then fst b else snd b)\n\n(** appending bytes **)\nval append:\n b1:bytes\n -> b2:bytes\n -> Pure bytes\n (requires (UInt.size (length b1 + length b2) U32.n))\n\nPartial implementation:\nlet op_At_Bar =\n \n"
},
{
"role": "assistant",
"content": "append"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: \n a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} ->\n modBits: Hacl.Impl.RSAPSS.modBits_t t\n -> Hacl.Impl.RSAPSS.rsapss_sign_msg_to_bn_st t a modBits\nEffect: Prims.Tot\n\nContext:\nmodule Hacl.Impl.RSAPSS\n\nopen FStar.HyperStack\nopen FStar.HyperStack.ST\nopen FStar.Mul\n\nopen Lib.IntTypes\nopen Lib.Buffer\n\nopen Hacl.Bignum.Definitions\n\nmodule ST = FStar.HyperStack.ST\n\nmodule Hash = Spec.Agile.Hash\nmodule SB = Hacl.Spec.Bignum\nmodule BB = Hacl.Spec.Bignum.Base\nmodule SD = Hacl.Spec.Bignum.Definitions\nmodule SM = Hacl.Spec.Bignum.Montgomery\nmodule SE = Hacl.Spec.Bignum.Exponentiation\n\nmodule BN = Hacl.Bignum\nmodule BE = Hacl.Bignum.Exponentiation\nmodule BM = Hacl.Bignum.Montgomery\n\nmodule S = Spec.RSAPSS\nmodule LS = Hacl.Spec.RSAPSS\nmodule LSeq = Lib.Sequence\n\nmodule RP = Hacl.Impl.RSAPSS.Padding\nmodule RM = Hacl.Impl.RSAPSS.MGF\nmodule RK = Hacl.Impl.RSAPSS.Keys\n\n#reset-options \"--z3rlimit 150 --fuel 0 --ifuel 0\"\n\ninline_for_extraction noextract\nlet modBits_t (t:limb_t) = modBits:size_t{1 < v modBits /\\ 2 * bits t * SD.blocks (v modBits) (bits t) <= max_size_t}\n\n\ninline_for_extraction noextract\nlet rsapss_sign_bn_st (t:limb_t) (ke:BE.exp t) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n eBits:size_t\n -> dBits:size_t{LS.skey_len_pre t (v modBits) (v eBits) (v dBits)}\n -> skey:lbignum t (2ul *! len +! blocks eBits (size (bits t)) +! blocks dBits (size (bits t)))\n -> m:lbignum t len\n -> m':lbignum t len\n -> s:lbignum t len ->\n Stack bool\n (requires fun h -> len == ke.BE.bn.BN.len /\\\n live h skey /\\ live h m /\\ live h s /\\ live h m' /\\\n disjoint s m /\\ disjoint s skey /\\ disjoint m skey /\\\n disjoint m m' /\\ disjoint m' s /\\ disjoint m' skey /\\\n LS.rsapss_skey_pre (v modBits) (v eBits) (v dBits) (as_seq h skey) /\\\n bn_v h m < bn_v h (gsub skey 0ul len))\n (ensures fun h0 r h1 -> modifies (loc s |+| loc m') h0 h1 /\\\n (r, as_seq h1 s) == LS.rsapss_sign_bn (v modBits) (v eBits) (v dBits) (as_seq h0 skey) (as_seq h0 m))\n\n\ninline_for_extraction noextract\nval rsapss_sign_bn: #t:limb_t -> ke:BE.exp t -> modBits:modBits_t t -> rsapss_sign_bn_st t ke modBits\nlet rsapss_sign_bn #t ke modBits eBits dBits skey m m' s =\n [@inline_let] let bits : size_pos = bits t in\n let nLen = blocks modBits (size bits) in\n let eLen = blocks eBits (size bits) in\n let dLen = blocks dBits (size bits) in\n\n let n = sub skey 0ul nLen in\n let r2 = sub skey nLen nLen in\n let e = sub skey (nLen +! nLen) eLen in\n let d = sub skey (nLen +! nLen +! eLen) dLen in\n\n Math.Lemmas.pow2_le_compat (bits * v nLen) (v modBits);\n let h0 = ST.get () in\n SM.bn_precomp_r2_mod_n_lemma (v modBits - 1) (as_seq h0 n);\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_ct_precomp n r2 m dBits d s;\n BE.mk_bn_mod_exp_precompr2 nLen ke.BE.exp_vt_precomp n r2 s eBits e m';\n let h1 = ST.get () in\n SD.bn_eval_inj (v nLen) (as_seq h1 s)\n (SE.bn_mod_exp_consttime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h0 m) (v dBits) (as_seq h0 d));\n SD.bn_eval_inj (v nLen) (as_seq h1 m')\n (SE.bn_mod_exp_vartime_precompr2 (v nLen) (as_seq h0 n) (as_seq h0 r2)\n (as_seq h1 s) (v eBits) (as_seq h0 e));\n let eq_m = BN.bn_eq_mask nLen m m' in\n mapT nLen s (logand eq_m) s;\n BB.unsafe_bool_of_limb eq_m\n\n\ninline_for_extraction noextract\nlet rsapss_sign_msg_to_bn_st (t:limb_t) (a:Hash.hash_alg{S.hash_is_supported a}) (modBits:modBits_t t) =\n let len = blocks modBits (size (bits t)) in\n saltLen:size_t\n -> salt:lbuffer uint8 saltLen\n -> msgLen:size_t\n -> msg:lbuffer uint8 msgLen\n -> m:lbignum t len ->\n Stack unit\n (requires fun h ->\n live h salt /\\ live h msg /\\ live h m /\\\n disjoint salt msg /\\ disjoint m msg /\\ disjoint m salt /\\\n as_seq h m == LSeq.create (v len) (uint #t 0) /\\\n LS.rsapss_sign_pre a (v modBits) (v saltLen) (as_seq h salt) (v msgLen) (as_seq h msg))\n (ensures fun h0 _ h1 -> modifies (loc m) h0 h1 /\\\n as_seq h1 m == LS.rsapss_sign_msg_to_bn a (v modBits) (v saltLen) (as_seq h0 salt) (v msgLen) (as_seq h0 msg))\n\n\ninline_for_extraction noextract\nval rsapss_sign_msg_to_bn:\n #t:limb_t\n -> a:Hash.hash_alg{S.hash_is_supported a}\n -> modBits:modBits_t t ->\n rsapss_sign_msg_to_bn_st t a modBits\n\nPartial implementation:\nlet rsapss_sign_msg_to_bn #t a modBits saltLen salt msgLen msg m =\n \n"
},
{
"role": "assistant",
"content": "push_frame ();\n[@@ inline_let ]let bits:size_pos = bits t in\n[@@ inline_let ]let numb:size_pos = numbytes t in\nlet nLen = blocks modBits (size bits) in\nlet emBits = modBits -! 1ul in\nlet emLen = blocks emBits 8ul in\n[@@ inline_let ]let mLen = blocks emLen (size numb) in\nlet em = create emLen (u8 0) in\nRP.pss_encode a saltLen salt msgLen msg emBits em;\nLS.blocks_bits_lemma t (v emBits);\nLS.blocks_numb_lemma t (v emBits);\nassert (SD.blocks (v emBits) bits = v mLen);\nassert (numb * v mLen <= max_size_t);\nassert (v mLen <= v nLen);\nlet h' = ST.get () in\nupdate_sub_f h'\n m\n 0ul\n mLen\n (fun h -> SB.bn_from_bytes_be (v emLen) (as_seq h' em))\n (fun _ -> BN.bn_from_bytes_be emLen em (sub m 0ul mLen));\npop_frame ()"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: b: FStar.Bytes.bytes -> FStar.UInt.uint_t 32\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2017 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(*\nA standard library for manipulation of value bytes.\n\nThis model is realized by Bytes.bytes in OCaml and by\nstruct {uintX_t size; char *bytes} (or similar) in C.\n\nThis file is essentially a specialized version of FStar.Seq,\nwith lemmas and refinements taylored for typical operations on\nbytes, and with support for machine integers and C-extractible versions\n(which Seq does not provide.)\n\n@summary Value bytes standard library\n*)\nmodule FStar.Bytes\n\nmodule S = FStar.Seq\nmodule U = FStar.UInt\nmodule U8 = FStar.UInt8\nmodule U16 = FStar.UInt16\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule Str = FStar.String\nmodule Chr = FStar.Char\n\nunfold let u8 = U8.t\nunfold let u16 = U16.t\nunfold let u32 = U32.t\n\n(** Realized by uint8_t in C and int in OCaml (char does not have necessary operators...) *)\nunfold type byte = u8\n\n(** Realized in C by a pair of a length field and uint8_t* in C\n Realized in OCaml by a string *)\nval bytes : t:Type0{hasEq t}\nval len : bytes -> u32\n\nPartial implementation:\nlet length b =\n \n"
},
{
"role": "assistant",
"content": "FStar.UInt32.v (len b)"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: Prims.eqtype\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2017 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(*\nA standard library for manipulation of value bytes.\n\nThis model is realized by Bytes.bytes in OCaml and by\nstruct {uintX_t size; char *bytes} (or similar) in C.\n\nThis file is essentially a specialized version of FStar.Seq,\nwith lemmas and refinements taylored for typical operations on\nbytes, and with support for machine integers and C-extractible versions\n(which Seq does not provide.)\n\n@summary Value bytes standard library\n*)\nmodule FStar.Bytes\n\nmodule S = FStar.Seq\nmodule U = FStar.UInt\nmodule U8 = FStar.UInt8\nmodule U16 = FStar.UInt16\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule Str = FStar.String\nmodule Chr = FStar.Char\n\nunfold let u8 = U8.t\n\nPartial implementation:\nlet u32 =\n \n"
},
{
"role": "assistant",
"content": "U32.t"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: b: FStar.Bytes.bytes -> pos: FStar.Bytes.u32{FStar.UInt32.v pos < FStar.Bytes.length b}\n -> Prims.Pure FStar.Bytes.byte\nEffect: Prims.Pure\n\nContext:\n(*\n Copyright 2008-2017 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n(*\nA standard library for manipulation of value bytes.\n\nThis model is realized by Bytes.bytes in OCaml and by\nstruct {uintX_t size; char *bytes} (or similar) in C.\n\nThis file is essentially a specialized version of FStar.Seq,\nwith lemmas and refinements taylored for typical operations on\nbytes, and with support for machine integers and C-extractible versions\n(which Seq does not provide.)\n\n@summary Value bytes standard library\n*)\nmodule FStar.Bytes\n\nmodule S = FStar.Seq\nmodule U = FStar.UInt\nmodule U8 = FStar.UInt8\nmodule U16 = FStar.UInt16\nmodule U32 = FStar.UInt32\nmodule U64 = FStar.UInt64\nmodule Str = FStar.String\nmodule Chr = FStar.Char\n\nunfold let u8 = U8.t\nunfold let u16 = U16.t\nunfold let u32 = U32.t\n\n(** Realized by uint8_t in C and int in OCaml (char does not have necessary operators...) *)\nunfold type byte = u8\n\n(** Realized in C by a pair of a length field and uint8_t* in C\n Realized in OCaml by a string *)\nval bytes : t:Type0{hasEq t}\nval len : bytes -> u32\n\nunfold let length b = FStar.UInt32.v (len b)\n\n(** representation for specs that need lemmas not defined here. *)\nval reveal:\n bytes\n -> GTot (S.seq byte)\n\nval length_reveal:\n x:bytes\n -> Lemma (ensures (S.length (reveal x) = length x))\n [SMTPatOr [[SMTPat (S.length (reveal x))];\n [SMTPat (len x)]]]\n\nval hide:\n s:S.seq byte{S.length s < pow2 32}\n -> GTot bytes\n\nval hide_reveal:\n x:bytes\n -> Lemma (ensures (hide (reveal x) = x))\n [SMTPat (reveal x)]\n\nval reveal_hide:\n x:S.seq byte{S.length x < pow2 32}\n -> Lemma (ensures (reveal (hide x) == x))\n [SMTPat (hide x)]\n\ntype lbytes (l:nat) = b:bytes{length b = l}\ntype kbytes (k:nat) = b:bytes{length b < pow2 k}\n\nlet lbytes32 (l:UInt32.t) = b:bytes{len b = l}\n\nval empty_bytes : lbytes 0\nval empty_unique:\n b:bytes\n -> Lemma (length b = 0 ==> b = empty_bytes)\n [SMTPat (len b)]\n\n(** If you statically know the length, it is OK to read at arbitrary indexes *)\nval get:\n b:bytes\n -> pos:u32{U32.v pos < length b}\n -> Pure byte\n (requires True)\n (ensures (fun y -> y == S.index (reveal b) (U32.v pos)))\n\nPartial implementation:\nlet op_String_Access =\n \n"
},
{
"role": "assistant",
"content": "get"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: g: Pulse.Typing.Env.env -> ctxt: Pulse.Syntax.Base.term\n -> Pulse.Checker.Base.continuation_elaborator g ctxt g ctxt\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nPartial implementation:\nlet k_elab_unit (g: env) (ctxt: term) : continuation_elaborator g ctxt g ctxt =\n \n"
},
{
"role": "assistant",
"content": "fun p r -> r"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: c: Pulse.Syntax.Base.comp_st -> pre: Pulse.Syntax.Base.term -> Pulse.Syntax.Base.comp\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq\n\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv\n\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))\n\nlet simplify_lemma (c:comp_st) (c':comp_st) (post_hint:option post_hint_t)\n : Lemma\n (requires\n comp_post_matches_hint c post_hint /\\\n effect_annot_of_comp c == effect_annot_of_comp c' /\\\n comp_res c' == comp_res c /\\\n comp_u c' == comp_u c /\\\n comp_post c' == tm_star (comp_post c) tm_emp)\n (ensures comp_post_matches_hint (comp_st_with_post c' (comp_post c)) post_hint /\\\n comp_pre (comp_st_with_post c' (comp_post c)) == comp_pre c')\n = ()\n\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing\n\nPartial implementation:\nlet comp_with_pre (c: comp_st) (pre: term) =\n \n"
},
{
"role": "assistant",
"content": "match c with\n| C_ST st -> C_ST ({ st with pre = pre })\n| C_STGhost st -> C_STGhost ({ st with pre = pre })\n| C_STAtomic i obs st -> C_STAtomic i obs ({ st with pre = pre })"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: x: a -> DM4F_layered5.wp st a\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2008-2018 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule DM4F_layered5\n\n(* Same as DM4F, but layered over a layered PURE without monotonicity *)\nopen ID5\nopen DM4F_Utils\n\nunfold\nlet pure_bind_wp (#a #b : Type) (w1 : ID5.wp a) (w2 : a -> ID5.wp b) : ID5.wp b =\n ID5.bind_wp w1 w2\n\n(* Simulating state effect in DM4F, hopefully doable by a tactic. *)\n\ntype post_t st a = a -> st -> Type0\n\ntype wp0 (st:Type u#0) (a:Type u#ua) : Type u#(max 1 ua) =\n st -> post_t st a -> Type0\n\nlet st_monotonic #st #a (w : wp0 st a) : Type0 =\n //forall s0 p1 p2. (forall r. p1 r ==> p2 r) ==> w s0 p1 ==> w s0 p2\n // ^ this version seems to be less SMT-friendly\n forall s0 p1 p2. (forall x s1. p1 x s1 ==> p2 x s1) ==> w s0 p1 ==> w s0 p2\n\ntype wp st a = w:(wp0 st a){st_monotonic w}\n\nopen FStar.Monotonic.Pure\n\ntype repr (a:Type u#ua) (st:Type0) (wp : wp u#ua st a) : Type u#(max 1 ua) =\n s0:st -> ID (a & st) (as_pure_wp (fun p -> wp s0 (curry p)))\n\nPartial implementation:\nlet return_wp (#a: Type) (#st: Type0) (x: a) : wp st a =\n \n"
},
{
"role": "assistant",
"content": "fun s0 p -> p x s0"
}
] |
[
{
"role": "user",
"content": "Complete this F* function with a correct proof.\n\nType: g: Pulse.Typing.Env.env -> vp: Pulse.Syntax.Base.term\n -> FStar.Pervasives.Native.option (Pulse.Typing.vprop_equiv g vp Pulse.Syntax.Base.tm_emp)\nEffect: Prims.Tot\n\nContext:\n(*\n Copyright 2023 Microsoft Research\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n*)\n\nmodule Pulse.Checker.Base\n\nmodule T = FStar.Tactics.V2\nmodule RT = FStar.Reflection.Typing\nmodule Metatheory = Pulse.Typing.Metatheory\nmodule CP = Pulse.Checker.Pure\nmodule RU = Pulse.RuntimeUtils\nmodule FV = Pulse.Typing.FV\nmodule P = Pulse.Syntax.Printer\n\nopen Pulse.Typing.Combinators\nopen Pulse.Typing.Metatheory\n\nlet debug (g:env) (f: unit -> T.Tac string) : T.Tac unit =\n if RU.debug_at_level (fstar_env g) \"pulse.checker\" then\n T.print (f())\n\nlet format_failed_goal (g:env) (ctxt:list term) (goal:list term) =\n let terms_to_strings (ts:list term)= T.map Pulse.Syntax.Printer.term_to_string ts in\n let numbered_list ss = \n let _, s = T.fold_left (fun (i, acc) s -> (i+1, Printf.sprintf \"%d. %s\" i s :: acc)) (1, []) ss in\n String.concat \"\\n \" (List.rev s)\n in\n let format_terms (ts:list term) = numbered_list (terms_to_strings ts) in\n Printf.sprintf \n \"Failed to prove the following goals:\\n \\\n %s\\n\\\n The remaining conjuncts in the separation logic context available for use are:\\n \\\n %s\\n\\\n The typing context is:\\n \\\n %s\\n\"\n (format_terms goal)\n (format_terms ctxt)\n (env_to_string g)\n\n\nlet mk_arrow ty t = RT.mk_arrow (elab_term ty) T.Q_Explicit (elab_term t)\nlet mk_abs ty t = RT.(mk_abs (elab_term ty) T.Q_Explicit (elab_term t))\n\nlet intro_comp_typing (g:env) \n (c:comp_st)\n (pre_typing:tot_typing g (comp_pre c) tm_vprop)\n (i_typing:effect_annot_typing g (effect_annot_of_comp c))\n (res_typing:universe_of g (comp_res c) (comp_u c))\n (x:var { fresh_wrt x g (freevars (comp_post c)) })\n (post_typing:tot_typing (push_binding g x ppname_default (comp_res c)) (open_term (comp_post c) x) tm_vprop)\n : T.Tac (comp_typing g c (universe_of_comp c))\n = let intro_st_comp_typing (st:st_comp { comp_u c == st.u /\\\n comp_pre c == st.pre /\\\n comp_res c == st.res /\\\n comp_post c == st.post } )\n : T.Tac (st_comp_typing g st)\n = STC g st x res_typing pre_typing post_typing\n in\n match c with\n | C_ST st -> \n let stc = intro_st_comp_typing st in\n CT_ST _ _ stc\n | C_STAtomic i obs st -> \n let stc = intro_st_comp_typing st in\n CT_STAtomic _ i obs _ i_typing stc\n | C_STGhost st -> \n let stc = intro_st_comp_typing st in\n CT_STGhost _ _ stc\n\nirreducible\nlet post_typing_as_abstraction\n (#g:env) (#x:var) (#ty:term) (#t:term { fresh_wrt x g (freevars t) })\n (_:tot_typing (push_binding g x ppname_default ty) (open_term t x) tm_vprop)\n : FStar.Ghost.erased (RT.tot_typing (elab_env g) (mk_abs ty t) (mk_arrow ty tm_vprop)) \n = admit()\n\nlet check_effect_annot (g:env) (e:effect_annot) : T.Tac (effect_annot_typing g e) =\n match e with\n | EffectAnnotSTT\n | EffectAnnotGhost -> ()\n | EffectAnnotAtomic { opens } ->\n CP.core_check_term g opens T.E_Total tm_inames\n\nlet intro_post_hint g effect_annot ret_ty_opt post =\n let x = fresh g in\n let ret_ty = \n match ret_ty_opt with\n | None -> tm_fstar RT.unit_ty FStar.Range.range_0\n | Some t -> t\n in\n let ret_ty, _ = CP.instantiate_term_implicits g ret_ty in\n let (| u, ty_typing |) = CP.check_universe g ret_ty in\n let (| post, post_typing |) = CP.check_vprop (push_binding g x ppname_default ret_ty) (open_term_nv post (v_as_nv x)) in \n let post' = close_term post x in\n Pulse.Typing.FV.freevars_close_term post x 0;\n let effect_annot_typing = check_effect_annot g effect_annot in\n assume (open_term post' x == post);\n { g;\n effect_annot;\n effect_annot_typing;\n ret_ty; u; ty_typing;\n post=post';\n x; post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction #_ #_ #_ #post' post_typing }\n\n\nlet comp_typing_as_effect_annot_typing (#g:env) (#c:comp_st) (ct:comp_typing_u g c)\n: effect_annot_typing g (effect_annot_of_comp c)\n= let _, iname_typing = Metatheory.comp_typing_inversion ct in\n match c with\n | C_ST _ -> ()\n | C_STGhost _ -> ()\n | C_STAtomic opens obs _ -> iname_typing\n \n\nlet post_hint_from_comp_typing #g #c ct = \n let st_comp_typing, _ = Metatheory.comp_typing_inversion ct in\n let (| ty_typing, pre_typing, x, post_typing |) = Metatheory.st_comp_typing_inversion st_comp_typing in\n let effect_annot_typing = comp_typing_as_effect_annot_typing ct in\n let p : post_hint_t = \n { g;\n effect_annot=_;\n effect_annot_typing;\n ret_ty = comp_res c; u=comp_u c; \n ty_typing=ty_typing;\n post=comp_post c;\n x;\n post_typing_src=post_typing;\n post_typing=post_typing_as_abstraction post_typing }\n in\n p\n\nlet comp_typing_from_post_hint\n (#g: env)\n (c: comp_st)\n (pre_typing: tot_typing g (comp_pre c) tm_vprop)\n (p:post_hint_for_env g { comp_post_matches_hint c (Some p) })\n: T.Tac (comp_typing_u g c)\n= let x = fresh g in\n if x `Set.mem` freevars p.post //exclude this\n then fail g None \"Impossible: unexpected freevar in post, please file a bug-report\"\n else let post_typing = post_hint_typing g p x in\n intro_comp_typing g c pre_typing\n post_typing.effect_annot_typing\n post_typing.ty_typing \n x post_typing.post_typing\n\n\nlet extend_post_hint g p x tx conjunct conjunct_typing =\n let g' = push_binding g x ppname_default tx in\n let y = fresh g' in\n let g'' = push_binding g' y ppname_default p.ret_ty in\n let p_post_typing_src\n : tot_typing (push_binding p.g p.x ppname_default p.ret_ty)\n (open_term p.post p.x) tm_vprop\n = p.post_typing_src\n in\n let p_post_typing_src''\n : tot_typing g'' (open_term p.post y) tm_vprop\n = RU.magic () //weaken, rename\n in\n let conjunct_typing'\n : tot_typing g' conjunct tm_vprop\n = conjunct_typing\n in\n let conjunct_typing''\n : tot_typing g'' (open_term conjunct y) tm_vprop\n = RU.magic () //weaken\n in\n let new_post = tm_star p.post conjunct in\n let new_post_typing\n : tot_typing g'' (open_term new_post y) tm_vprop\n = Pulse.Typing.star_typing p_post_typing_src'' conjunct_typing''\n in\n assume (fresh_wrt y g'' (freevars new_post));\n let new_post_abs_typing\n : Ghost.erased (RT.tot_typing (elab_env g'') (mk_abs p.ret_ty new_post) (mk_arrow p.ret_ty tm_vprop))\n = post_typing_as_abstraction new_post_typing\n in\n { p with\n g=g';\n post=new_post;\n x=y;\n post_typing_src=new_post_typing;\n post_typing=new_post_abs_typing }\n\nlet k_elab_unit (g:env) (ctxt:term)\n : continuation_elaborator g ctxt g ctxt\n = fun p r -> r\n\nlet k_elab_trans\n (#g0:env) (#g1:env { g1 `env_extends` g0 }) (#g2:env { g2 `env_extends` g1 }) (#ctxt0 #ctxt1 #ctxt2:term)\n (k0:continuation_elaborator g0 ctxt0 g1 ctxt1)\n (k1:continuation_elaborator g1 ctxt1 g2 ctxt2 { g1 `env_extends` g0})\n : continuation_elaborator g0 ctxt0 g2 ctxt2\n = fun post_hint res -> k0 post_hint (k1 post_hint res)\n\nlet comp_st_with_post (c:comp_st) (post:term)\n : c':comp_st { st_comp_of_comp c' == ({ st_comp_of_comp c with post} <: st_comp) } =\n match c with\n | C_ST st -> C_ST { st with post }\n | C_STGhost st -> C_STGhost { st with post }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with post}\n\nlet ve_unit_r g (p:term) : vprop_equiv g (tm_star p tm_emp) p = \n VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Unit _ _)\n\nlet st_equiv_trans (#g:env) (#c0 #c1 #c2:comp) (d01:st_equiv g c0 c1) (d12:st_equiv g c1 c2)\n : option (st_equiv g c0 c2)\n = \n match d01 with\n | ST_VPropEquiv _f _c0 _c1 x c0_pre_typing c0_res_typing c0_post_typing eq_res_01 eq_pre_01 eq_post_01 -> (\n let ST_VPropEquiv _f _c1 _c2 y c1_pre_typing c1_res_typing c1_post_typing eq_res_12 eq_pre_12 eq_post_12 = d12 in\n if x = y && eq_tm (comp_res c0) (comp_res c1)\n then Some (\n ST_VPropEquiv g c0 c2 x c0_pre_typing c0_res_typing c0_post_typing\n (RT.Rel_trans _ _ _ _ _ eq_res_01 eq_res_12)\n (VE_Trans _ _ _ _ eq_pre_01 eq_pre_12)\n (VE_Trans _ _ _ _ eq_post_01 eq_post_12)\n )\n else None\n )\n | ST_TotEquiv g t1 t2 u typing eq ->\n let ST_TotEquiv _g _t1 t3 _ _ eq' = d12 in\n let eq'' = Ghost.hide (RT.Rel_trans _ _ _ _ _ eq eq') in\n Some (ST_TotEquiv g t1 t3 u typing eq'')\n\nlet t_equiv #g #st #c (d:st_typing g st c) (#c':comp) (eq:st_equiv g c c')\n : st_typing g st c'\n = match d with\n | T_Equiv _ _ _ _ d0 eq' -> (\n match st_equiv_trans eq' eq with\n | None -> T_Equiv _ _ _ _ d eq\n | Some eq'' -> T_Equiv _ _ _ _ d0 eq''\n )\n | _ -> T_Equiv _ _ _ _ d eq\n\nlet st_equiv_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { freevars post `Set.subset` freevars (comp_post c)})\n (veq: (x:var { fresh_wrt x g (freevars (comp_post c)) } ->\n vprop_equiv (push_binding g x ppname_default (comp_res c)) \n (open_term (comp_post c) x)\n (open_term post x)))\n : st_typing g t (comp_st_with_post c post)\n = if eq_tm post (comp_post c) then d\n else\n let c' = comp_st_with_post c post in\n let (| u_of, pre_typing, x, post_typing |) = Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let veq = veq x in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) (VE_Refl _ _) veq\n in\n t_equiv d st_equiv\n\nlet simplify_post (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (post:term { comp_post c == tm_star post tm_emp})\n : st_typing g t (comp_st_with_post c post)\n = st_equiv_post d post (fun x -> ve_unit_r (push_binding g x ppname_default (comp_res c)) (open_term post x))\n\nlet simplify_lemma (c:comp_st) (c':comp_st) (post_hint:option post_hint_t)\n : Lemma\n (requires\n comp_post_matches_hint c post_hint /\\\n effect_annot_of_comp c == effect_annot_of_comp c' /\\\n comp_res c' == comp_res c /\\\n comp_u c' == comp_u c /\\\n comp_post c' == tm_star (comp_post c) tm_emp)\n (ensures comp_post_matches_hint (comp_st_with_post c' (comp_post c)) post_hint /\\\n comp_pre (comp_st_with_post c' (comp_post c)) == comp_pre c')\n = ()\n\nlet vprop_equiv_typing_bk (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g p ctxt)\n : tot_typing g p tm_vprop \n = let _, bk = vprop_equiv_typing d in\n bk ctxt_typing\n\nlet comp_with_pre (c:comp_st) (pre:term) =\n match c with\n | C_ST st -> C_ST { st with pre }\n | C_STGhost st -> C_STGhost { st with pre }\n | C_STAtomic i obs st -> C_STAtomic i obs {st with pre}\n\n\nlet st_equiv_pre (#g:env) (#t:st_term) (#c:comp_st) (d:st_typing g t c)\n (pre:term)\n (veq: vprop_equiv g (comp_pre c) pre)\n : st_typing g t (comp_with_pre c pre)\n = if eq_tm pre (comp_pre c) then d\n else\n let c' = comp_with_pre c pre in\n let (| u_of, pre_typing, x, post_typing |) =\n Metatheory.(st_comp_typing_inversion (fst (comp_typing_inversion (st_typing_correctness d)))) in\n let st_equiv : st_equiv g c c' =\n ST_VPropEquiv g c c' x pre_typing u_of post_typing (RT.Rel_refl _ _ _) veq (VE_Refl _ _)\n in\n t_equiv d st_equiv\n\n\n#push-options \"--z3rlimit_factor 4 --ifuel 2 --fuel 0\"\nlet k_elab_equiv_continuation (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt #ctxt1 #ctxt2:term)\n (k:continuation_elaborator g1 ctxt g2 ctxt1)\n (d:vprop_equiv g2 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt g2 ctxt2 =\n fun post_hint res ->\n let (| st, c, st_d |) = res in\n let st_d : st_typing g2 st c = st_d in\n assert (comp_pre c == ctxt2);\n let st_d' : st_typing g2 st (comp_with_pre c ctxt1) = st_equiv_pre st_d _ (VE_Sym _ _ _ d) in\n k post_hint (| st, _, st_d' |)\n#pop-options\n\nlet vprop_equiv_typing_fwd (#g:env) (#ctxt:_) (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#p:_) (d:vprop_equiv g ctxt p)\n : tot_typing g p tm_vprop \n = let fwd, _ = vprop_equiv_typing d in\n fwd ctxt_typing\n\n#push-options \"--z3rlimit_factor 4 --ifuel 1 --fuel 0\"\nlet k_elab_equiv_prefix\n (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt1 #ctxt2 #ctxt:term)\n (k:continuation_elaborator g1 ctxt1 g2 ctxt)\n (d:vprop_equiv g1 ctxt1 ctxt2)\n : continuation_elaborator g1 ctxt2 g2 ctxt =\n fun post_hint res ->\n let framing_token : frame_for_req_in_ctxt g1 ctxt2 ctxt1 = \n let d = VE_Trans _ _ _ _ (VE_Comm _ _ _) (VE_Trans _ _ _ _ (VE_Unit _ _) d) in\n (| tm_emp, emp_typing, d |)\n in\n let res = k post_hint res in\n let (| st, c, st_d |) = res in\n assert (comp_pre c == ctxt1);\n (| _, _, st_equiv_pre st_d _ d |)\n #pop-options\n\nlet k_elab_equiv\n (#g1:env) (#g2:env { g2 `env_extends` g1 }) (#ctxt1 #ctxt1' #ctxt2 #ctxt2':term) \n (k:continuation_elaborator g1 ctxt1 g2 ctxt2)\n (d1:vprop_equiv g1 ctxt1 ctxt1')\n (d2:vprop_equiv g2 ctxt2 ctxt2')\n : continuation_elaborator g1 ctxt1' g2 ctxt2' =\n \n let k : continuation_elaborator g1 ctxt1 g2 ctxt2' =\n k_elab_equiv_continuation k d2 in\n let k : continuation_elaborator g1 ctxt1' g2 ctxt2' =\n k_elab_equiv_prefix k d1 in\n k\n\n#push-options \"--query_stats --fuel 2 --ifuel 2 --split_queries no --z3rlimit_factor 20\"\nopen Pulse.PP\nlet continuation_elaborator_with_bind (#g:env) (ctxt:term)\n (#c1:comp{stateful_comp c1})\n (#e1:st_term)\n (e1_typing:st_typing g e1 c1)\n (ctxt_pre1_typing:tot_typing g (tm_star ctxt (comp_pre c1)) tm_vprop)\n (x:nvar { None? (lookup g (snd x)) })\n : T.Tac (continuation_elaborator\n g\n (tm_star ctxt (comp_pre c1))\n (push_binding g (snd x) (fst x) (comp_res c1))\n (tm_star (open_term (comp_post c1) (snd x)) ctxt)) =\n\n let pre1 = comp_pre c1 in\n let res1 = comp_res c1 in\n let post1 = comp_post c1 in\n let ctxt_typing = star_typing_inversion_l ctxt_pre1_typing in\n // let p_prop = Metatheory.pure_typing_inversion pure_typing in\n let v_eq = VE_Comm g ctxt pre1 in\n let framing_token : frame_for_req_in_ctxt g (tm_star ctxt pre1) pre1 = \n (| ctxt, ctxt_typing, VE_Comm g pre1 ctxt |)\n in\n let (| c1, e1_typing |) =\n apply_frame ctxt_pre1_typing e1_typing framing_token in\n let (| u_of_1, pre_typing, _, _ |) =\n Metatheory.(st_comp_typing_inversion (fst <| comp_typing_inversion (st_typing_correctness e1_typing))) in\n let b = res1 in\n let ppname, x = x in\n let g' = push_binding g x ppname b in\n \n let post1_opened = open_term_nv post1 (v_as_nv x) in\n let k : continuation_elaborator g (tm_star ctxt pre1) g' (tm_star post1_opened ctxt) =\n fun post_hint res ->\n let (| e2, c2, e2_typing |) = res in\n assert (comp_post_matches_hint c2 post_hint);\n let e2_typing : st_typing g' e2 c2 = e2_typing in\n let e2_closed = close_st_term e2 x in\n assume (open_st_term e2_closed x == e2);\n assert (comp_pre c1 == (tm_star ctxt pre1));\n assert (comp_post c1 == tm_star post1 ctxt);\n assert (comp_pre c2 == tm_star post1_opened ctxt);\n assert (open_term (comp_post c1) x == tm_star post1_opened (open_term ctxt x));\n // ctxt is well-typed, hence ln\n assume (open_term ctxt x == ctxt);\n assert (open_term (comp_post c1) x == comp_pre c2);\n // we closed e2 with x\n assume (~ (x `Set.mem` freevars_st e2_closed));\n if x `Set.mem` freevars (comp_post c2)\n then fail g' None \"Impossible: freevar clash when constructing continuation elaborator for bind, please file a bug-report\"\n else (\n let t_typing, post_typing =\n Pulse.Typing.Combinators.bind_res_and_post_typing g c2 x post_hint in\n let g = push_context g \"mk_bind\" e1.range in\n // info_doc g None\n // [prefix 4 1 (doc_of_string \"mk_bind e1 = \") (doc_of_string (Pulse.Syntax.Printer.st_term_to_string e1));\n // prefix 4 1 (doc_of_string \"mk_bind c1 = \") (pp #comp c1);\n // prefix 4 1 (doc_of_string \"mk_bind e2 = \") (doc_of_string (Pulse.Syntax.Printer.st_term_to_string e2));\n // prefix 4 1 (doc_of_string \"mk_bind c2 = \") (pp #comp c2)]\n // ;\n let (| e, c, e_typing |) =\n Pulse.Typing.Combinators.mk_bind\n g (tm_star ctxt pre1) \n e1 e2_closed c1 c2 (ppname, x) e1_typing\n u_of_1 \n e2_typing\n t_typing\n post_typing\n (Some? post_hint)\n in\n (| e, c, e_typing |)\n )\n in\n k\n#pop-options\n\nmodule LN = Pulse.Typing.LN\n#push-options \"--z3rlimit_factor 4 --fuel 1 --ifuel 1\"\n\n\nlet st_comp_typing_with_post_hint \n (#g:env) (#ctxt:_)\n (ctxt_typing:tot_typing g ctxt tm_vprop)\n (post_hint:post_hint_opt g { Some? post_hint })\n (c:comp_st { comp_pre c == ctxt /\\ comp_post_matches_hint c post_hint })\n: st_comp_typing g (st_comp_of_comp c)\n= let st = st_comp_of_comp c in\n let Some ph = post_hint in\n let post_typing_src\n : tot_typing (push_binding ph.g ph.x ppname_default ph.ret_ty)\n (open_term ph.post ph.x) tm_vprop\n = ph.post_typing_src\n in\n let x = fresh g in\n assume (fresh_wrt x g (freevars ph.post));\n assume (None? (lookup g ph.x));\n let post_typing_src\n : tot_typing (push_binding ph.g x ppname_default ph.ret_ty)\n (open_term ph.post x) tm_vprop\n = if x = ph.x\n then post_typing_src\n else \n let open Pulse.Typing.Metatheory.Base in\n let tt :\n tot_typing\n (push_binding ph.g x ppname_default ph.ret_ty)\n (subst_term (open_term ph.post ph.x) (renaming ph.x x))\n (subst_term tm_vprop (renaming ph.x x)) =\n tot_typing_renaming1 ph.g ph.x ph.ret_ty (open_term ph.post ph.x) tm_vprop post_typing_src x\n in\n assert (subst_term tm_vprop (renaming ph.x x) == tm_vprop);\n assume (subst_term (open_term ph.post ph.x) (renaming ph.x x) ==\n open_term ph.post x);\n tt\n in\n let post_typing_src\n : tot_typing (push_binding g x ppname_default ph.ret_ty)\n (open_term ph.post x) tm_vprop\n = //weakening: TODO\n RU.magic ()\n in\n let ty_typing : universe_of ph.g st.res st.u = ph.ty_typing in\n let ty_typing : universe_of g st.res st.u =\n Pulse.Typing.Metatheory.tot_typing_weakening_standard ph.g ty_typing g\n in\n assert (st.res == ph.ret_ty);\n assert (st.post == ph.post);\n STC g st x ty_typing ctxt_typing post_typing_src\n\nlet continuation_elaborator_with_bind_fn (#g:env) (#ctxt:term)\n (ctxt_typing:tot_typing g ctxt tm_vprop)\n (#e1:st_term)\n (#c1:comp { C_Tot? c1 })\n (b:binder{b.binder_ty == comp_res c1})\n (e1_typing:st_typing g e1 c1)\n (x:nvar { None? (lookup g (snd x)) })\n: T.Tac (continuation_elaborator\n g ctxt\n (push_binding g (snd x) ppname_default (comp_res c1)) ctxt)\n= let t1 = comp_res c1 in\n assert ((push_binding g (snd x) (fst x) t1) `env_extends` g);\n fun post_hint (| e2, c2, d2 |) ->\n if None? post_hint then T.fail \"bind_fn: expects the post_hint to be set\";\n let ppname, x = x in\n let e2_closed = close_st_term e2 x in\n assume (open_st_term (close_st_term e2 x) x == e2);\n let e = wr c2 (Tm_Bind {binder=b; head=e1; body=e2_closed}) in\n let (| u, c1_typing |) = Pulse.Typing.Metatheory.Base.st_typing_correctness_ctot e1_typing in\n let c2_typing : comp_typing g c2 (universe_of_comp c2) =\n match c2 with\n | C_ST st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n CT_ST _ _ stc\n \n | C_STAtomic i obs st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n let i_typing = CP.core_check_term g i T.E_Total tm_inames in\n CT_STAtomic _ _ obs _ i_typing stc\n\n | C_STGhost st -> \n let stc = st_comp_typing_with_post_hint ctxt_typing post_hint c2 in\n CT_STGhost _ _ stc\n in\n let d : st_typing g e c2 =\n T_BindFn g e1 e2_closed c1 c2 b x e1_typing u c1_typing d2 c2_typing\n in\n (| e, c2, d |)\n\nPartial implementation:\nlet rec check_equiv_emp (g: env) (vp: term) : option (vprop_equiv g vp tm_emp) =\n \n"
},
{
"role": "assistant",
"content": "match vp.t with\n| Tm_Emp -> Some (VE_Refl _ _)\n| Tm_Star vp1 vp2 ->\n (match check_equiv_emp g vp1, check_equiv_emp g vp2 with\n | Some d1, Some d2 ->\n let d3:vprop_equiv g (tm_star vp1 vp2) (tm_star tm_emp tm_emp) = VE_Ctxt _ _ _ _ _ d1 d2 in\n let d4:vprop_equiv g (tm_star tm_emp tm_emp) tm_emp = VE_Unit _ _ in\n Some (VE_Trans _ _ _ _ d3 d4)\n | _, _ -> None)\n| _ -> None"
}
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.