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text string | meta dict |
|---|---|
data Unit : Set where
unit : Unit
P : Unit → Set
P unit = Unit
postulate
Q : (u : Unit) → P u → Set
variable
u : Unit
p : P u
postulate
q : P u → Q u p
q' : (u : Unit) (p : P u) → P u → Q u p
q' u p = q {u} {p}
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data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
{-# BUILTIN NATURAL ℕ #-}
infixl 6 _+_
infix 6 _∸_
_+_ : ℕ → ℕ → ℕ
zero + n = n
suc m + n = suc (m + n)
_∸_ : ℕ → ℕ → ℕ
m ∸ zero = m
zero ∸ suc n = zero
suc m ∸ suc n = m ∸ n
should-be-rejected : ℕ
should-be-rejected = 1 + 0 ∸ 1
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-- {-# OPTIONS -v term:20 #-}
-- Andreas, 2011-04-19 (Agda list post by Leonard Rodriguez)
module TerminationSubExpression where
infixr 3 _⇨_
data Type : Set where
int : Type
_⇨_ : Type → Type → Type
test : Type → Type
test int = int
test (φ ⇨ int) = test φ
test (φ ⇨ (φ′ ⇨ φ″)) = test (φ′ ⇨ φ″)
-- this should ... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Sets.EquivalenceRelations
open import Setoids.Setoids
open import Functions.Definition
open import Groups.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Subgroups.Definition
open import Groups.Subgroups.Normal.Definition
module ... | {
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{-# BUILTIN NATURAL ℕ #-}
module the-naturals where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl)
open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; _∎)
infixl 6 _+_ _∸_
infixl 7 _*_
-- the naturals
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
-- addition
_+_ : ℕ → ℕ → ℕ
zero + n = n
(suc ... | {
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module Category.Functor.Arr where
open import Agda.Primitive using (_⊔_)
open import Category.Functor using (RawFunctor ; module RawFunctor )
open import Category.Applicative using (RawApplicative; module RawApplicative)
open import Function using (_∘_)
open import Category.Functor.Lawful
open import Relation... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Universe levels
------------------------------------------------------------------------
module Level where
-- Levels.
open import Agda.Primitive public
using (Level; _⊔_)
renaming (lzero to zero; lsuc ... | {
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{-# OPTIONS --without-K #-}
open import lib.Basics
open import lib.NConnected
open import lib.types.Nat
open import lib.types.TLevel
open import lib.types.Empty
open import lib.types.Group
open import lib.types.Pi
open import lib.types.Pointed
open import lib.types.Paths
open import lib.types.Sigma
open import lib.typ... | {
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open import Prelude
module Implicits.Syntax.Term where
open import Implicits.Syntax.Type
infixl 9 _[_] _·_
data Term (ν n : ℕ) : Set where
var : (x : Fin n) → Term ν n
Λ : Term (suc ν) n → Term ν n
λ' : Type ν → Term ν (suc n) → Term ν n
_[_] : Term ν n → Type ν → Term ν n
_·_ : Term ν n → Term ν n ... | {
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
module Light.Library where
module Literals where open import Light.Literals public
module Data where
module Empty where open import Light.Library.Data.Empty public
module Either where open import Light.Library.Data.Either pub... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.CommRing.Instances.Polynomials where
open import Cubical.Foundations.Prelude
open import Cubical.Algebra.CommRing
open import Cubical.Algebra.Polynomials
private
variable
ℓ : Level
Poly : (CommRing ℓ) → CommRing ℓ
Poly R = (PolyMod.Poly R) , str
where
o... | {
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module empty where
open import level
----------------------------------------------------------------------
-- datatypes
----------------------------------------------------------------------
data ⊥ {ℓ : Level} : Set ℓ where
----------------------------------------------------------------------
-- syntax
----------... | {
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-- Andreas, 2015-08-11, issue reported by G.Allais
-- The `a` record field of `Pack` is identified as a function
-- (coloured blue, put in a \AgdaFunction in the LaTeX backend)
-- when it should be coloured pink.
-- The problem does not show up when dropping the second record
-- type or removing the module declaration... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Data.Nat.GCD where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Induction.... | {
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{-# OPTIONS --prop --without-K --rewriting #-}
module Calf.Types.Bool where
open import Calf.Prelude
open import Calf.Metalanguage
open import Data.Bool public using (Bool; true; false; if_then_else_)
bool : tp pos
bool = U (meta Bool)
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{-# OPTIONS --safe #-}
module MissingDefinition where
T : Set -> Set
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{- Cubical Agda with K
This file demonstrates the incompatibility of the --cubical
and --with-K flags, relying on the well-known incosistency of K with
univalence.
The --safe flag can be used to prevent accidentally mixing such
incompatible flags.
-}
{-# OPTIONS --with-K #-}
module Cubical.WithK where
open import... | {
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module WrongNamedArgument2 where
postulate
f : {A : Set₁} → A
test : Set
test = f {B = Set}
-- Unsolved meta.
-- It is not an error since A could be instantiated to a function type
-- accepting hidden argument with name B.
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Argument information used in the reflection machinery
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Reflection.Argument.Information where
op... | {
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{-# OPTIONS --rewriting #-}
module FFI.Data.Vector where
open import Agda.Builtin.Equality using (_≡_)
open import Agda.Builtin.Equality.Rewrite using ()
open import Agda.Builtin.Int using (Int; pos; negsuc)
open import Agda.Builtin.Nat using (Nat)
open import Agda.Builtin.Bool using (Bool; false; true)
open import F... | {
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open import Function using (_∘_)
open import Category.Functor
open import Category.Monad
open import Data.Empty using (⊥; ⊥-elim)
open import Data.Fin as Fin using (Fin; zero; suc)
open import Data.Fin.Props as FinProps using ()
open import Data.Maybe as Maybe using (Maybe; maybe; just; nothing)
open import Data.Nat us... | {
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{-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.ZCohomology.RingStructure.GradedCommutativity where
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Function
open import Cubical.Foundations.Transport
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.I... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Divisibility
------------------------------------------------------------------------
module Data.Nat.Divisibility where
open import Data.Nat as Nat
open import Data.Nat.DivMod
import Data.Nat.Properties as Nat... | {
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------------------------------------------------------------------------
-- An alternative (non-standard) classical definition of weak
-- bisimilarity
------------------------------------------------------------------------
-- This definition is based on the function "wb" in Section 6.5.1 of
-- Pous and Sangiorgi's "E... | {
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------------------------------------------------------------------------------
-- Properties related with the group commutator
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-p... | {
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-- 2014-01-01 Andreas, test case constructed by Christian Sattler
{-# OPTIONS --allow-unsolved-metas #-}
-- unguarded recursive record
record R : Set where
constructor cons
field
r : R
postulate F : (R → Set) → Set
q : (∀ P → F P) → (∀ P → F P)
q h P = h (λ {(cons x) → {!!}})
-- ISSUE WAS: Bug in implement... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Examples of format strings and printf
------------------------------------------------------------------------
{-# OPTIONS --safe --without-K #-}
module README.Text.Printf where
open import Data.Nat.Base
open ... | {
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module Inference-of-implicit-function-space where
postulate
_⇔_ : Set → Set → Set
equivalence : {A B : Set} → (A → B) → (B → A) → A ⇔ B
A : Set
P : Set
P = {x : A} → A ⇔ A
works : P ⇔ P
works = equivalence (λ r {x} → r {x = x}) (λ r {x} → r {x = x})
works₂ : P ⇔ P
works₂ = equivalence {A = P... | {
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{-# OPTIONS --safe #-}
open import Definition.Typed.EqualityRelation
module Definition.LogicalRelation.Substitution.Introductions.Transp {{eqrel : EqRelSet}} where
open EqRelSet {{...}}
open import Definition.Untyped as U hiding (wk)
open import Definition.Untyped.Properties
open import Definition.Typed
open import ... | {
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--------------------------------------------------------------------------------
-- This is part of Agda Inference Systems
{-# OPTIONS --sized-types --guardedness #-}
open import Data.Product
open import Data.Vec
open import Codata.Colist as Colist
open import Agda.Builtin.Equality
open import Size
open import Codata... | {
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{-# OPTIONS --cubical-compatible #-}
open import Common.Prelude
open import Common.Equality
open import Common.Product
data _≅_ {A : Set} (a : A) : {B : Set} (b : B) → Set₁ where
refl : a ≅ a
data D : Bool → Set where
x : D true
y : D false
P : Set -> Set₁
P S = Σ S (\s → s ≅ x)
pbool : P (D true)
pbool = _... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category.Monoidal.Bundle
using (SymmetricMonoidalCategory)
module Categories.Category.Construction.SymmetricMonoidalFunctors
{o ℓ e o′ ℓ′ e′}
(C : SymmetricMonoidalCategory o ℓ e)
(D : SymmetricMonoidalCategory o′ ℓ′ e′) where
-- The symmetric monoida... | {
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{-
This file contains:
- An implementation of the free group of a type of generators as a HIT
-}
{-# OPTIONS --safe #-}
module Cubical.HITs.FreeGroup.Base where
open import Cubical.Foundations.Prelude
private
variable
ℓ : Level
data FreeGroup (A : Type ℓ) : Type ℓ where
η : A → FreeGroup A
_·_ : ... | {
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------------------------------------------------------------------------
-- A type-checker
------------------------------------------------------------------------
import Axiom.Extensionality.Propositional as E
import Level
open import Data.Universe
-- The code makes use of the assumption that propositional equality ... | {
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{-# OPTIONS --without-K --safe #-}
module Relation.Binary.Construct.Closure.SymmetricTransitive where
open import Level
open import Function
open import Relation.Binary
private
variable
a ℓ ℓ′ : Level
A B : Set a
module _ {A : Set a} (_≤_ : Rel A ℓ) where
private
variable
x y z : A
data ... | {
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module L.Data.Bool where
-- Reexport definitions
open import L.Data.Bool.Core public
open import L.Data.Bool.Properties public
-- Functions on Bools
infix 7 not_
infixr 6 _∧_
infixr 5 _∨_ _xor_
not_ : Bool → Bool
not x = if (λ _ → Bool) ff tt x
_∧_ : Bool → Bool → Bool
x ∧ y = if (λ _ → Bool) y ff x
_∨_ : Bool → ... | {
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------------------------------------------------------------------------------
-- FOTC version of a nested recursive function by the
-- Bove-Capretta method
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Instantiates the natural coefficients ring solver, using coefficient
-- equality induced by ℕ.
--
-- This is sufficient for proving equalities that are independent of the
-- characteristic. In particular, this i... | {
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-- Andreas, 2016-10-30, issue #2286 reported by carlostome
-- {-# OPTIONS -v interaction.give:40 #-}
-- {-# OPTIONS -v tc.term.expr:40 #-}
-- {-# OPTIONS -v tc.meta:40 #-}
-- {-# OPTIONS -v 10 #-}
data Nat : Set where
zero : Nat
succ : Nat → Nat
data _==_ {A : Set} (x : A) : A → Set where
refl : x == x
f : Na... | {
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-- Andreas, 2018-06-14, issue #2513, parsing attributes
-- Run-time only use.
postulate
@0 RT₁ : Set
@erased RT₂ : Set
-- Default: unrestricted use.
postulate
@ω CT₁ : Set
@plenty CT₂ : Set
-- Irrelevance.
postulate
. I₀ : Set
@irr I₁ : Set
@irrelevant I₂ : Set
-- Shape-i... | {
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{-# OPTIONS --without-K --exact-split #-}
module 20-pullbacks where
import 19-fundamental-cover
open 19-fundamental-cover public
-- Section 13.1 Cartesian squares
{- We introduce the basic concepts of this chapter: commuting squares, cospans,
cones, and pullback squares. Pullback squares are also called cartesia... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Base.Types
import LibraBFT.Impl.Consensus.Consensus... | {
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{-# OPTIONS --type-in-type #-}
open import Data.Unit
open import Data.Product hiding ( curry ; uncurry )
open import Data.List hiding ( concat )
open import Data.String
open import Relation.Binary.PropositionalEquality
open import Function
module Spire.Examples.CompLev where
-------------------------------------------... | {
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module Issue87 where
data I : Set where
data D : I -> Set where
d : forall {i} (x : D i) -> D i
bar : forall {i} -> D i -> D i -> D i
bar (d x) (d y) with y
bar (d x) (d {i} y) | z = d {i} y
-- ERROR WAS:
-- Panic: unbound variable i
-- when checking that the expression i has type I
-- Andreas, 2016-06-02
--... | {
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open import Agda.Builtin.Equality
_∘_ : ∀ {a b c}
{A : Set a} {B : A → Set b} {C : {x : A} → B x → Set c} →
(f : ∀ {x} (y : B x) → C y) →
(g : (x : A) → B x) →
((x : A) → C (g x))
f ∘ g = λ x → f (g x)
postulate
A : Set
B : A → Set
C : {x : A} → B x → Set
f : ∀ {x : A} (y : B x... | {
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open import Data.Natural using ( Natural ; # ; _+_ )
module System.IO.Examples.Four where
four : Natural
four = # 2 + # 2 | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Sets.EquivalenceRelations
open import Setoids.Setoids
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Groups.Definition
module Groups.Homomorphisms.Definition where
record GroupHom {m n o p : _} {A : Set m} {S : Setoid {m} {o} A} {... | {
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-- Andreas, 2017-02-14 issue #2455 reported by mechvel
-- Test case by Andrea
-- Seem that the fix for issue #44 was not complete.
-- When inserting module parameters for a definition,
-- we need to respect polarities!
-- {-# OPTIONS -v tc.decl:10 -v tc.polarity:70 -v tc.sig.inst:30 #-}
module Issue2455 where
data... | {
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module ShouldBeApplicationOf where
data One : Set where one : One
data Two : Set where two : Two
f : One -> Two
f two = two
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-- Andreas, bug found 2011-12-31
{-# OPTIONS --irrelevant-projections #-}
module Issue543 where
open import Common.Equality
data ⊥ : Set where
record ⊤ : Set where
constructor tt
data Bool : Set where
true false : Bool
T : Bool → Set
T true = ⊤
T false = ⊥
record Squash {ℓ}(A : Set ℓ) : Set ℓ where
cons... | {
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{-# OPTIONS --without-K --exact-split --safe #-}
module HoTT.Ident where
data Id (X : Set) : X → X → Set where
refl : (x : X) → Id X x x
_≡_ : {X : Set} → X → X → Set
x ≡ y = Id _ x y
𝕁 : {X : Set}
→ (A : (x y : X) → x ≡ y → Set)
→ ((x : X) → A x x (refl x))
→ (x y : X) → (p : x ≡ y) → A x y p
𝕁 A f x x (... | {
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------------------------------------------------------------------------
-- Compiler correctness
------------------------------------------------------------------------
open import Prelude
import Lambda.Syntax
module Lambda.Compiler-correctness
{Name : Type}
(open Lambda.Syntax Name)
(def : Name → Tm 1)
whe... | {
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{-# OPTIONS --cubical-compatible #-}
data Bool : Set where
true : Bool
false : Bool
data ℕ : Set where
zero : ℕ
suc : (n : ℕ) → ℕ
data Fin : ℕ → Set where
zero : {n : ℕ} → Fin (suc n)
suc : {n : ℕ} (i : Fin n) → Fin (suc n)
infixr 5 _∷_
data Vec {a} (A : Set a) : ℕ → Set a where
[] : Vec A zero
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module STLC1.Kovacs.Soundness where
open import STLC1.Kovacs.Convertibility public
open import STLC1.Kovacs.PresheafRefinement public
--------------------------------------------------------------------------------
infix 3 _≈_
_≈_ : ∀ {A Γ} → Γ ⊩ A → Γ ⊩ A → Set
_≈_ {⎵} {Γ} M₁ M₂ = M₁ ≡ M₂
_≈_ {A ⇒ B} {Γ} f... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Decision procedures for finite sets and subsets of finite sets
--
-- This module is DEPRECATED. Please use the Data.Fin.Properties
-- and Data.Fin.Subset.Properties directly.
-------------------------------------... | {
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module ial where
open import ial-datatypes public
open import logic public
open import thms public
open import termination public
open import error public
open import io public
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------------------------------------------------------------------------
-- Values
------------------------------------------------------------------------
open import Atom
module Values (atoms : χ-atoms) where
open import Equality.Propositional
open import Prelude hiding (const)
open import Chi atoms
open import D... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.Semigroup.Properties where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Function using (_∘_; id)
open import Cubical.Foundations.Equiv
ope... | {
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{-# OPTIONS --prop #-}
data _≡_ {A : Set} (a : A) : A → Set where
refl : a ≡ a
postulate
funextP : {A : Prop} {B : A → Set} {f g : (a : A) → B a} (h : (x : A) → f x ≡ g x) → f ≡ g
test : {A : Prop} {B : A → Set} {f g : (a : A) → B a} (h : (x : A) → f x ≡ g x) → f ≡ g
test h = funextP h
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------------------------------------------------------------------------------
-- Parametrized preorder reasoning
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #... | {
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{-# OPTIONS --without-K #-}
module SubstLemmas where
open import Level using (Level)
open import Relation.Binary.PropositionalEquality
using (_≡_; refl; sym; trans; subst; cong₂)
open import Data.Nat using (ℕ; _+_; _*_)
------------------------------------------------------------------------------
-- Lemmas about ... | {
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-- Andreas, 2015-12-29
-- with-clause stripping for record patterns
-- {-# OPTIONS -v tc.with.strip:60 #-}
record R : Set1 where
field
f : Set
test : R → Set1
test record{ f = a } with a
... | x = R
test1 : R → Set1
test1 record{ f = a } with a
test1 record{ f = a } | _ = R
test2 : R → Set1
test2 record{ f =... | {
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{-# OPTIONS --without-K --safe #-}
module TypeTheory.HoTT.Data.Sum.Properties where
-- agda-stdlib
open import Level
open import Data.Empty
open import Data.Product
open import Data.Sum
open import Function.Base
open import Relation.Binary.PropositionalEquality
open import Relation.Nullary
-- agda-misc
open import T... | {
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module Proofs where
open import Agda.Builtin.Equality
open import Relation.Binary.PropositionalEquality.Core
open import Data.Nat
open ≡-Reasoning
open import Classes
data Vec : ℕ → Set → Set where
Nil : ∀ {a} → Vec 0 a
Cons : ∀ {n A} → (a : A) → Vec n A → Vec (suc n) A
cons-cong : ∀ {n A} {a c : A} {b d : V... | {
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{-# OPTIONS --without-K #-}
module Model.Term where
open import Cats.Category
open import Model.Size as MS using (_<_ ; ⟦_⟧Δ ; ⟦_⟧n ; ⟦_⟧σ)
open import Model.Type as MT
open import Util.HoTT.Equiv
open import Util.Prelude hiding (id ; _∘_ ; _×_)
open import Source.Size as SS using (v0 ; v1 ; ⋆)
open import Source.Siz... | {
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------------------------------------------------------------------------------
-- Co-inductive natural numbers
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
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------------------------------------------------------------------------
-- The Agda standard library
--
-- An equality postulate which evaluates
------------------------------------------------------------------------
module Relation.Binary.PropositionalEquality.TrustMe where
open import Relation.Binary.Propositiona... | {
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{-# OPTIONS --safe #-}
module Cubical.Categories.Instances.Semilattice where
open import Cubical.Foundations.Prelude
open import Cubical.Algebra.Semilattice
open import Cubical.Categories.Category
open import Cubical.Categories.Instances.Poset
open Category
module _ {ℓ} (L : Semilattice ℓ) where
-- more convenie... | {
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{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Functions.Definition
open import Setoids.Setoids
open import Setoids.Subset
open import Graphs.Definition
open import Sets.FinSet.Definition
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-- Care needs to be taken to distinguish between instance solutions with and
-- without leftover constraints.
module _ where
_∘_ : ∀ {A B C : Set} → (B → C) → (A → B) → A → C
(f ∘ g) x = f (g x)
postulate
Functor : (Set → Set) → Set₁
fmap : ∀ {F} {{_ : Functor F}} {A B} → (A → B) → F A → F B
List : Set → Set
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-- There was a problem with reordering telescopes.
module Issue234 where
postulate
A : Set
P : A → Set
data List : Set where
_∷ : A → List
data _≅_ {x : A}(p : P x) : ∀ {y} → P y → Set where
refl : p ≅ p
data _≡_ (x : A) : A → Set where
refl : x ≡ x
data Any (x : A) : Set where
here : P x → Any x
it :... | {
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{-# OPTIONS --without-K #-}
open import HoTT
module lib.Quaternions where
data Sign : Type₀ where
plus : Sign
minus : Sign
opposite : Sign → Sign
opposite plus = minus
opposite minus = plus
_·_ : Sign → Sign → Sign
plus · x = x
minus · x = opposite x
·unitr : (x : Sign) → x · plus == x
·unitr plus = idp
·unit... | {
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open import SOAS.Metatheory.Syntax
-- Initial (⅀, 𝔛)-meta-algebra 𝕋 𝔛 is the free ⅀-monoid on 𝔛
module SOAS.Metatheory.FreeMonoid {T : Set} (Syn : Syntax {T}) where
open Syntax Syn
open import SOAS.Common
open import SOAS.Families.Core {T}
open import SOAS.Context {T}
open import SOAS.Variable {T}
open import S... | {
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{- Name: Bowornmet (Ben) Hudson
--Type safety and meaning functions for L{⇒,+,×,unit}--
-}
open import Preliminaries
open import Preorder
open import Preorder-repackage
module L where
-- => and + and × and unit
data Typ : Set where
_⇒_ : Typ → Typ → Typ
_×'_ : Typ → Typ → Typ
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{-# OPTIONS --cubical --safe #-}
module Data.Nat where
open import Data.Nat.Base public
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open import Common.Prelude
open import Common.Reflection
open import Common.Equality
open import Agda.Builtin.Sigma
magic₁ : ⊥ → Nat
magic₁ = λ ()
magic₂ : ⊥ → Nat
magic₂ = λ { () }
magic₃ : ⊥ → Nat
magic₃ ()
data Wrap (A : Set) : Set where
wrap : A → Wrap A
magic₄ : Wrap ⊥ → Nat
magic₄ (wrap ())
data OK : Set... | {
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import cedille-options
open import general-util
module untyped-spans (options : cedille-options.options) {F : Set → Set} {{monadF : monad F}} where
open import lib
open import ctxt
open import cedille-types
open import spans options {F}
open import syntax-util
open import to-string options
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data unit : Set where tt : unit
record Y (A : Set) : Set where field y : A
record Z (A : Set) : Set where field z : A
instance
-- Y[unit] : Y unit
-- Y.y Y[unit] = tt
Z[unit] : Z unit
Z.z Z[unit] = tt
foo : ∀ (A : Set) {{YA : Y A}} {{ZA : Z A}} → unit
foo A = tt
foo[unit] : unit
foo[unit] = foo unit -- {{Z... | {
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module L.Base.Empty where
-- Reexport definitions
open import L.Base.Empty.Core public
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Base
open import lib.Equivalence
open import lib.PathGroupoid
open import lib.NType
open import lib.Univalence
open import lib.path-seq.Concat
open import lib.path-seq.Split
module lib.path-seq.Reasoning where
infix 30 _=↯=_
_=↯=_ : ∀ {i} {A : Type i} {a a' : A... | {
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{-# OPTIONS --prop --rewriting #-}
open import Examples.Sorting.Parallel.Comparable
module Examples.Sorting.Parallel.MergeSortPar (M : Comparable) where
open Comparable M
open import Examples.Sorting.Parallel.Core M
open import Calf costMonoid
open import Calf.ParMetalanguage parCostMonoid
open import Calf.Types.Na... | {
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{-# OPTIONS --without-K #-}
module Model.Exponential where
open import Cats.Category
open import Model.RGraph as RG using (RGraph)
open import Model.Type.Core
open import Model.Product
open import Util.HoTT.HLevel
open import Util.Prelude hiding (_×_ ; id ; _∘_)
open RGraph
open RG._⇒_
private
variable Δ : RGrap... | {
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------------------------------------------------------------------------
-- Simple expressions
------------------------------------------------------------------------
-- Several examples based on Matsuda and Wang's "FliPpr: A Prettier
-- Invertible Printing System".
{-# OPTIONS --guardedness #-}
module Examples.Exp... | {
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open import Data.Empty using ( ⊥ ; ⊥-elim )
open import Data.Nat using ( ℕ ; zero ; suc )
open import Data.Product using ( ∃ ; _×_ ; _,_ )
open import FRP.LTL.RSet.Core using ( RSet ; _[_,_⟩ ; _[_,_] ; ⟦_⟧ )
open import FRP.LTL.RSet.Causal using ( _⊵_ ; identity )
open import FRP.LTL.RSet.Stateless using ( _⇒_ )
open i... | {
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-- Correctness conditions for the boolean AND gate
f : Tensor Real [2] -> Tensor Real [1]
f = evaluate _ _
truthy : Real -> Set
truthy x = x >= 0.5
falsey : Real -> Set
falsey x = x <= 0.5
validInput : Tensor Real [2] -> Set
validInput x = All (λ xi -> 0 <= xi ∧ xi <= 1) x
correctOutput : Tensor Real [2] -> Set
co... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module Sequent where
open import OscarPrelude
open import Formula
infix 15 _╱_
record Sequent : Set
where
constructor _╱_
field
statement : Formula
suppositions : List Formula
open Sequent public
instance EqSequent : Eq Sequent
Eq._==_ EqSequent ( φᵗ₁ ╱ φˢs₁ ) ( φ... | {
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{-# OPTIONS --without-K --safe #-}
module Dodo.Binary.Subtraction where
-- Stdlib imports
open import Level using (Level; _⊔_)
open import Relation.Binary using (REL)
-- Local imports
open import Dodo.Binary.Empty using (¬₂_)
open import Dodo.Binary.Intersection using (_∩₂_)
-- # Definitions
infixl 30 _\₂_
_\₂_ :... | {
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{-# OPTIONS --rewriting #-}
module Properties.StrictMode where
import Agda.Builtin.Equality.Rewrite
open import Agda.Builtin.Equality using (_≡_; refl)
open import FFI.Data.Maybe using (Maybe; just; nothing)
open import Luau.Heap using (Heap; Object; function_is_end; defn; alloc; ok; next; lookup-not-allocated) renam... | {
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------------------------------------------------------------------------------
-- Properties for the relation LTL
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #... | {
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module Optics.Lens where
open import Agda.Primitive using (Level; _⊔_; lsuc)
open import Data.Product using (_×_; _,_; ∃-syntax)
open import Function.Inverse using (_↔_; inverse)
open import Relation.Binary.PropositionalEquality using (_≡_; refl; module ≡-Reasoning; cong)
open import Category.Functor.Arr
open import C... | {
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{-# OPTIONS --without-K --rewriting #-}
{-
Imports everything that is not imported by something else.
This is not supposed to be used anywhere, this is just a simple way to
do `make all'
This file is intentionally named index.agda so that
Agda will generate index.html.
-}
module index where
{- some group theory res... | {
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module cedille where
open import lib
open import cedille-types public
----------------------------------------------------------------------------------
-- Run-rewriting rules
----------------------------------------------------------------------------------
data gratr2-nt : Set where
_ws-plus-77 : gratr2-nt
_ws... | {
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{-# OPTIONS --rewriting --confluence-check #-}
data _==_ {i} {A : Set i} : (x y : A) → Set i where
refl : {a : A} → a == a
{-# BUILTIN REWRITE _==_ #-}
data ⊥ : Set where
record ⊤ : Set where
constructor tt
module Test (p : ⊥ == ⊤) where
abstract
A : Set
A = ⊥
q : A == ⊤
q = p
{-# REWRI... | {
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module interfaceExtensionAndDelegation where
open import Data.Product
open import Data.Nat.Base
open import Data.Nat.Show
open import Data.String.Base using (String; _++_)
open import Size
open import NativeIO
open import interactiveProgramsAgda using (ConsoleInterface; _>>=_; do;
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{-# OPTIONS --cubical #-}
module Integer.Univalence where
open import Cubical.Foundations.NTypes
open import Data.Empty
open import Data.Product as Σ
open import Data.Product.Relation.Pointwise.NonDependent
open import Data.Unit
open import Equality
open import Function
open import Integer.Difference as D
open import... | {
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postulate anything : ∀{a}{A : Set a} → A
data N : Set where
suc : (n : N) → N
data Val : (n : N) → Set where
valSuc : (n : N) → Val (suc n)
-- valSuc : (n : N) → Val n -- internal error disappears
Pred : Set₁
Pred = (n : N) → Set
postulate
Any : (P : Pred) → Set
F : (P : Pred) → Pred
anyF : {P : Pre... | {
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{-# OPTIONS --without-K --safe #-}
-- The 'Identity' instance, with all of Setoids as models
module Categories.Theory.Lawvere.Instance.Identity where
open import Data.Fin using (splitAt)
open import Data.Sum using ([_,_]′)
open import Data.Unit.Polymorphic using (⊤; tt)
open import Level
open import Relation.Binary.... | {
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-- Andreas, 2016-11-02, issue #2285
-- double check for record types
record Big : _ where
field any : ∀{a} → Set a
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{-# OPTIONS --allow-unsolved-metas
--no-positivity-check
--no-termination-check
--type-in-type
--sized-types
--injective-type-constructors
--guardedness-preserving-type-constructors
--experimental-irrelevance #-}
module SafeFlagPragmas ... | {
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-- Andreas, 2020-09-26, issue #4944.
-- Size solver got stuck on projected variables which are left over
-- in some size constraints by the generalization feature.
-- {-# OPTIONS --sized-types #-}
-- {-# OPTIONS --show-implicit #-}
-- {-# OPTIONS -v tc.conv.size:60 -v tc.size:30 -v tc.meta.assign:10 #-}
open import A... | {
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