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{-# OPTIONS --without-K #-}
module ConcretePermutation where
import Level using (zero)
open import Data.Nat using (ℕ; _+_; _*_)
open import Data.Fin using (Fin)
open import Data.Product using (proj₁; proj₂)
open import Data.Vec using (tabulate)
open import Algebra using (CommutativeSemiring)
open import Algebra.Str... | {
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
open import Light.Library.Data.Natural as ℕ using (ℕ)
open import Light.Package using (Package)
module Light.Literals.Natural ⦃ package : Package record { ℕ } ⦄ where
open import Light.Literals.Definition.Natural using (FromNatural)
open... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Decorated star-lists
------------------------------------------------------------------------
{-# OPTIONS --with-K --safe #-}
module Data.Star.Decoration where
open import Data.Unit
open import Function
open i... | {
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module Category.Fibration where
open import Data.Product
open import Category.Category
open import Category.Subcategory
open import Category.Funct
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-- 2010-10-04
-- termination checker no longer counts stripping off a record constructor
-- as decrease
module Issue334 where
data Unit : Set where
unit : Unit
record E : Set where
inductive
constructor mkE
field
fromE : E
spam : Unit
f : E -> Set
f (mkE e unit) = f e
-- the record pattern translati... | {
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open import Relation.Binary.PropositionalEquality
open import Data.Unit using (⊤ ; tt)
open import Data.Product renaming (_×_ to _∧_ ; proj₁ to fst ; proj₂ to snd)
open import Data.Sum renaming (_⊎_ to _∨_ ; inj₁ to left ; inj₂ to right)
open import Data.Nat using (ℕ ; zero ; suc)
open import Data.Product renaming (pro... | {
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record R : Set₁ where
X = Y -- should get error here
field A : Set
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Simple combinators working solely on and with functions
------------------------------------------------------------------------
-- The contents of this file can be accessed from `Function`.
{-# OPTIONS --witho... | {
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open import Relation.Binary.Core
module PLRTree.Insert {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import Data.Sum
open import PLRTree {A}
insert : A → PLRTree → PLRTree
insert x leaf = node perfect x leaf leaf
insert x (node perfect y l r)
with tot≤ x... | {
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open import Common.Prelude
open import Common.Equality
infixr 5 _∷_
data Vec (A : Set) : Nat → Set where
[] : Vec A zero
_∷_ : ∀ {n} → A → Vec A n → Vec A (suc n)
record Eq (A : Set) : Set where
field
_==_ : (x y : A) → Maybe (x ≡ y)
open Eq {{...}}
data Σ (A : Set) (B : A → Set) : Set where
_,_ : (x ... | {
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-- Quotient category
{-# OPTIONS --safe #-}
module Cubical.Categories.Constructions.Quotient where
open import Cubical.Categories.Category.Base
open import Cubical.Categories.Functor.Base
open import Cubical.Categories.Limits.Terminal
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Prelude
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Foundations.Pointed.Properties where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Pointed.Base
open import Cubical.Foundations.Function
open import Cubical.Foundations.GroupoidLaws
open import Cubical.Foundations.Isomorphism
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{-# OPTIONS --safe #-}
module Definition.Typed.EqRelInstance where
open import Definition.Untyped
open import Definition.Typed
open import Definition.Typed.Properties
open import Definition.Typed.Weakening
open import Definition.Typed.Properties
open import Definition.Typed.Reduction
open import Definition.Typed.Equa... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 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.Abstract.Types
open import LibraBFT.Abstract.Types... | {
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module Data.List.First.Properties {ℓ}{A : Set ℓ} where
open import Data.Product
open import Data.List
open import Data.List.Any
open import Relation.Binary.PropositionalEquality
open import Function
open import Data.Empty
open import Data.List.First
open import Data.List.Membership.Propositional
first⟶∈ : ∀ {B : A → ... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Categories.Category.Construction.Spans {o ℓ e} (𝒞 : Category o ℓ e) where
open import Level
open import Categories.Category.Diagram.Span 𝒞
open import Categories.Morphism.Reasoning 𝒞
open Category 𝒞
open HomReasoning
open Equiv
open Spa... | {
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{- Definition of join for ◇ and associated lemmas. -}
module TemporalOps.Diamond.JoinLemmas where
open import CategoryTheory.Categories
open import CategoryTheory.Instances.Reactive
open import CategoryTheory.Functor
open import CategoryTheory.NatTrans
open import CategoryTheory.Monad
open import TemporalOps.Common
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
module Light.Subtyping where
open import Light.Level using (_⊔_ ; ++_)
open import Light.Variable.Levels
open import Light.Variable.Sets
record DirectSubtyping (𝕒 : Set aℓ) (𝕓 : Set bℓ) : Set (aℓ ⊔ bℓ) where
constructor #_
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module Issue561 where
open import Common.Char
open import Common.Prelude
primitive
primIsDigit : Char → Bool
postulate
IO : Set → Set
return : ∀ {A} → A → IO A
{-# BUILTIN IO IO #-}
main : IO Bool
main = return true | {
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{-# OPTIONS --without-K #-}
module library.types.Types where
open import library.Basics
open import library.types.Empty public
open import library.types.Unit public
open import library.types.Bool public
open import library.types.Nat public
open import library.types.Int public
open import library.types.TLevel public
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record Unit : Set where
constructor tt
postulate
C : Set
c : C
g : C
f : Unit → C
f tt = c
record R : Set where
constructor r
g = c
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-- A variant of code reported by Andreas Abel (who suggested that this
-- way to trigger the bug might have been due to NAD).
{-# OPTIONS --guardedness --sized-types #-}
open import Agda.Builtin.Sigma
open import Agda.Builtin.Size
data ⊥ : Set where
record Delay (A : Set) : Set where
coinductive
constructor ♯
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test = forall _let_ → Set
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module SystemF.BigStep.Types where
open import Prelude
-- types are indexed by the number of open tvars
infixl 10 _⇒_
data Type (n : ℕ) : Set where
Unit : Type n
ν : (i : Fin n) → Type n
_⇒_ : Type n → Type n → Type n
∀' : Type (suc n) → Type n
open import Data.Fin.Substitution
open import Data.Vec
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record R (A : Set) : Set where
constructor c₂
field
f : A → A
open module R′ (A : Set) (r : R A) = R {A = A} r
renaming (f to f′)
_ : (@0 A : Set) → R A → A → A
_ = λ A → f′ {A = A}
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.Magma.Properties where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Algebra
open import Cubical.Algebra.Magma.Morphism
open import Cubical.Algebra.Magma... | {
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module Numeral.Natural.Oper.Summation.Range where
import Lvl
open import Data.List
open import Data.List.Functions
open import Numeral.Natural
open import Type
_‥_ : ℕ → ℕ → List(ℕ)
_ ‥ 𝟎 = ∅
𝟎 ‥ 𝐒 b = 𝟎 ⊰ map 𝐒(𝟎 ‥ b)
𝐒 a ‥ 𝐒 b = map 𝐒(a ‥ b)
‥_ : ℕ → List(ℕ)
‥ b = 𝟎 ‥ b
_‥₌_ : ℕ → ℕ → List(ℕ)... | {
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{-# OPTIONS --without-K --safe #-}
module Dodo.Unary.Equality where
-- Stdlib imports
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl)
open import Level using (Level; _⊔_)
open import Function using (_∘_)
open import Relation.Unary using (Pred)
-- # Definitions
infix 4 _⊆₁'_ _⊆₁_ _⇔₁_
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{-# OPTIONS --cubical --safe --postfix-projections #-}
module Data.Bool.Properties where
open import Prelude
open import Data.Bool
open import Data.Unit.Properties
T? : ∀ x → Dec (T x)
T? x .does = x
T? false .why = ofⁿ id
T? true .why = ofʸ tt
isPropT : ∀ x → isProp (T x)
isPropT false = isProp⊥
isPropT true = i... | {
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{-# OPTIONS --without-K #-}
module P where
open import Data.Empty
open import Data.Unit
open import Data.Sum
open import Data.Product
open import Relation.Binary.PropositionalEquality
------------------------------------------------------------------------------
-- For now, a groupoid is just a set
G... | {
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-- Basic intuitionistic logic of proofs, without ∨, ⊥, or +.
-- Gentzen-style formalisation of syntax with context pairs.
-- Normal forms and neutrals.
module BasicILP.Syntax.DyadicGentzenNormalForm where
open import BasicILP.Syntax.DyadicGentzen public
-- Derivations.
mutual
-- Normal forms, or introductions.
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module EquationalTheory where
open import Library
open import Syntax
open import RenamingAndSubstitution
-- Single collapsing substitution.
sub1 : ∀{Γ σ τ} → Tm Γ σ → Tm (Γ , σ) τ → Tm Γ τ
sub1 {Γ}{σ}{τ} u t = sub (subId , u) t
-- Typed β-η-equality.
data _≡βη_ {Γ : Cxt} : ∀{σ} → Tm Γ σ → Tm Γ σ → Set where
-- ... | {
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open import Relation.Binary.Core
module InsertSort.Impl2.Correctness.Order {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import Data.List
open import Function using (_∘_)
open import InsertSort.Impl2 _≤_ tot≤
open import List.Sorted _≤_
open import OList _≤_
open imp... | {
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{-# OPTIONS --prop #-}
open import Agda.Builtin.Nat
data T : Nat → Prop where
To : T zero
Tn : ∀ n → T n
ummm : ∀ n → T n → {! !}
ummm n t = {! t !}
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-- A variant of code reported by Andreas Abel.
{-# OPTIONS --guardedness --sized-types #-}
open import Common.Coinduction renaming (∞ to Delay)
open import Common.Size
open import Common.Product
data ⊥ : Set where
record Stream (A : Set) : Set where
inductive
constructor delay
field
force : Delay (A × Str... | {
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open import Oscar.Prelude
open import Oscar.Class
open import Oscar.Class.IsPrecategory
open import Oscar.Class.IsCategory
open import Oscar.Class.HasEquivalence
open import Oscar.Class.Reflexivity
open import Oscar.Class.Symmetry
open import Oscar.Class.Transextensionality
open import Oscar.Class.Transassociativity
o... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Floats
------------------------------------------------------------------------
module Data.Float where
open import Data.Bool hiding (_≟_)
open import Relation.Nullary.Decidable
open import Relation.Nullary
ope... | {
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module Issue2447.Type-error where
import Issue2447.M
Rejected : Set
Rejected = Set
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Homomorphisms.Definition
open import Groups.Definition
open import Setoids.Setoids
open import Rings.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.Homomorphisms.Definition where
record RingHom {m n o p : _} {A... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Relation.Binary.Base where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Equiv
open import Cubical.Foundat... | {
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module Thesis.SIRelBigStep.Types where
open import Data.Empty
open import Data.Product
open import Relation.Nullary
open import Relation.Binary.PropositionalEquality
open import Relation.Binary hiding (_⇒_)
data Type : Set where
_⇒_ : (σ τ : Type) → Type
pair : (σ τ : Type) → Type
nat : Type
infixr 20 _⇒_
open... | {
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module MLib.Prelude where
open import MLib.Prelude.FromStdlib public
module Fin where
open import MLib.Prelude.Fin public
open Fin using (Fin; zero; suc) hiding (module Fin) public
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open import Agda.Builtin.Nat
data Vec (A : Set) : Nat → Set where
[] : Vec A 0
_∷_ : ∀ {n} → A → Vec A n → Vec A (suc n)
infixr 5 _∷_ _++_
_++_ : ∀ {A m n} → Vec A m → Vec A n → Vec A (m + n)
[] ++ ys = ys
(x ∷ xs) ++ ys = x ∷ xs ++ ys
T : ∀ {A n} → Vec A n → Set
T [] = Nat
T (x ∷ xs) = Vec Nat 0
foo : ... | {
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module HelloWorld where
open import Common.IO
open import Common.Unit
main : IO Unit
main = putStr "Hello World"
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open import Agda.Builtin.Equality
data D (A : Set) : Set where
{-# INJECTIVE D #-}
test : {A₁ A₂ : Set} → D A₁ ≡ D A₂ → A₁ ≡ A₂
test refl = refl
postulate f : Set → Set
{-# INJECTIVE f #-}
test₂ : {A₁ A₂ : Set} → f A₁ ≡ f A₂ → A₁ ≡ A₂
test₂ refl = refl
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module Avionics.Bool where
open import Data.Bool using (Bool; true; false; _∧_; T)
open import Data.Unit using (⊤; tt)
open import Data.Product using (_×_; _,_)
open import Relation.Binary.PropositionalEquality using (_≡_; refl; inspect; [_])
--open import Avionics.Product using (_×_; ⟨_,_⟩)
--TODO: Replace with T⇔≡... | {
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{-# OPTIONS --universe-polymorphism #-}
open import Level
open import Categories.Category
module Categories.Power.Functorial {o ℓ e : Level} (C : Category o ℓ e) where
open import Relation.Binary.PropositionalEquality using (≡-irrelevance)
open import Data.Unit using (⊤; tt)
open import Function using () renaming (_∘_... | {
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{-# OPTIONS --without-K --exact-split --allow-unsolved-metas #-}
module 16-sets where
import 15-number-theory
open 15-number-theory public
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module examplesPaperJFP.ConsoleInterface where
open import examplesPaperJFP.NativeIOSafe
open import examplesPaperJFP.BasicIO hiding (main)
module _ where
data ConsoleCommand : Set where
getLine : ConsoleCommand
putStrLn : String → ConsoleCommand
ConsoleResponse : ConsoleCommand → Set
ConsoleRespo... | {
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------------------------------------------------------------------------
-- A variant of the set quotients from Quotient
------------------------------------------------------------------------
{-# OPTIONS --erased-cubical --safe #-}
-- Partly following the HoTT book.
--
-- Unlike the HoTT book, but following the cub... | {
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module List.Sorted {A : Set}(_≤_ : A → A → Set) where
open import Data.List
data Sorted : List A → Set where
nils : Sorted []
singls : (x : A)
→ Sorted [ x ]
conss : {x y : A}{xs : List A}
→ x ≤ y
→ Sorted (y ∷ xs)
→ Sorted (x ∷ y... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.TypeQuotients where
open import Cubical.HITs.TypeQuotients.Base public
open import Cubical.HITs.TypeQuotients.Properties public
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{-
Descriptor language for easily defining structures
-}
{-# OPTIONS --cubical --no-import-sorts --no-exact-split --safe #-}
module Cubical.Structures.Macro where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.E... | {
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------------------------------------------------------------------------
-- Lists where all elements satisfy a given property
------------------------------------------------------------------------
module Data.List.All where
open import Data.Function
open import Data.List as List hiding (map; all)
open import Data.L... | {
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open import Agda.Builtin.List
open import Agda.Builtin.Reflection renaming (bindTC to _>>=_)
open import Agda.Builtin.Bool
open import Agda.Builtin.Equality
open import Agda.Builtin.Nat
open import Agda.Builtin.Sigma
data Unit : Set where
unit : Unit
data Empty : Set where
qq : ∀ {a} {A : Set a} → A → Term → TC _... | {
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module API.Theorems where
open import Algebra
open import Algebra.Theorems
open import API
open import Prelude
open import Reasoning
-- vertices [x] == vertex x
vertices-vertex : ∀ {A} {x : A} -> vertices [ x ] ≡ vertex x
vertices-vertex = +identity >> reflexivity
-- edge x y == clique [x, y]
edge-cliqu... | {
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module LC.Reduction where
open import LC.Base
open import LC.Subst
open import Data.Nat
open import Data.Nat.Properties
open import Relation.Nullary
-- β-reduction
infix 3 _β→_
data _β→_ : Term → Term → Set where
β-ƛ-∙ : ∀ {M N} → ((ƛ M) ∙ N) β→ (M [ N ])
β-ƛ : ∀ {M N} → M β→ N → ƛ M β→ ƛ N
β-∙-l : ∀ ... | {
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-- Copyright: (c) 2016 Ertugrul Söylemez
-- License: BSD3
-- Maintainer: Ertugrul Söylemez <esz@posteo.de>
--
-- This module contains definitions that are fundamental and/or used
-- everywhere.
module Core where
open import Agda.Builtin.Equality public
renaming (refl to ≡-refl)
using (_≡_)
open import Agda.Bu... | {
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module Oscar.Data.Term.AlphaConversion.internal {𝔣} (FunctionName : Set 𝔣) where
open import Oscar.Data.Term FunctionName
open import Oscar.Data.Equality
open import Oscar.Data.Fin
open import Oscar.Data.Vec
open import Oscar.Function
open import Oscar.Relation
infixr 19 _◂_ _◂s_
mutual
_◂_ : ∀ {m n} → m ⟨ Fi... | {
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{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Numbers.Naturals.Definition
module Numbers.Naturals.Addition where
infix 15 _+N_
_+N_ : ℕ → ℕ → ℕ
zero +N y = y
succ x +N y = succ (x +N y)
{-# BUILTIN NATPLUS _+N_ #-}
addZeroRight : (x : ℕ) → (x +N zero) ≡ x
addZeroRight ze... | {
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module ProcessSyntax where
open import Data.List
open import Typing
open import Syntax
-- processes
data Proc (Φ : TCtx) : Set where
exp : (e : Expr Φ TUnit)
→ Proc Φ
par : ∀ {Φ₁ Φ₂}
→ (sp : Split Φ Φ₁ Φ₂)
→ (P₁ : Proc Φ₁)
→ (P₂ : Proc Φ₂)
→ Proc Φ
res : (s : SType)
→ (P : Proc (TChan... | {
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------------------------------------------------------------------------------
-- Distributive laws on a binary operation: Task B
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-univers... | {
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module Sandbox.IndRec where
-- Ornamental Algebras, Algebraic Ornaments, CONOR McBRIDE
-- https://personal.cis.strath.ac.uk/conor.mcbride/pub/OAAO/Ornament.pdf
-- A Finite Axiomtization of Inductive-Recursion definitions, Peter Dybjer, Anton Setzer
-- http://www.cse.chalmers.se/~peterd/papers/Finite_IR.pdf
open import... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Finite where
open import Level
open import Data.Nat using (ℕ)
open import Data.Fin
open import Categories.Adjoint.Equivalence
open import Categories.Category
open import Categories.Functor
open import Categories.Category.Finite.Fin
-- definition of a fin... | {
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module Generic.Lib.Data.Maybe where
open import Data.Maybe.Base using (Maybe; just; nothing; maybe; maybe′; from-just; fromMaybe) public
open import Generic.Lib.Intro
open import Generic.Lib.Category
infixr 0 _?>_
instance
MaybeMonad : ∀ {α} -> RawMonad {α} Maybe
MaybeMonad = record
{ return = just
; _>... | {
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open import Type
module Relator.Sets {ℓ ℓₑ ℓₛ} {E : Type{ℓₑ}} {S : Type{ℓₛ}} (_∈_ : E → S → Type{ℓ}) where
open import Functional
open import Logic.Propositional
open import Logic.Predicate
_∉_ : E → S → Type
_∉_ = (¬_) ∘₂ (_∈_)
_∋_ : S → E → Type
_∋_ = swap(_∈_)
_∌_ : S → E → Type
_∌_ = (¬_) ∘₂ (_∋_)
_⊆_ : S → S... | {
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module Issue804 where
mutual
{-# NO_TERMINATION_CHECK #-}
Foo : Set
Foo = Foo
-- WAS: The pragma above doesn't apply to Foo. An informative error message
-- could be helpful.
-- NOW: The pragma does apply to Foo.
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------------------------------------------------------------------------
-- A type used to index a combined definition of strong and weak
-- bisimilarity and expansion
------------------------------------------------------------------------
{-# OPTIONS --safe #-}
module Delay-monad.Bisimilarity.Kind where
open impor... | {
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{-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.Algebra.CommRing.BinomialThm where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Data.Nat renaming ( _+_ to _+ℕ_ ; _·_ to _·ℕ_ ; _^_ to _^ℕ_
; +-comm to +... | {
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postulate
Bool : Set
D : Bool → Set
f : (a : Bool) → D a
⟦_⟧ : ∀ {a} → D a → Bool
record State : Set where
field bool : Bool
open State {{...}}
postulate
guard : {S : Set} → ({{_ : S}} → Bool) → S
test : State
test = guard ⟦ f bool ⟧ -- doesn't work, used to work in agda 2.4
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Unbundled where
-- This is basically identical to Category, except that the
-- Obj type is a parameter rather than a field.
open import Level
open import Function.Base using (flip)
open import Relation.Binary using (Rel; IsEquivalence)
record Category {o... | {
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open import Agda.Builtin.Unit
open import Agda.Builtin.Sigma
open import Agda.Builtin.List
open import Agda.Builtin.Equality
open import Agda.Builtin.Reflection renaming (bindTC to infixl 4 _>>=_)
macro
quoteDef : Name → Term → TC ⊤
quoteDef f hole = (getDefinition f >>= quoteTC) >>= unify hole
postulate
A : S... | {
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-- Andreas, 2012-09-17 documenting an internal error in InternalToAbstract.hs
-- {-# OPTIONS -v syntax.reify.con:30 -v tc.with.type:30 #-}
module NameFirstIfHidden where
Total : (D : (A : Set) → A → Set)(A : Set) → Set
Total D A = forall a → D A a
data D (A : Set) : (a : A) → Set where
c : Total D A
postulate P : ... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Definition
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Groups.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Groups.Subgroups.Definition
open import Groups.Subgroups.Normal.Definition
o... | {
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open import Categories
open import Functors
open import RMonads
module RMonads.CatofRAdj {a b c d}{C : Cat {a}{b}}{D : Cat {c}{d}}{J : Fun C D}
(M : RMonad J) where
open import Library
open import RAdjunctions
open Fun
open Cat
record ObjAdj {e f} : Set ((a ⊔ b ⊔ c ⊔ d ⊔ lsuc e ⊔ lsuc f))... | {
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{-# OPTIONS --universe-polymorphism #-}
open import Categories.Category
module Categories.Functor.Core where
open import Level
open import Categories.Support.EqReasoning
record Functor {o ℓ e o′ ℓ′ e′} (C : Category o ℓ e) (D : Category o′ ℓ′ e′) : Set (o ⊔ ℓ ⊔ e ⊔ o′ ⊔ ℓ′ ⊔ e′) where
eta-equality
private modul... | {
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module FunClause where
f
: {A : Set}
→ A
→ A
f x
= y
where
y = x
z = x
data List
(A : Set)
: Set
where
nil
: List A
cons
: A
→ List A
→ List A
snoc
: {A : Set}
→ List A
→ A
→ List A
snoc nil y
= cons y nil
snoc (cons x xs) y
= cons x (snoc xs y)
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------------------------------------------------------------------------
-- Brandt and Henglein's subterm relation
------------------------------------------------------------------------
module RecursiveTypes.Subterm where
open import Algebra
open import Data.Fin using (Fin; zero; suc; lift)
open import Data.Nat
ope... | {
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-- {-# OPTIONS -v reify:80 #-}
open import Common.Prelude
open import Common.Reflection
open import Common.Equality
module Issue1345 (A : Set) where
unquoteDecl idNat = define (vArg idNat)
(funDef (pi (vArg (def (quote Nat) [])) (abs "" (def (quote Nat) [])))
(clause (vArg (var "") ∷ []) (var 0 []) ∷ [])... | {
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------------------------------------------------------------------------------
-- Testing the erasing of the duplicate definitions required by a conjecture
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-... | {
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{-# OPTIONS --cubical --safe --postfix-projections #-}
module Cardinality.Infinite.ManifestEnumerable where
open import Prelude
open import Data.List.Kleene
open import Data.Fin
import Data.Nat as ℕ
open import Data.Nat using (_+_)
open import Cubical.Data.Sigma.Properties
open import Cubical.Foundations.Prelude usin... | {
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{-# OPTIONS --rewriting #-}
open import Agda.Primitive
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
variable
ℓ ℓ' : Level
A : Set ℓ
B : Set ℓ'
x y z : A
sym : x ≡ y → y ≡ x
sym refl = refl
_∙_ : x ≡ y → y ≡ z → x ≡ z
refl ∙ refl = refl
leftId : (p : x ≡ y) → refl ∙ p ≡ p
left... | {
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----------------------------------------------------------------------------
-- Well-founded induction on the relation _◁_
----------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymor... | {
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{-# OPTIONS --no-qualified-instances #-}
module NoQualifiedInstances-ParameterizedImport where
postulate
T : Set
open import NoQualifiedInstances.ParameterizedImport.A T as A
postulate
f : {{A.I}} → A.I
test : A.I
test = f
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021 Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
module LibraBFT.ImplShared.Util.Dijkstra.All where
open import Dijkstra... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module lambda.system-d where
open import Data.Nat
open import Data.Fin hiding (lift)
open import lambda.vec
open import lambda.untyped
infixr 21 _∧_
infixr 22 _⇒_
data type : Set where
base : ℕ → type
_⇒_ _∧_ : type → type → type
context : ℕ → Set
context = vec type
in... | {
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module README where
------------------------------------------------------------------------
-- The Agda "standard" library, version 0.2
--
-- Author: Nils Anders Danielsson, with contributions from
-- Jean-Philippe Bernardy, Samuel Bronson, Liang-Ting Chen, Dan Doel,
-- Patrik Jansson, Shin-Cheng Mu, and Ulf Norell
-... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Functors
------------------------------------------------------------------------
-- Note that currently the functor laws are not included here.
module Category.Functor where
open import Function
open import L... | {
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------------------------------------------------------------------------------
-- Testing variable names clash
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
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-- Solver for Functor
{-# OPTIONS --without-K --safe #-}
open import Categories.Category
open import Categories.Functor renaming (id to idF)
module Experiment.Categories.Solver.Functor
{o ℓ e o′ ℓ′ e′} {𝒞 : Category o ℓ e} {𝒟 : Category o′ ℓ′ e′}
(F : Functor 𝒞 𝒟)
where
open import Level
open import Relat... | {
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module Thesis.LangChanges where
open import Thesis.Changes
open import Thesis.IntChanges
open import Thesis.Types
open import Thesis.Contexts
open import Thesis.Environments
open import Relation.Binary.PropositionalEquality
Chτ : (τ : Type) → Set
Chτ τ = ⟦ Δt τ ⟧Type
ΔΓ : Context → Context
ΔΓ ∅ = ∅
ΔΓ (τ • Γ) = Δt τ... | {
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{-# OPTIONS --cubical --guardedness --safe #-}
module Data.PolyP.Universe where
open import Prelude hiding (_⟨_⟩_)
open import Data.Vec.Iterated
open import Data.Fin.Indexed
--------------------------------------------------------------------------------
--
-- The Universe of functors we're interested in.
--
------... | {
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------------------------------------------------------------------------------
-- The alternating bit protocol (ABP) is correct
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-... | {
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{-# OPTIONS --safe #-}
module Cubical.Categories.Instances.Rings where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Algebra.Ring
open import Cubical.Categories.Category
open Category
open RingHoms
RingsCategory : ∀ {ℓ} → Category (ℓ-suc ℓ) ℓ
ob RingsCategory ... | {
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-- Algorithmic equality.
{-# OPTIONS --without-K --safe #-}
module Definition.Conversion where
open import Definition.Untyped
open import Definition.Typed
open import Tools.Nat
open import Tools.Product
import Tools.PropositionalEquality as PE
infix 10 _⊢_~_↑_
infix 10 _⊢_~_↓_
infix 10 _⊢_[conv↑]_
infix 10 _⊢_[co... | {
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{-# OPTIONS --without-K #-}
open import HoTT
open import cohomology.Theory
{- Ordinary cohomology groups of the n-torus Tⁿ = (S¹)ⁿ.
- We have Cᵏ(Tⁿ) == C⁰(S⁰)^(n choose' k) where _choose'_ defined as below.
- This argument could give Cᵏ((Sᵐ)ⁿ) with a little more work. -}
module cohomology.Torus {i} (OT : OrdinaryT... | {
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module Languages.ILL.TypeCheck where
open import bool
open import maybe
open import Languages.ILL.TypeSyntax
open import Languages.ILL.Syntax
open import Utils.HaskellTypes
open import Utils.HaskellFunctions
open import Utils.Exception
data StateT (s : Set) (m : Set → Set) (a : Set) : Set where
stateT : (s → m (Pr... | {
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module Examples.Resolution where
open import Prelude
open import Implicits.Syntax
open import Implicits.Syntax.Type.Constructors
open import Implicits.WellTyped
open import Implicits.Substitutions
open import Extensions.ListFirst
open Rules
unit = 0
-- simple implicit resolution by implication
module ex₁ where
r :... | {
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module foldr-monoid-foldl where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; sym; trans; cong)
open Eq.≡-Reasoning
open import lists using (List; []; _∷_; [_]; [_,_]; [_,_,_]; foldr; IsMonoid)
open IsMonoid
open import foldl using (foldl)
postulate
-- 外延性の公理
extensionality : ∀ {A ... | {
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module Human.Empty where
data Empty : Set where
void : ∀ {P : Set} → Empty → P
void ()
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