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text string | meta dict |
|---|---|
module Numeral.Sign.Oper0 where
open import Numeral.Sign
-- Negation
−_ : (+|0|−) → (+|0|−)
− (➕) = (➖)
− (𝟎) = (𝟎)
− (➖) = (➕)
-- Bounded addition
_+_ : (+|0|−) → (+|0|−) → (+|0|−)
(➕) + (➕) = (➕)
(➕) + (➖) = (𝟎)
(➕) + (𝟎) = (➕)
(➖) + (➕) = (𝟎)
(➖) + (➖) = (➖)
(➖) + (𝟎) = (➖)
(𝟎) + (➕) = (➕)
(𝟎) + (➖) = (➖)... | {
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module n2o.Network.Core where
open import proto.Base
open import proto.IO
open import n2o.Network.Internal
{-# FOREIGN GHC import Network.N2O.Core #-}
postulate
protoRun : ∀ {F : Set → Set} {A : Set} → F A → List (Proto F A) → N2O F A (Result (F A))
{-# COMPILE GHC protoRun = Network.N2O.Core.protoRun #-}
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{-# OPTIONS --cubical --safe --guardedness #-}
module Data.PolyP.Composition where
open import Function hiding (_⟨_⟩_)
open import Data.Sum
open import Data.Sigma
open import Level
open import Data.Unit
open import Data.Nat
open import Data.Vec
open import Data.Empty
open import WellFounded
open import Literals.Numbe... | {
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{-# OPTIONS --cubical --safe #-}
module Data.Binary.Multiplication.Properties where
open import Prelude
open import Data.Binary.Definition
open import Data.Binary.Addition
open import Data.Binary.Addition.Properties using (+-cong)
open import Data.Binary.Multiplication
open import Data.Binary.Conversion
import Data.N... | {
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import Lvl
open import Structure.Operator.Vector
open import Structure.Setoid
open import Type
module Structure.Operator.Vector.Subspace
{ℓᵥ ℓₛ ℓᵥₑ ℓₛₑ}
{V : Type{ℓᵥ}} ⦃ equiv-V : Equiv{ℓᵥₑ}(V) ⦄
{S : Type{ℓₛ}} ⦃ equiv-S : Equiv{ℓₛₑ}(S) ⦄
{_+ᵥ_ : V → V → V}
{_⋅ₛᵥ_ : S → V → V}
{_+ₛ_ _⋅ₛ_ : S → S → S}
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module plfa-code.Relations where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; cong; sym; trans)
open import Data.Nat using (ℕ; zero; suc; _+_; _*_)
open import Data.Nat.Properties using (+-comm)
open Eq.≡-Reasoning using (begin_; _≡⟨⟩_)
open import plfa-code.Reasoning-legacy
open impor... | {
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------------------------------------------------------------------------
-- Pointwise equalities can be lifted
------------------------------------------------------------------------
module Stream.Pointwise where
open import Codata.Musical.Notation hiding (∞)
open import Stream
open import Stream.Equality
import Str... | {
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-- from http://wiki.portal.chalmers.se/agda/pmwiki.php?n=ReferenceManual.LocalDefinition
module Local where
data Nat : Set where
zero : Nat
succ : Nat -> Nat
infixl 5 _+_
_+_ : Nat -> Nat -> Nat
zero + n = n
(succ m) + n = succ (m + n)
infixl 6 _*_
_*_ : Nat -> Nat -> Nat
zero * _ = zero
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{-
This second-order equational theory was created from the following second-order syntax description:
syntax TLC | Λ
type
N : 0-ary
_↣_ : 2-ary | r30
𝟙 : 0-ary
_⊗_ : 2-ary | l40
𝟘 : 0-ary
_⊕_ : 2-ary | l30
term
app : α ↣ β α -> β | _$_ l20
lam : α.β -> α ↣ β | ƛ_ r10
unit : 𝟙
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
module Light.Implementation.Data.Unit where
open import Light.Library.Data.Unit using (Library ; Dependencies)
instance dependencies : Dependencies
dependencies = record {}
instance library : Library dependencies
library = record { Impl... | {
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-- 2018-09-05, reported by Andreas Abel
-- The new type-directed rewriting was using the wrong type for
-- constructors of parametrized datatypes.
{-# OPTIONS --rewriting #-}
module _ where
module _ (Form : Set) where
open import Agda.Builtin.Equality
{-# BUILTIN REWRITE _≡_ #-}
data Cxt : Set where
_∙_ ... | {
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module Syntax.Transitivity where
import Lvl
open import Logic
import Structure.Relator.Names as Names
open import Structure.Relator.Properties
open import Type
private variable ℓ₁ ℓ₂ ℓ₃ : Lvl.Level
private variable T : Type{ℓ₁}
-- The transitivity operator
infixl 1000 _🝖_
_🝖_ : ∀{_▫_ : T → T → Stmt{ℓ₂}} ... | {
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module UniDB.Subst.Inst where
open import UniDB.Spec
open import UniDB.Subst.Core
open import UniDB.Subst.Pair
open import UniDB.Subst.Shifts
open import UniDB.Morph.Pair
open import UniDB.Morph.Shift
open import UniDB.Morph.Shifts
open import UniDB.Morph.Unit
-- These are two unused instances. Just to show that ApHC... | {
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{-# OPTIONS --copatterns #-}
module Issue950a where
postulate
A : Set
record R : Set where
field
x : A
record S : Set where
field
y : A
open R
f : A
x f = ?
-- Bad error:
-- Arguments left we cannot split on. TODO: better error message
-- when checking that the clause x f = ? has type A
-- Better... | {
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module FFI.System.Exit where
open import Agda.Builtin.Int using (Int)
open import Agda.Builtin.IO using (IO)
open import Agda.Builtin.Unit using (⊤)
data ExitCode : Set where
ExitSuccess : ExitCode
ExitFailure : Int → ExitCode
{-# FOREIGN GHC data AgdaExitCode = AgdaExitSuccess | AgdaExitFailure Integer #-}
{-# ... | {
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module Issue566 where
open import Common.Level using (Level; _⊔_)
data D (a : Level) (A : Set a) : Set a where
d : D a A → D a A
P-level : (a : Level) (A : Set a) → D a A → Level
P-level a A (d x) = P-level a A x
P : (a : Level) (A : Set a) (x : D a A) → Set (P-level a A x)
P a A (d x) = P a A x
postulate
a : L... | {
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-- MIT License
-- Copyright (c) 2021 Luca Ciccone and Luca Padovani
-- Permission is hereby granted, free of charge, to any person
-- obtaining a copy of this software and associated documentation
-- files (the "Software"), to deal in the Software without
-- restriction, including without limitation the rights to use... | {
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module Lvl.MultiFunctions.Proofs where
open import Data
open import Lvl hiding (𝐒)
open import Lvl.MultiFunctions
open import Data.Tuple.Raise
open import Data.Tuple.Raiseᵣ.Functions
open import Lvl.MultiFunctions
open import Numeral.Natural
open import Relator.Equals
open import Syntax.Number
max-repeat : ∀{n}{ℓ} →... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions.Definition
open import Sets.EquivalenceRelations
open import Rings.Definition
module Rings.Divisible.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
-- Definition of the Arrow Category of a Category C
module Categories.Category.Construction.Arrow {o ℓ e} (C : Category o ℓ e) where
open import Level
open import Data.Product using (_,_; _×_; map; zip)
open import Function using (_$_)
open import Rel... | {
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data Fun (A B : Set) : Set where
fun : (A → B) → Fun A B
syntax fun (λ x → y) = fn x , y
foo : ∀ {A} → Fun A A → A
foo (fn x , y) = y
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------------------------------------------------------------------------
-- Coinductive lists
------------------------------------------------------------------------
module Data.Colist where
open import Coinduction
open import Data.Bool using (Bool; true; false)
open import Data.Maybe using (Maybe; ... | {
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open import Categories
open import Monads
module Monads.CatofAdj.TermAdj {a b}{C : Cat {a}{b}}(M : Monad C) where
open import Library
open import Functors
open import Monads.CatofAdj M
open import Categories.Terminal
open import Monads.CatofAdj.TermAdjObj M
open import Monads.CatofAdj.TermAdjHom M
open import Monads.... | {
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{-
Finitely presented algebras.
An R-algebra A is finitely presented, if there merely is an exact sequence
of R-modules:
(a₁,⋯,aₘ) → R[X₁,⋯,Xₙ] → A → 0
-}
{-# OPTIONS --safe #-}
module Cubical.Algebra.CommAlgebra.FPAlgebra where
open import Cubical.Foundations.Prelude
open import Cubical.Data.FinData
open i... | {
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{-# OPTIONS --without-K #-}
open import Level renaming (zero to lzero ; suc to lsuc)
open import Syntax
open import Data.List using (length ; [] ; _∷_ ) renaming ( _++_ to _++L_ )
open import Data.Vec using ([] ; _∷_ ) renaming ( _++_ to _++V_ )
open import Data.Vec.Relation.Unary.All using (All ; [] ; _∷_)
open i... | {
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{-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.Algebra.Polynomials.Multivariate.Properties where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Nat renaming(_+_ to _+n_; _·_ to _·n_)
open import Cubical.Data.Vec
open import Cubical.Algebra.Ring
open import Cubical.Algebra.Co... | {
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{-# OPTIONS --cubical --no-import-sorts #-}
open import Cubical.Foundations.Everything renaming (_⁻¹ to _⁻¹ᵖ; assoc to ∙-assoc)
open import Function.Base using (_∋_; _$_)
open import Cubical.Data.Sum.Base renaming (_⊎_ to infixr 4 _⊎_)
open import Cubical.HITs.PropositionalTruncation.Base -- ∣_∣
open import Cubical.H... | {
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-- Liang-Ting, 2022-01-14, issue #5734
{-# OPTIONS --cubical-compatible #-}
open import Agda.Builtin.Unit
open import Agda.Builtin.List
open import Agda.Builtin.Sigma
open import Agda.Builtin.Reflection
renaming (returnTC to return; bindTC to _>>=_)
open import Agda.Primitive
private variable
A B : Set _
revers... | {
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module _ where
open import Common.IO
renaming (then to _>>_
)
open import Agda.Builtin.Unit
open import Agda.Builtin.Bool
open import Agda.Builtin.Equality using (_≡_; refl)
open import Agda.Builtin.Float
renaming ( primFloatEquality to _≡ᵇ_
; primFloatInequality to _≤ᵇ_
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open import Prelude
open import core
module ground-decidable where
ground-decidable : (τ : htyp) → (τ ground) + ((τ ground) → ⊥)
ground-decidable b = Inl GBase
ground-decidable ⦇-⦈ = Inr (λ ())
ground-decidable (b ==> b) = Inr (λ ())
ground-decidable (b ==> ⦇-⦈) = Inr (λ ())
ground-decidable (b ==> τ' ==> ... | {
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module ListsWithIrrelevantProofs where
data _≡_ {A : Set}(a : A) : A → Set where
refl : a ≡ a
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
{-# BUILTIN NATURAL ℕ #-}
postulate
_≤_ : ℕ → ℕ → Set
p1 : 0 ≤ 1
p2 : 0 ≤ 1
-- descending lists indexed by upper bound for largest element
data SList (bound : ℕ) ... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.Monoid.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Equiv.HalfAdjoint
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open impor... | {
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module _ where
data Nat : Set where
zero : Nat
suc : Nat → Nat
{-# BUILTIN NATURAL Nat #-}
_+_ : (m n : Nat) → Nat
zero + n = n
suc m + n = suc (m + n)
data Th : (m n : Nat) → Set where
os : ∀ {m n} → Th m n → Th (suc m) (suc n)
Fin : Nat → Set
Fin = Th (suc zero)
infixl 6 _++_
inf... | {
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{-# OPTIONS --prop --rewriting #-}
module Examples.Sorting.Sequential.Comparable where
open import Calf.CostMonoid
open import Calf.CostMonoids
costMonoid = ℕ-CostMonoid
open import Data.Nat using (ℕ)
open CostMonoid costMonoid using (ℂ)
fromℕ : ℕ → ℂ
fromℕ n = n
open import Examples.Sorting.Comparable costMonoid... | {
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module Type.Properties.Homotopy where
open import Functional
import Lvl
open import Numeral.Natural
open import Structure.Setoid
open import Type
open import Type.Dependent
open import Syntax.Function
private variable ℓ ℓ₁ ℓ₂ ℓₑ : Lvl.Level
private variable T A B : Type{ℓ}
private variable n : ℕ
module _ {ℓ} ⦃ ... | {
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open import Common.Prelude
_test_test_ : Nat → Nat → Nat → Nat
m test_test n = λ i → m + i + n
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-- A brief Agda tutorial.
-- Martín Escardó, 7 Sep 2012 (updated to be compatible with Agda 2.4.2 2 Oct 2014).
--
-- Agda is a computer-implemented dialect of Martin-Löf type theory.
-- It can both check and run proofs.
--
-- Propositions are types (also called sets, indicated by the keyword
-- Set), and their witness... | {
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------------------------------------------------------------------------------
-- Testing the translation of definitions
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymor... | {
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{-# OPTIONS --no-syntactic-equality #-}
open import Agda.Primitive
variable
ℓ : Level
A : Set ℓ
P : A → Set ℓ
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{-# OPTIONS --safe #-}
module Cubical.Algebra.CommRingSolver.EvalHom where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Nat using (ℕ)
open import Cubical.Data.Int.Base hiding (_+_ ; _·_ ; -_)
open import Cubical.Data.FinData
open import Cubical.Data.Vec
open import Cubical.Data.Bool
open import Cu... | {
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-- Applicative with law
{-# OPTIONS --without-K --safe #-}
module Experiment.Applicative where
open import Data.Product as Prod
open import Data.Unit
open import Function.Base
open import Relation.Binary.PropositionalEquality
record Functor (F : Set → Set) : Set₁ where
field
fmap : ∀ {A B} → (A → B) → F A →... | {
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------------------------------------------------------------------------------
-- FOTC version of a nested recursive function
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-po... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.Bouquet
{-
Various lemmas that will be used in cohomology.DisjointlyPointedSet.
Many of them, for example the choice lemma about coproducts, should be
put into core/.
-}
module homotopy.DisjointlyPointedSet where
module _ {i} where
is-... | {
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------------------------------------------------------------------------
-- Normalisation by evaluation
------------------------------------------------------------------------
import Axiom.Extensionality.Propositional as E
import Level
open import Data.Universe
-- The code makes use of the assumption that propositio... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Showing natural numbers
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Nat.Show where
open import Data.Nat
open import Relation.Nullary.... | {
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module Issue641 where
Foo : Set
Foo = Set
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.Group.Subgroup where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.Sigma
open import Cubical.Algebra
open import Cubical.Algebra.Group.Morphism
open ... | {
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-- An ATP definition must be used with functions.
-- This error is detected by Syntax.Translation.ConcreteToAbstract.
module ATPBadDefinition1 where
data Bool : Set where
false true : Bool
{-# ATP definition false #-}
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-- Andreas, 2017-01-20, issue #2329
-- Neutral sizes cannot be used by the size solver,
-- thus, should be handled by coerceSize.
-- {-# OPTIONS -v tc:10 #-}
-- {-# OPTIONS -v tc.conv.coerce:20 #-}
-- {-# OPTIONS -v tc.size:20 #-}
-- {-# OPTIONS -v tc.size.solve:50 #-}
open import Agda.Builtin.Size
record R (i : Si... | {
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module VecMap where
open import Prelude
map : forall {A B n} -> (A -> B) -> Vec A n -> Vec B n
map f xs = {!!}
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open import Relation.Binary.PropositionalEquality using (_≡_; refl; sym)
open import Function.Equivalence using (_⇔_; equivalence; Equivalence)
open import Data.Bool using (Bool; true; false; if_then_else_)
open import Data.Product using (_×_; _,_; proj₁; proj₂)
open import Data.Sum using (_⊎_)
open import IMP
open im... | {
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{-# OPTIONS --type-in-type #-}
module DescFix where
open import DescTT
aux : (C : Desc)(D : Desc)(P : Mu C -> Set)(x : [| D |] (Mu C)) -> Set
aux C id P (con y) = P (con y) * aux C C P y
aux C (const K) P k = Unit
aux C (prod D D') P (s , t) = aux C D P s * aux C D' P t
aux C (sigma S T) P (s , t)... | {
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-- Andreas, 2014-09-23
-- Syntax declaration for overloaded constructor.
-- {-# OPTIONS -v scope.operators:50 #-}
syntax c x = ⟦ x ⟧
data D1 : Set where
c : D1
data D2 : Set where
c : D1 → D2
test : D2
test = ⟦ c ⟧
-- Should work.
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-- P: (vcd) <E[send c v]> | <F[recv d]> --> (vcd) <E[c]> | <F[(d,v)]>
-- P: (vcd) <E[close c]> | <F[wait d]> --> (vcd) <E[()]> | <F[()]>
module Properties.StepCloseWait where
open import Data.Maybe hiding (All)
open import Data.List
open import Data.List.All
open import Data.Product
open import Data.Sum
open impor... | {
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module Prelude.Level where
open import Agda.Primitive public
using (Level)
renaming (lzero to zero; lsuc to suc; _⊔_ to max)
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open import Everything
module Test.Symmetrical where
test-𝓢ymmetrical𝓢ymmetry : ∀
{𝔬} {𝔒 : Ø 𝔬}
{ℓ} {_∼_ : 𝔒 → 𝔒 → Ø ℓ}
⦃ _ : Symmetry.class _∼_ ⦄
→ Symmetry.type _∼_
-- test-𝓢ymmetrical𝓢ymmetry = symmetrical _ _ -- FIXME no longer works after 𝓢ymmetrical𝓢ymmetry was "rationalised"
t... | {
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{-# OPTIONS --rewriting #-}
module DualLMRefined where
open import Data.Bool
open import Data.Nat hiding (compare)
open import Data.Nat.Properties
open import Data.Fin hiding (_+_)
open import Data.Product
open import Function
open import Relation.Binary.PropositionalEquality hiding (Extensionality)
open import Agda.B... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.RingSolver.Solver where
open import Cubical.Foundations.Prelude
open import Cubical.Data.FinData
open import Cubical.Data.Nat using (ℕ)
open import Cubical.Data.Nat.Order using (zero-≤)
open import Cubical.Data.Vec.Base
open import Cubical.Alge... | {
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{-# OPTIONS --cubical --no-import-sorts #-}
module Number.Instances.Nat where
open import Agda.Primitive renaming (_⊔_ to ℓ-max; lsuc to ℓ-suc; lzero to ℓ-zero)
open import Cubical.Foundations.Everything renaming (_⁻¹ to _⁻¹ᵖ; assoc to ∙-assoc)
open import Cubical.Foundations.Logic renaming (inl to inlᵖ; inr to inrᵖ)... | {
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{- https://lists.chalmers.se/pipermail/agda/2013/006033.html http://code.haskell.org/~Saizan/unification/ 18-Nov-2013 Andrea Vezzosi -}
module Unify-monolithic-EnhancedTerm where
-- some equivalences needed to adapt Tactic.Nat to the standard library
module EquivalenceOf≤ where
open import Agda.Builtin.Equality
op... | {
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------------------------------------------------------------------------------
-- The Collatz function: A function without a termination proof
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS... | {
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module STLC.Kovacs.Completeness where
open import STLC.Kovacs.Normalisation public
open import STLC.Kovacs.Convertibility public
--------------------------------------------------------------------------------
-- (_≈_)
infix 3 _≫_
_≫_ : ∀ {A Γ} → Γ ⊢ A → Γ ⊩ A → Set
_≫_ {⎵} {Γ} M N = M ∼ embⁿᶠ N
_≫_ {A ⇒ B}... | {
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------------------------------------------------------------------------
-- Upper bounds of colists containing natural numbers
------------------------------------------------------------------------
module Upper-bounds where
open import Equality.Propositional
open import Logical-equivalence using (_⇔_)
open import P... | {
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{-# OPTIONS --without-K #-}
open import Base
module Algebra.FreeGroupAsReducedWords {i} (A : Set i) (eq : has-dec-eq A) where
A-is-set : is-set A
A-is-set = dec-eq-is-set eq
data word : Set i where
ε : word
_∷_ : A → word → word
_′∷_ : A → word → word
is-reduced : word → Set i
is-reduced ε = unit
is-reduced ... | {
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{-
Types Summer School 2007
Bertinoro
Aug 19 - 31, 2007
Agda
Ulf Norell
-}
module Filter where
open import Nat
data Bool : Set where
false : Bool
true : Bool
infixr 40 _::_
data List (A : Set) : Set where
[] : List A
_::_ :... | {
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module local where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
infixr 15 _::_
data List (A : Set) : Set where
nil : List A
_::_ : A -> List A -> List A
reverse : {A : Set} -> List A -> List A
reverse {A} xs = rev xs nil
where
rev : List A -> List A -> List A
rev nil ys = ys
rev (... | {
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{-
This file contains:
- Rijke finiteness is closed under forming Σ-type.
-}
{-# OPTIONS --safe #-}
module Cubical.Data.FinType.Sigma where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.HITs.SetTruncation as Set
open import Cubical.HITs.SetTruncation.Fibers
open... | {
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------------------------------------------------------------------------------
-- Comparing styles for equational reasoning
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-poly... | {
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module _ where
data N : Set where
zero : N
suc : N → N
record P : Set where
constructor p
field fst : N
snd : N
open P
-- f = λ z → z internally
f : P → P
f z = p (fst z) (snd z)
-- This should also be λ z → z, but was not due to #2157.
g : P → P
g (p x y) = p x y
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{-# OPTIONS --safe --without-K #-}
module JVM.Types where
open import Data.Empty using (⊥)
open import Data.Unit using (⊤; tt)
open import Data.Product
open import Data.List
open import Data.String
open import Relation.Binary
open import Relation.Binary.PropositionalEquality
open import Relation.Nullary.Decidable
ope... | {
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{-
The Existence of Smith Normal Form for Integer Matrices (KANG Rongji, Jan. 2022)
-}
{-# OPTIONS --safe #-}
module Cubical.Algebra.IntegerMatrix.Smith.Normalization where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.Nat
hiding (_·_)
renaming (_+_ t... | {
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{-# OPTIONS --cubical #-}
module SolutionsSession1 where
open import Part1 hiding (B)
variable
B : A → Type ℓ
-- Solutions to ExerciseSession1
-- Exercise 1:
funExtDep : {f g : (x : A) → B x}
→ ((x : A) → f x ≡ g x)
→ f ≡ g
funExtDep p i x = p x i
-- Exercise 2:
congP : {x y : A} {B : A → Typ... | {
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{-# OPTIONS --cubical --no-import-sorts --postfix-projections --safe #-}
module Cubical.Categories.TypesOfCategories.TypeCategory where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv
open import Cubical.Data.Sigma
import Cubical.Functions.Fibratio... | {
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-- This bug was reported by Christian Sattler. (I modified his example
-- slightly.)
-- {-# OPTIONS -v tc.meta.assign:49 #-}
module Issue903 where
record T : Set where
constructor tt
postulate
Id : (A : Set) → A → Set
e : (B : Set) (f : T → B) → Id B (f tt) → Id (T → B) f
k : (P : Set → Set) (u : P T) → I... | {
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-- Andreas, 2017-06-14, issue #2603
-- reported by rfindler, shrunk test case by Ulf
-- {-# OPTIONS -v tc.conv:40 -v tc.conv.atom:50 -v tc:80 -v tc.meta.assign:70 #-}
{-# OPTIONS --allow-unsolved-metas #-}
open import Agda.Builtin.Equality
data List (A : Set) : Set where
[] : List A
postulate
Signal : Set
dat... | {
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module Prelude.Fin where
open import Prelude.Eq
open import Prelude.Nat
data Fin : Nat -> Set where
fz : ∀{n} -> Fin (S n)
fs : ∀{n} -> Fin n -> Fin (S n)
forget : {n : Nat} -> Fin n -> Nat
forget fz = Z
forget (fs n) = S (forget n)
inject : (n : Nat) -> Fin (S n)
inject Z = fz
inject (S n) = fs (inject n)
... | {
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module Thesis.Lang where
open import Thesis.Syntax public
open import Thesis.Environments public
⟦_⟧Const : ∀ {τ} → Const τ → ⟦ τ ⟧Type
⟦ unit ⟧Const = tt
⟦ lit n ⟧Const = n
⟦ plus ⟧Const = _+_
⟦ minus ⟧Const = _-_
⟦ cons ⟧Const v1 v2 = v1 , v2
⟦ fst ⟧Const (v1 , v2) = v1
⟦ snd ⟧Const (v1 , v2) = v2
⟦ linj ⟧Const v1 ... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.Ints.HAEquivInt.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HAEquiv
data HAEquivInt : Type₀ where
zero : HAEquivInt
suc : HAEquivInt -> HAEquivInt
-- suc is a HAEquiv:
pred : HAEquivInt -> HAEquivInt
suc-pred : ∀ z... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Strings: builtin type and basic operations
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.String.Base where
open import Data.Nat.Base as... | {
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{-# OPTIONS --without-K --safe #-}
open import Algebra.Bundles using (Semiring)
-- Credit: This definition is taken from the stdlib issue #1175
-- As given by @MatthewDaggitt and @mechvel
module Definitions.Semiring {α α≈} (R : Semiring α α≈)
where
open Semiring R
record NonZero (x : Carrier) : Set α≈ where
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{-# OPTIONS --without-K #-}
open import library.Basics hiding (Type ; Σ ; S)
open import library.types.Sigma
open import Sec2preliminaries
open import Sec3hedberg
open import Sec4hasConstToSplit
open import Sec5factorConst
open import Sec6hasConstToDecEq
open import Sec7populatedness
module Sec8taboos where
-- S... | {
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module Issue268 where
module Example₁ where
open import Common.Coinduction
module Record where
record Stream : Set where
constructor cons
field
tail : ∞ Stream
module Data where
data Stream : Set where
cons : ∞ Stream → Stream
-- open Data
open Record
id : Stream → S... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.Group.DirProd where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.Sigma
open import Cubical.Algebra.Group.Base
open import Cubical.Algebra.Monoid
open import Cubical.Algebra.Semigroup
open GroupStr
open IsGroup hi... | {
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{-# OPTIONS --warning=error --allow-unsolved-metas #-}
-- This file contains everything that cannot be compiled in --safe mode.
--open import Lists.SortList
module Everything.Unsafe where
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module StrongArrows where
open import Library
open import Categories
open import Functors
open import MonoidalCat
open import WeakArrows
record SArrow {l m}(J : Monoidal {l}{m}) : Set (lsuc (l ⊔ m)) where
constructor sarrow
open Monoidal J
open Cat C
open Fun
field A : Arrow C
open Arrow A
field fst' : ... | {
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{-
Functions between structures S and T: X ↦ S X → T X
-}
{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Structures.Function where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Function
open import Cubical.Foundations.Isomorphism
open... | {
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module examplesPaperJFP.triangleRightOperator where
_▹_ : ∀{A B : Set} → A → (A → B) → B
a ▹ f = f a
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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.PKCS
open import LibraBFT.Base.Types
open import Lib... | {
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{-# OPTIONS --cubical-compatible #-}
postulate
A : Set
B : A → Set
@0 T : Set
T = (@0 x : A) → B x
_ : Set₁
_ = (@0 A : Set) → @0 A → (@0 x : A) → Set
data D : Set₁ where
@0 c : (@0 A : Set) → A → (x : A) → D
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------------------------------------------------------------------------------
-- Inductive Peano arithmetic base
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.MonoidSolver.Reflection where
open import Cubical.Foundations.Prelude hiding (Type)
open import Agda.Builtin.Reflection hiding (Type)
open import Agda.Builtin.String
open import Cubical.Reflection.Base
open import Cubical.Data.Maybe
open import Cubical.Data.Sigma
open ... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category using (Category; module Commutation)
-- The "four middle interchange" for monoidal categories.
--
-- Aka the "interchange law" or "exchange law" (though those terms are
-- more comonly used in the more general context of composition in
-- 2-categories... | {
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postulate A : Set
data D : Set where
c : A → D
data P : D → Set where
d : (x : A) → P (c x)
g : (x : D) → P x → D
g blargh (d y) with Set
g glurph (d y) | w = {!!}
-- Expected: glurph = c y : D, y : A, w : Set₁
h : D → D
h x@(c y) with Set
h (c z) | w = {!!}
-- Expected: z : A, w : Set₁
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-- 2018-05-25, Reported by Sergei Meshveliani on the Agda list
open import Common.Prelude
record _×_ (A B : Set) : Set where
constructor _,_
field
fst : A
snd : B
f : List (Nat × Nat) → List (Nat × Nat)
f ps =
map (\p → let (x , y) = p in (x , suc y)) ps
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module Esterel.CompletionCode where
open import Data.Nat
using (ℕ ; zero ; suc) renaming (_≟_ to _≟ℕ_ ; _⊔_ to _⊔ℕ_ ; _≤_ to _≤N_ ; _≤?_ to _≤?N_)
open import Data.Nat.Properties
using (⊔-⊓-isCommutativeSemiringWithoutOne)
open import Function
using (_∘_)
open import Relation.Nullary
using (Dec ; yes ; no)
ope... | {
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mmodule silly1 where
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module Values where
open import Data.Bool
open import Data.List
open import Data.List.All
open import Data.Nat
open import Data.Product
open import Data.Sum
open import Relation.Binary.PropositionalEquality
open import Typing
open import Syntax
open import Global
open import Channel
mutual
-- a value indexed by a *r... | {
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open import Oscar.Prelude
open import Oscar.Class
open import Oscar.Class.IsEquivalence
open import Oscar.Data.𝟙
module Oscar.Class.HasEquivalence where
module _
{𝔬} (𝔒 : Ø 𝔬) ℓ
where
𝔥asEquivalence : Rℭlass 𝟙
𝔥asEquivalence = ∁ (𝔒 → 𝔒 → Ø ℓ) IsEquivalence
open Rℭlass 𝔥asEquivalence using () rena... | {
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module _ where
module A where
postulate C : Set → Set → Set
syntax C X Y = X , Y
module B where
postulate C : Set
open A
open B
Foo : Set → Set
Foo X = X , X
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open import Type
open import Structure.Relator
open import Structure.Setoid renaming (_≡_ to _≡ₑ_)
module Structure.Sets.Quantifiers.Proofs {ℓₛ ℓₗ ℓₑ} {S : Type{ℓₛ}} ⦃ equiv : Equiv{ℓₑ}(S) ⦄ (_∈_ : S → S → Type{ℓₗ}) ⦃ [∈]-binaryRelator : BinaryRelator(_∈_) ⦄ where
import Lvl
open import Structure.Relator.Proofs ... | {
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