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{-# OPTIONS --cubical #-}
module Cubical.Experiments.Brunerie where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.Equiv
open import Cubical.Data.Bool
open import Cubical.Data.Nat
open import Cubical.Data.Int
open imp... | {
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{-# OPTIONS --cubical-compatible #-}
postulate
A : Set
B : A → Set
T = (@0 x : A) → B x
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------------------------------------------------------------------------
-- The Agda standard library
--
-- The basic code for equational reasoning with a partial relation
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary
module Re... | {
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{-# OPTIONS --universe-polymorphism #-}
open import Data.Bool using ( Bool ; true ; false ; _∧_ )
open import Data.Empty using ()
open import Data.List using ( List ; [] ; _∷_ ; _++_ ; map )
open import Data.List.Any using ( here ; there )
open import Data.List.Membership.Propositional using ()
open import Data.Sum us... | {
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module Fail.TuplePat where
open import Haskell.Prelude
fst₃ : a × b × c → a
fst₃ (x ∷ xs) = x
{-# COMPILE AGDA2HS fst₃ #-}
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{-
This second-order signature was created from the following second-order syntax description:
syntax Lens | L
type
S : 0-ary
A : 0-ary
term
get : S -> A
put : S A -> S
theory
(PG) s : S a : A |> get (put (s, a)) = a
(GP) s : S |> put (s, get(s)) = s
(PP) s : S a b : A |> put (p... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.Modulo.Properties where
open import Cubical.Data.Nat
open import Cubical.Data.Nat.Order
open import Cubical.Data.Fin
open import Cubical.Data.Sigma
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open import Cubic... | {
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open import OutsideIn.Prelude
open import OutsideIn.X
module OutsideIn.Constraints( x : X) where
open X(x)
data Strata : Set where
Flat : Strata
Extended : Strata
data Implication (knot : Set → Set)(n : Set) : Set where
∃_·_⊃_ : (v : ℕ) → QConstraint n → knot (n ⨁ v) → Implication knot n
{- S... | {
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module Agda.Builtin.TrustMe where
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Erase
private
postulate
unsafePrimTrustMe : ∀ {a} {A : Set a} {x y : A} → x ≡ y
primTrustMe : ∀ {a} {A : Set a} {x y : A} → x ≡ y
primTrustMe = primEraseEquality unsafePrimTrustMe
{-# DISPLAY primEraseEqualit... | {
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{-
This second-order term syntax was created from the following second-order syntax description:
syntax Ring | R
type
* : 0-ary
term
zero : * | 𝟘
add : * * -> * | _⊕_ l20
one : * | 𝟙
mult : * * -> * | _⊗_ l30
neg : * -> * | ⊖_ r50
theory
(𝟘U⊕ᴸ) a |> add (zero, a) = a
(𝟘U⊕ᴿ) a |> add (... | {
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module Issue826-2 where
open import Common.Coinduction
data _≡_ {A : Set} (x y : A) : Set where
data D : Set where
c : ∞ D → D
delay : D → ∞ D
delay x = ♯ x
data P : D → Set where
o : (x : ∞ D) → P (♭ x) → P (c x)
postulate
h : (x : D) → P x → P x
f : (x : D) → P (c (delay x)) → P x
f x (o .(delay x) p) = ... | {
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{- 2010-09-17 a small case study to test irrelevance -}
module IrrelevanceCaseStudyPartialFunctions where
data _≡_ {A : Set}(a : A) : A → Set where
refl : a ≡ a
record ⊤ : Set where
record Sigma (A : Set)(B : A → Set) : Set where
constructor _,_
field
fst : A
snd : B fst
syntax Sigma A (λ x → B) = Σ ... | {
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-- P: <E[new s]> --> (vcd) <E[(c,d)]>
module Properties.StepNew where
open import Data.Maybe hiding (All)
open import Data.List
open import Data.List.All
open import Data.Product
open import Relation.Nullary
open import Relation.Binary.PropositionalEquality
open import Typing
open import Syntax
open import Global
o... | {
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-- Andreas, 2019-06-17, LAIM 2019, issue #3855
-- Only allow erased definitions in erased context.
open import Common.IO
open import Common.Unit
open import Common.String
open import Common.Bool
@0 noWorld : String
noWorld = "Hallo, Welt!"
-- Illegal definition, should raise a type error.
world : Bool → String
worl... | {
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{-# OPTIONS --copatterns #-}
open import Common.Size
record R (i : Size) : Set where
inductive
constructor delay
field
force : (j : Size< i) → R j
open R
inh : (i : Size) → R i
force (inh i) j = inh j
-- Should give termination error
data ⊥ : Set where
elim : R ∞ → ⊥
elim (delay f) = elim (f ∞)
-- Giv... | {
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module WrongNamedArgument where
postulate
f : {A : Set₁} → A → A
test : Set → Set
test = f {B = Set}
-- Good error:
-- Function does not accept argument {B = _}
-- when checking that {B = Set} are valid arguments to a function of
-- type {A : Set₁} → A → A
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-----------------------------------
-- First order logic
-----------------------------------
module sv20.assign2.SetTheory.Logic where
infix 4 _,_
infix 3 ¬_
infix 1 _∧_
infix 1 _∨_
infix 0 _⇔_
-- Some First order logic I need.
-- ∧ data type (conjunction).
data _∧_ (A B : Set) : Set where
_,_ : A → B → A ∧ B
∧... | {
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module Issue690a where
postulate A : Set
data T : Set → Set where
c : T (T A)
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open import Oscar.Prelude
open import Oscar.Class
module Oscar.Class.Hmap where
module Hmap
{𝔵₁} {𝔛₁ : Ø 𝔵₁}
{𝔵₂} {𝔛₂ : Ø 𝔵₂}
{𝔯₁} {𝔯₂}
(ℜ₁ : 𝔛₁ → 𝔛₂ → Ø 𝔯₁)
(ℜ₂ : 𝔛₁ → 𝔛₂ → Ø 𝔯₂)
= ℭLASS (ℜ₁ , ℜ₂)
(∀ x y
→ ℜ₁ x y → ℜ₂ x y)
module _
{𝔵₁} {𝔛₁ : Ø 𝔵₁}
{𝔵₂} {𝔛₂ :... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- This module is DEPRECATED. Please use
-- Data.List.Relation.Binary.Equality.DecSetoid directly.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open i... | {
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{-# OPTIONS --safe --warning=error --cubical --without-K #-}
open import Agda.Primitive
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Isomorphism
open import Naturals
open import Basic
module File1 where
{-
Let's define the integers. Answers can be found ... | {
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module Issue2845 where
open import Agda.Builtin.Nat
open import Agda.Primitive.Cubical
open import Agda.Builtin.Equality
Ex1 : Nat
Ex1 = primComp (λ i → Nat) i0 (λ i → isOneEmpty) zero
test1 : Ex1 ≡ zero
test1 = refl
Ex2 : (i : I) → Nat
Ex2 i = primComp (λ i → Nat) i (λ { _ (i = i1) → zero}) zero
test2 : ∀ i → Ex2... | {
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{-# OPTIONS --without-K --exact-split --safe #-}
module Universes where
open import Agda.Primitive public
renaming (
Level to Universe -- We speak of universes rather than of levels.
; lzero to 𝓤₀ -- Our first universe is called 𝓤₀
; lsuc to _⁺ -- The universe after 𝓤 ... | {
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{-# OPTIONS --cubical --safe #-}
module Lemmas where
open import Cubical.Core.Everything using (_≡_; Level; Type)
open import Data.Fin using (Fin; toℕ; fromℕ<; zero; suc)
open import Data.Integer using (ℤ; +_; -[1+_])
open import Data.Nat
open import Data.Nat.Properties usin... | {
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open import Data.ByteString.Primitive using ( ByteStringStrict ; ByteStringStrict² ; ByteStringLazy ; ByteStringLazy² )
open import Data.Bool using ( Bool )
open import Data.Char using ( Char )
open import Data.Natural using ( Natural )
open import Data.String using ( String )
module Data.ByteString.UTF8.Primitive w... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.CommSemiring where
open import Cubical.Algebra.CommSemiring.Base public
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import cw.CW
open import cw.FinCW
open import cw.FinBoundary
open import cohomology.Theory
{- The reason that RephraseDualizedFirstFinBoundary did not handle this case
is because [FinSkeleton n] does not compute. -}
module cw.cohomology.cochainequiv.Du... | {
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-- Andreas, 2021-12-22, issue #5705 reported by ksqsf
open import Agda.Builtin.Equality
crash : Set ≡ Set9223372036854775808
crash = refl
-- This should fail, but crashes in Agda 2.6.2 due to Int overflow.
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module Categories.Coend where
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.DStructures.Structures.Type where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.HLevels
open import Cubical.Functions.FunExtEquiv
open import Cubical.Foundations.Univalence
open import C... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Rational numbers
------------------------------------------------------------------------
module Data.Rational where
import Algebra
import Data.Bool.Properties as Bool
open import Function
open import Data.Inte... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Construction.Properties.Presheaves.CartesianClosed where
open import Level
open import Data.Unit
open import Data.Product using (_,_; proj₁; proj₂)
open import Function.Equality using (Π) renaming (_∘_ to _∙_)
open import Relation.Binary
open import Categ... | {
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------------------------------------------------------------------------
-- The delay monad, defined using increasing sequences of potential
-- values
------------------------------------------------------------------------
{-# OPTIONS --safe #-}
module Delay-monad.Alternative where
open import Equality.Propositiona... | {
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module Issue481InstantiatedImportOnly where
import Common.Issue481ParametrizedModule Set
-- pointless, should yield error
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{-# OPTIONS --cubical --safe #-}
module HITs.PropositionalTruncation where
open import Cubical.HITs.PropositionalTruncation
using (squash; ∥_∥; ∣_∣; rec)
renaming (rec→Set to rec→set)
public
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------------------------------------------------------------------------
-- Lists with fast append
------------------------------------------------------------------------
module Data.DifferenceList where
open import Data.List as L using (List)
open import Data.Function
open import Data.Nat
infixr 5 _∷_ _++_
DiffLi... | {
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module FStream.Core where
------------------------------------------------------------------------
-- Core module of effectful streams
------------------------------------------------------------------------
open import Library
mutual
record FStream {i : Size} {ℓ₁ ℓ₂} (C : Container ℓ₁) (A : Set ℓ₂) : Set (ℓ₁ ⊔ ℓ₂... | {
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module lift-tests where
open import lib
open import cedille-types
open import convervsion
open import ctxt
open import lift
open import syntax-util
open import to-string
t0 = Lft posinfo-gen "X" (Parens posinfo-gen (mlam "x" (mlam "y" (mvar "y"))) posinfo-gen)
(LiftArrow (LiftStar posinfo-gen) (LiftArrow (Lift... | {
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-- 2012-03-08 Andreas
module NoTerminationCheck3 where
data Bool : Set where
true false : Bool
f : Bool -> Bool
f true = true
{-# NO_TERMINATION_CHECK #-}
f false = false
-- error: cannot place pragma inbetween clauses
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module Foundation.Primitive where
open import Agda.Primitive
infix -65536 ℞_
℞_ : ∀ ℓ → Set _
℞_ ℓ = Set ℓ
⟰ : Level → Level
⟰ = lsuc
infix -65536 ℞₁_
℞₁_ : ∀ ℓ → Set _
℞₁_ ℓ = ℞ ⟰ ℓ
𝟘 : Level
𝟘 = lzero
open import Agda.Primitive using (_⊔_) public
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{-# OPTIONS --safe #-}
module Cubical.Codata.EverythingSafe where
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module OscarEverything where
open import OscarPrelude
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.SphereEndomorphism
open import groups.Pointed
open import groups.SphereEndomorphism
open import groups.FromSusp
open import cohomology.Theory
module cohomology.SphereEndomorphism (CT : CohomologyTheory lzero) (n : ℤ) (m : ℕ) where
open C... | {
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{-# OPTIONS --rewriting #-}
module CF.Contexts.Rewriting where
open import Data.List
open import Data.List.Properties
open import Agda.Builtin.Equality.Rewrite
open import Relation.Binary.PropositionalEquality
open import CF.Types
++-assoc-← : ∀ (xs ys zs : List Ty) → xs ++ (ys ++ zs) ≡ (xs ++ ys) ++ zs
++-assoc-← =... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Examples showing how the reflective ring solver may be used.
------------------------------------------------------------------------
module README.Tactic.RingSolver where
-- You can ignore this bit! We're just... | {
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{-# OPTIONS --sized-types #-}
-- {-# OPTIONS -v tc.size.solve:100 -v tc.meta.new:50 #-}
module CheckSizeMetaBounds where
open import Common.Size
postulate
Size< : (_ : Size) → Set
{-# BUILTIN SIZELT Size< #-}
data Nat {i : Size} : Set where
zero : Nat
suc : {j : Size< i} → Nat {j} → Nat
one : Nat
one = suc {... | {
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-- The bug documented below was exposed by the fix to issue 274.
module Issue274 where
open import Common.Level
record Q a : Set (a ⊔ a) where
record R a : Set a where
field q : Q a
A : Set₁
A = Set
postulate
ℓ : Level
r : R (ℓ ⊔ ℓ)
foo : R ℓ
foo = r
-- Issue274.agda:32,7-8
-- ℓ ⊔ ℓ !=< ℓ of type Leve... | {
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{-# OPTIONS --copatterns #-}
module SplitResult where
open import Common.Product
test : {A B : Set} (a : A) (b : B) → A × B
test a b = {!!}
-- expected:
-- proj₁ (test a b) = {!!}
-- proj₂ (test a b) = {!!}
testFun : {A B : Set} (a : A) (b : B) → A × B
testFun = {!!}
-- expected:
-- testFun a b = {!!}
record FunRe... | {
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{-# OPTIONS --without-K --rewriting #-}
module lib.types.Suspension where
open import lib.types.Suspension.Core public
open import lib.types.Suspension.Flip public
open import lib.types.Suspension.Iterated public
open import lib.types.Suspension.IteratedFlip public
open import lib.types.Suspension.IteratedTrunc publi... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Rational numbers
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Rational where
open import Data.Integer as ℤ using (ℤ; +_)
open import D... | {
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module Data.Num.Redundant.Properties where
open import Data.Num.Bij
open import Data.Num.Redundant renaming (_+_ to _+R_)
open import Data.Nat renaming (_<_ to _<ℕ_)
open import Data.Nat.Etc
open import Data.Nat.Properties.Simple
open import Data.Sum
open import Data.List hiding ([_])
open import Relation.Nullary
op... | {
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-- Andreas, 2018-03-03, issue #2989
-- Internal error, fixable with additional 'reduce'.
-- {-# OPTIONS --show-implicit --show-irrelevant #-}
-- {-# OPTIONS -v tc.rec:70 -v tc:10 #-}
postulate
N : Set
P : N → Set
record Σ (A : Set) (B : A → Set) : Set where
constructor pair
field
fst : A
snd : B fst
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module Derivative where
open import Sets
open import Functor
import Isomorphism
∂ : U -> U
∂ (K A) = K [0]
∂ Id = K [1]
∂ (F + G) = ∂ F + ∂ G
∂ (F × G) = ∂ F × G + F × ∂ G
open Semantics
-- Plugging a hole
plug-∂ : {X : Set}(F : U) -> ⟦ ∂ F ⟧ X -> X -> ⟦ F ⟧ X
plug-∂ (K _) () x
pl... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.CommAlgebra where
open import Cubical.Algebra.CommAlgebra.Base public
open import Cubical.Algebra.CommAlgebra.Properties public
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-- Andreas, 2012-01-12
module Common.Irrelevance where
open import Common.Level
postulate
.irrAxiom : ∀ {a}{A : Set a} → .A → A
{-# BUILTIN IRRAXIOM irrAxiom #-}
record Squash {a}(A : Set a) : Set a where
constructor squash
field
.unsquash : A
open Squash public
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-- define ∑ and ∏ as the bigOps of a Ring when interpreted
-- as an additive/multiplicative monoid
{-# OPTIONS --safe #-}
module Cubical.Algebra.Ring.BigOps where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Data.Bool
open import Cubical.Data.Nat using (ℕ ; zer... | {
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module UpTo where
open import Level
open import Relation.Binary using (Rel; IsEquivalence)
open import Data.Product
open import Categories.Support.Equivalence
open import Categories.Category
open import Categories.2-Category
open import Categories.Functor
open import Categories.NaturalTransformation
renaming (id to ... | {
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open import Oscar.Prelude
open import Oscar.Class.IsDecidable
open import Oscar.Data.Fin
open import Oscar.Data.Decidable
open import Oscar.Data.Proposequality
module Oscar.Class.IsDecidable.Fin where
instance
IsDecidableFin : ∀ {n} → IsDecidable (Fin n)
IsDecidableFin .IsDecidable._≟_ ∅ ∅ = ↑ ∅
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------------------------------------------------------------------------------
-- Even predicate
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.LawvereTheories where
-- Category of Lawvere Theories
open import Level
open import Categories.Category.Core using (Category)
open import Categories.Functor.Cartesian using (CartesianF)
open import Categories.NaturalTransformation.NaturalIsomorph... | {
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module Oscar.Data.Maybe where
open import Data.Maybe public using (Maybe; nothing; just)
-- open import Oscar.Data.Maybe.Core public
-- --open import Data.Maybe public using (maybe)
-- -- open import Relation.Binary.PropositionalEquality
-- -- open import Data.Empty
-- -- unMaybe : ∀ {A : Set} {x y : A} {B : Set}... | {
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{-# OPTIONS --rewriting #-}
module CF.Transform.Compile.ToJVM.Rewriting where
open import Data.List.Properties
open import Data.List.Relation.Binary.Permutation.Propositional
open import Agda.Builtin.Equality.Rewrite
{-# REWRITE map-++-commute #-}
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.RingSolver.RawRing where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Sigma
open import Cubical.Data.Nat using (ℕ)
open import Cubical.Algebra.RingSolver.AlmostRing hiding (⟨_⟩)
private
variable
ℓ : Level
record RawR... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Finite.Fin.Construction.Poset where
open import Data.Nat using (ℕ; z≤n; s≤s)
open import Data.Sum
open import Data.Product using (Σ; _,_; _×_)
open import Data.Fin
open import Data.Fin.Patterns
open import Relation.Binary.PropositionalEquality as ≡
open ... | {
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-- Andreas, 2017-01-05, issue #2376
-- Ensure correct printing for termination error
-- {-# OPTIONS -v term.clause:30 #-}
postulate
id : ∀{a}{A : Set a} → A → A
A : Set
P : A → Set
f : {a : A} → P a → {b : A} → P b → Set
f = λ p → f (id p) -- id to prevent eta-contration before termination checking
-- Expect... | {
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{-# OPTIONS --cubical --safe #-}
module Algebra.Construct.Free.Semilattice.Relation.Unary.Any.Properties where
open import Prelude hiding (⊥; ⊤)
open import Algebra.Construct.Free.Semilattice.Eliminators
open import Algebra.Construct.Free.Semilattice.Definition
open import Cubical.Foundations.HLevels
open import Data... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.Structures.NAryOp where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Functions.FunExtEquiv
open import Cubical.Data.Nat
open import Cubical.Data.Vec
open import Cubical.Fo... | {
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{-# OPTIONS --safe #-}
module STLC.Denotational where
open import STLC.Syntax
open import STLC.Typing
open import Data.Nat using (ℕ; suc)
open import Data.Fin using (Fin) renaming (zero to fzero; suc to fsuc)
open import Data.Product using (_×_; _,_; proj₁; proj₂)
open import Data.Unit using (⊤; tt)
private
variabl... | {
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module Types.Tail1 where
open import Data.Fin
open import Data.Nat
open import Function using (_∘_)
open import Types.Direction
import Types.IND1 as IND
private
variable
n : ℕ
-- session types restricted to tail recursion
-- can be recognized by type of TChan constructor
data Type : Set
data SType (n : ℕ) : ... | {
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-- A Beth model of normal forms
open import Library hiding (_∈_; All)
module NfModel (Base : Set) where
import Formulas ; open module Form = Formulas Base
import Derivations; open module Der = Derivations Base
-- Beth model
-- A cover for Γ is the skeleton of a case tree that can be formed in Γ.
-- It contai... | {
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module Computability.Enumeration.Diagonal where
open import Computability.Prelude
open import Computability.Function
open import Computability.Data.Fin.Opposite
open import Computability.Data.Nat.Iteration
open import Computability.Enumeration.Base
open import Data.Nat using (_∸_; pred; ⌊_/2⌋; _≤_; _<_; s≤s; z≤n)
open... | {
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module Issue4869 where
open import Agda.Builtin.Nat
infix 4 _≤_
data _≤_ : Nat → Nat → Set where
z≤n : ∀ {n} → zero ≤ n
s≤s : ∀ {m n} (m≤n : m ≤ n) → suc m ≤ suc n
foo : 2 ≤ 1 → Nat
foo (s≤s ()) = 123
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module RecursiveInstanceSearch where
open import Common.Prelude
open import Common.Product
_&&_ : Bool → Bool → Bool
true && b = b
false && _ = false
record Eq (A : Set) : Set where
constructor eq
field
_==_ : A → A → Bool
open Eq {{...}} public
instance
eq-Bool : Eq Bool
eq-Bool = eq aux where
au... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Nullary relations (some core definitions)
------------------------------------------------------------------------
-- The definitions in this file are reexported by Relation.Nullary.
module Relation.Nullary.Cor... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Definition
open import Setoids.Orders.Partial.Definition
open import Setoids.Setoids
open import Functions.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Groups.Orders.Partial.Definition {n m : _} {A : Set n} {S : Set... | {
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-- This test case is aimed at checking that one can give RTS options
-- (as well as other options) using the Emacs mode. It does not test
-- backend options.
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.ZCohomology.MayerVietorisUnreduced where
open import Cubical.ZCohomology.Base
open import Cubical.ZCohomology.Properties
open import Cubical.ZCohomology.GroupStructure
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Function
ope... | {
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module Lib where
open import Data.List
open import Relation.Binary.PropositionalEquality
data _∧_ (A : Set) (B : Set) : Set where
∧-intro : A → B → (A ∧ B)
--------------------------------
-- Extension with Pairs and Sums
--------------------------------
--------------------------------
-- Basic Set-up
----------... | {
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module Base where
module Classes where
record LeastUpperBound {ℓ} (A : Set ℓ) : Set ℓ where
infixl 6 _⊔_
field
_⊔_ : A → A → A
open LeastUpperBound ⦃ … ⦄ public
record Successor {ℓ} (A : Set ℓ) : Set ℓ where
field
↑ : A → A
open Successor ⦃ … ⦄ public
module Primitive where
impo... | {
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-- exercises-01-monday.agda
open import Data.Nat
variable
A B C : Set
-- Exercise 1
add3 : ℕ → ℕ
add3 x = x + 3
tw : (A → A) → A → A
tw f n = f (f n) -- tw = λ f n → f (f n)
-- evaluate: "tw tw add3 1"; derive the result (in a comment) step by step
{-
tw tw add3 1 =
= tw (tw add3) 1 =
= (tw add3) (tw ad... | {
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module Issue840a where
------------------------------------------------------------------------
-- Prelude
record ⊤ : Set where
data ⊥ : Set where
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
data Bool : Set where
true false : Bool
{-# BUILTIN BOOL Bool #-}
{-# BUILTIN TRUE true #-}
{-# BUILTIN... | {
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open import Relation.Binary.Core
module PLRTree.Insert.Heap {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_)
(trans≤ : Transitive _≤_) where
open import Data.Sum
open import Order.Total _≤_ tot≤
open import PLRTree {A}
open import PLRTree.Compound {A} ... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Categories.Yoneda where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Univalence using (ua)
open import Cubical.Foundations.Function renaming ... | {
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open import Relation.Binary.Core
module PLRTree.Push.Complete {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import Data.Sum
open import Induction.WellFounded
open import PLRTree {A}
open import PLRTree.Drop _≤_ tot≤
open import PLRTree.Complete {A}
open imp... | {
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{-# OPTIONS --experimental-irrelevance #-}
module ShapeIrrelevantIndexNoBecauseOfRecursion where
data ⊥ : Set where
record ⊤ : Set where
constructor trivial
data Bool : Set where
true false : Bool
True : Bool → Set
True false = ⊥
True true = ⊤
data D : ..(b : Bool) → Set where
c : {b : Bool} → True b → D b
... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category.Monoidal.Structure
using (BraidedMonoidalCategory)
module Categories.Functor.Monoidal.Braided {o o′ ℓ ℓ′ e e′}
(C : BraidedMonoidalCategory o ℓ e) (D : BraidedMonoidalCategory o′ ℓ′ e′)
where
open import Level
open import Data.Product using (_,... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- The reflexive transitive closures of McBride, Norell and Jansson
--
-- This module is DEPRECATED. Please use the
-- Relation.Binary.Construct.Closure.ReflexiveTransitive module directly
--------------------------... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.types.Truncation
open import lib.types.TwoSemiCategory
open import lib.two-semi-categories.Functor
open import lib.two-semi-categories.FunctorInverse
open import lib.two-semi-categories.GroupToCategory
module lib.two-semi-categories.Fundam... | {
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module Basic.SmallStep where
import Data.Bool as Bool using (not)
open import Data.Bool hiding (not; if_then_else_)
open import Data.Empty
open import Data.Fin using (Fin; suc; zero; #_)
open import Data.Nat
open import Data.Nat.Properties.Simple
open import Data.Vec
open import Function
open import Relation.Binar... | {
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-- Andreas, 2015-09-18 Andreas, reported by Andrea
-- {-# OPTIONS -v impossible:10 #-}
-- {-# OPTIONS -v tc.cover.splittree:10 #-}
-- {-# OPTIONS -v tc.cc:30 #-}
open import Common.Bool
open import Common.Product
open import Common.Equality
postulate
A : Set
a : A
Works : A × A → Bool → A
Works (x , y) true = y
Wo... | {
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-- Andreas, 2013-10-30
-- Test whether verbosity options are honored before file is loaded.
-- See Issue641.flags
module Issue641 where
-- Provoke a scope checking error.
open NoSuchModule
-- Expected output is some debug messages about importing, plus the error,
-- like:
-- Getting interface for Issue641
-- C... | {
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{-# OPTIONS --no-positivity-check #-}
module STLC.Coquand.Completeness where
open import STLC.Coquand.Normalisation public
open import STLC.Coquand.Convertibility public
--------------------------------------------------------------------------------
data CV : ∀ {Γ A} → Γ ⊢ A → Γ ⊩ A → Set
where
cv⎵ : ∀ {Γ}... | {
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{-# OPTIONS --warning=error #-}
module UselessPrivatePragma where
postulate Char : Set
private
{-# BUILTIN CHAR Char #-}
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{- SAMPLE PROGRAMS IN SOURCE LANGUAGE -}
open import Preliminaries
open import Source
open import Pilot2
open import Translation
open import Interp
open import Preorder
module Samples where
s2r : ∀ {Γ τ} → Γ Source.|- τ → (el ([ (⟨⟨ Γ ⟩⟩c) ]c ->p [ (|| τ ||) ]t))
s2r p = interpE || p ||e
-- this works
{- db... | {
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{-# OPTIONS --without-K #-}
open import HoTT
module homotopy.HopfJunior where
-- We define the negation function and prove that it’s an equivalence
not : Bool → Bool
not true = false
not false = true
not-not : (b : Bool) → not (not b) == b
not-not true = idp
not-not false = idp
not-equiv : Bool ≃ Bool
not-equiv =... | {
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-- Andreas, Jesper, 2015-07-02 Error in copyScope
-- To trigger the bug, it is important that
-- the main module is in a subdirectory of the imported module.
module Issue1597.Main where
open import Issue1597 -- external import is needed
module B where
open A public -- public is needed
module C = B
postulate p... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Lists where at least one element satisfies a given property
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.List.Relation.Unary.Any {a} {A... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.Posets where
-- The category of partially ordered sets and order-preserving maps.
open import Level
open import Relation.Binary using (Poset; IsEquivalence; _Preserves_⟶_)
open import Relation.Binary.OrderMorphism using (_⇒-Poset_; id; _∘_)
open ... | {
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module Automaton.NonDeterministic where
import Lvl
open import Data.Boolean
import Data.Boolean.Operators
open Data.Boolean.Operators.Programming
open import Data.List using (List) renaming (∅ to ε ; _⊰_ to _·_)
open import Functional
open import Logic
open import Sets.ExtensionalPredicateSet
open imp... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Monoidal.Construction.Product where
-- The product A × B of (braided/symmetric) monoidal categories
-- A and B is again (braided/symmetric) monoidal.
open import Level using (_⊔_)
open import Data.Product using (_,_; dmap; zip; curry′; uncurry′)
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