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-- Andreas, May-July 2016, implementing postfix projections {-# OPTIONS --postfix-projections #-} open import Common.Product open import Common.Bool pair : ∀{A : Set}(a : A) → A × A pair a = {!!} -- C-c C-c here outputs postfix projections record BoolFun : Set where field out : Bool → Bool open BoolFun neg : Boo...
module _ where open import Issue1278.A Set open import Agda.Builtin.Equality test : (c : D) -> (c ≡ c) test d = {!!} -- goal ".#A-60005532.d ≡ .#A-60005532.d"
------------------------------------------------------------------------ -- Eliminators and initiality ------------------------------------------------------------------------ {-# OPTIONS --erased-cubical --safe #-} module Partiality-algebra.Eliminators where open import Equality.Propositional.Cubical open import Lo...
{-# OPTIONS --universe-polymorphism #-} module Categories.NaturalIsomorphism where open import Level open import Relation.Binary using (IsEquivalence) open import Categories.Support.PropositionalEquality open import Categories.Support.Equivalence open import Categories.Category open import Categories.Functor hiding ...
{-# OPTIONS --sized-types #-} module SizedTypesVarSwap where open import Common.Size renaming (↑_ to _^) data Nat : {size : Size} -> Set where zero : {size : Size} -> Nat {size ^} suc : {size : Size} -> Nat {size} -> Nat {size ^} bad : {i j : Size} -> Nat {i} -> Nat {j} -> Nat {∞} bad (suc x) y = bad (suc y) x...
module Sessions.Semantics.Communication {E : Set} (delay : E) where open import Prelude open import Data.List.Relation.Ternary.Interleaving open import Data.List.Relation.Ternary.Interleaving.Propositional open import Data.List.Relation.Equality.Propositional open import Data.List.Properties import Data.List as L op...
-- 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...
open import Level hiding ( suc ; zero ) open import Algebra module sym5a where open import Symmetric open import Data.Unit using (⊤ ; tt ) open import Function.Inverse as Inverse using (_↔_; Inverse; _InverseOf_) open import Function hiding (flip) open import Data.Nat hiding (_⊔_) -- using (ℕ; suc; zero) open import ...
-- Andreas, 2016-02-11, bug reported by sanzhiyan module Issue610-module-alias-with where import Common.Level open import Common.Equality data ⊥ : Set where record ⊤ : Set where data A : Set₁ where set : .Set → A module M .(x : Set) where .out : _ out = x .ack : A → Set ack (set x) = M.out x hah : set ⊤ ≡...
{- Agda Implementors' Meeting VI Göteborg May 24 - 30, 2007 Hello Agda! Ulf Norell -} -- Something which is rather useful is the ability to pattern match -- on intermediate computations. That's where the with-construct comes -- in. module Te...
{-# OPTIONS --safe #-} module Cubical.Categories.Abelian where open import Cubical.Categories.Abelian.Base public
{-# OPTIONS --cubical --safe #-} module Categories.Product where open import Prelude hiding (_×_) open import Categories module _ {ℓ₁ ℓ₂} (C : Category ℓ₁ ℓ₂) where open Category C module _ (X Y : Ob) where record Product : Type (ℓ₁ ℓ⊔ ℓ₂) where field obj : Ob proj₁ : C [ obj , X ] ...
{- This file contains: - Definition of groupoid quotients -} {-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.HITs.GroupoidQuotients.Base where open import Cubical.Foundations.Prelude open import Cubical.Relation.Binary.Base -- Groupoid quotients as a higher inductive type: -- For the definition, ...
module Bee2.Crypto.Belt where open import Data.ByteString open import Data.ByteVec open import Data.Nat using (ℕ) open import Data.Product using (_,_) open import Agda.Builtin.TrustMe using (primTrustMe) import Bee2.Crypto.Defs open Bee2.Crypto.Defs open Bee2.Crypto.Defs using (Hash) public {-# FOREIGN GHC import qu...
module Structure.Sets.Operator where open import Data.Boolean open import Data.Boolean.Stmt open import Functional import Lvl open import Logic open import Logic.Propositional open import Logic.Predicate open import Structure.Function open import Structure.Relator open import Structure.Setoid using (Equiv) renami...
module Base.Change.Sums where open import Data.Sum open import Data.Product open import Relation.Binary.PropositionalEquality open import Level open import Base.Ascription open import Base.Change.Algebra open import Base.Change.Equivalence open import Base.Change.Equivalence.Realizers open import Postulate.Extensiona...
------------------------------------------------------------------------ -- The Agda standard library -- -- This module is DEPRECATED. Please use -- Data.Product.Relation.Binary.Lex.Strict directly. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data...
{-# OPTIONS --without-K --safe #-} open import Categories.Category module Categories.Functor.Hom.Properties.Covariant {o ℓ e} (C : Category o ℓ e) where open import Level open import Function.Equality using (Π) open import Relation.Binary using (Setoid) open import Categories.Category.Construction.Cones open import...
module Issue947 where A : Set₁ A = Set where B : Set₁ B = Set module _ where C : Set₁ C = Set module M where
{-# OPTIONS --safe #-} module Cubical.Algebra.Module.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Equiv.HalfAdjoint open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.SIP open i...
{-# OPTIONS --without-K --safe #-} open import Level using (Level) open import Relation.Binary.PropositionalEquality using (_≡_; _≢_) open import Data.Nat using (ℕ; suc; zero) open import Data.Empty using (⊥) open import Data.Vec using (Vec) renaming ([] to []ⱽ; _∷_ to _∷ⱽ_) module FLA.Data.Vec+....
{- This file contains: - The inductive construction of James. -} {-# OPTIONS --safe #-} module Cubical.HITs.James.Inductive.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Pointed open import Cubical.Foundations.Equiv open import Cubical.Foundations.Isomorphism open import Cubica...
{-# OPTIONS --erased-cubical --safe #-} module Note where open import Data.Integer using (ℤ) open import Data.Nat using (ℕ; _+_; _*_; ⌊_/2⌋) open import Function using (_∘_) open import Pitch using (Pitch; transposePitch) open import Interval using (Upi; Opi; transposePitchInterval) Duration : Se...
------------------------------------------------------------------------ -- A solution to a problem posed by Venanzio Capretta ------------------------------------------------------------------------ module VenanziosProblem where open import Codata.Musical.Notation open import Codata.Musical.Stream as Stream using ...
{-# OPTIONS --without-K --rewriting #-} open import HoTT open import groups.KernelImage module groups.KernelImageEmap where module _ {i₀ i₁ j₀ j₁ k₀ k₁} {G₀ : Group i₀} {H₀ : Group j₀} {K₀ : Group k₀} {G₁ : Group i₁} {H₁ : Group j₁} {K₁ : Group k₁} {ψ₀ : H₀ →ᴳ K₀} {φ₀ : G₀ →ᴳ H₀} (H₀-ab : is-abelian H₀) {ψ₁ ...
module WErrorOverride where postulate IO : Set → Set {-# COMPILED_TYPE IO IO #-} {-# BUILTIN IO IO #-} infixl 1 _>>=_ postulate return : {A : Set} → A → IO A _>>=_ : {A : Set} {B : Set} → IO A → (A → IO B) → IO B {-# COMPILED return (\_ -> return) #-} {-# COMPILED _>>=_ (\_ _ -> (>>=)) #-} ------------...
------------------------------------------------------------------------ -- The Agda standard library -- -- This module is DEPRECATED. Please use -- Data.Vec.Relation.Unary.All.Properties directly. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data....
{-# OPTIONS --prop --rewriting #-} module Examples where -- Sequential import Examples.Id import Examples.Gcd import Examples.Queue -- Parallel import Examples.TreeSum import Examples.Exp2 -- Hybrid import Examples.Sorting
{-# OPTIONS --without-K --rewriting #-} open import HoTT import homotopy.ConstantToSetExtendsToProp as ConstExt open import homotopy.RibbonCover module homotopy.GroupSetsRepresentCovers {i} (X : Ptd i) {{_ : is-connected 0 (de⊙ X)}} where open Cover private A : Type i A = de⊙ X a₁ : A a₁ = pt ...
{-# OPTIONS --sized-types #-} open import Relation.Binary.Core module Quicksort.Correctness.Order {A : Set} (_≤_ : A → A → Set) (tot≤ : Total _≤_) (trans≤ : Transitive _≤_) where open import Data.List open import Function using (_∘_) open import List.Sorted _≤_ o...
------------------------------------------------------------------------ -- Adjunctions and monads (for 1-categories) ------------------------------------------------------------------------ -- The code is based on the presentation in the HoTT book (but might -- not follow it exactly). {-# OPTIONS --without-K --safe ...
open import Common.Equality data Bool : Set where true false : Bool data IsTrue : Bool → Set where itis : IsTrue true module M (u : Bool) where foo bar : (p : IsTrue u) → Bool foo = \ { itis → true } bar = \ { itis → false } test : ∀ u → M.foo u ≡ M.bar u test u = refl -- Trigger printing of the extende...
module MultipleFixityDecl where infixl 40 _+_ infixr 60 _+_ _+_ : Set -> Set -> Set A + B = A
module Tactic.Reflection.Meta where open import Prelude open import Builtin.Reflection open import Tactic.Reflection.DeBruijn ensureNoMetas : Term → TC ⊤ noMetaArg : Arg Term → TC ⊤ noMetaArg (arg _ v) = ensureNoMetas v noMetaArgs : List (Arg Term) → TC ⊤ noMetaArgs [] = pure _ noMetaArgs (v ∷ vs) = noMetaArg v *>...
-------------------------------------------------------------------------------- -- This file provides the generateCFG function that turns a list of strings of -- the current syntax for grammars into a grammar as defined in Parser.agda -------------------------------------------------------------------------------- {-...
-- 2010-10-05 Andreas module TerminationRecordPatternLie where data Empty : Set where record Unit : Set where data Bool : Set where true false : Bool T : Bool -> Set T true = Unit T false = Empty -- Thorsten suggests on the Agda list thread "Coinductive families" -- to encode lists as records record List (A : ...
------------------------------------------------------------------------ -- The Agda standard library -- -- Lexicographic products of binary relations ------------------------------------------------------------------------ -- The definition of lexicographic product used here is suitable if -- the left-hand relation i...
{- Verified Koopa Troopa Movement Toon Nolten -} module koopa where open import Data.Nat open import Data.Fin renaming (_+_ to _F+_; _<_ to _F<_; suc to fsuc; zero to fzero) open import Data.Vec renaming (map to vmap; lookup to vlookup; replicate to vre...
module Equality where open import Agda.Builtin.Equality public open import Relation.Nullary infix 4 _≅_ _≢_ infixr 2 _≡⟨_⟩_ infix 3 _QED data _≅_ {ℓ} {A : Set ℓ} (x : A) : {B : Set ℓ} → B → Set ℓ where refl : x ≅ x ≡→≅ : ∀ {ℓ} {A : Set ℓ} {a b : A} → a ≡ b → a ≅ b ≡→≅ refl = refl sym : ∀ {ℓ} {A : Set ℓ} {a b :...
{-# OPTIONS --safe #-} module JVM.Model {ℓ} (T : Set ℓ) where open import Level hiding (Lift) open import Data.Product open import Data.Unit open import Data.List open import Relation.Binary.PropositionalEquality using (_≡_; refl) open import Relation.Ternary.Core open import Relation.Ternary.Structures open import ...
open import OutsideIn.Prelude open import OutsideIn.X module OutsideIn.Environments(x : X) where open import Data.Vec hiding (map) import OutsideIn.TypeSchema as TS import OutsideIn.Expressions as E open TS(x) open E(x) open X(x) private module TS-f {x} = Functor(type-schema-is-functor {x}) Env...
------------------------------------------------------------------------ -- The Agda standard library -- -- An inductive definition of the sublist relation. This is commonly -- known as Order Preserving Embeddings (OPE). ------------------------------------------------------------------------ {-# OPTIONS --without-K -...
module Verifier where open import Definitions open import DeMorgan using (deMorgan) check : {A B : Set} → ¬ A ∧ ¬ B → ¬ (A ∨ B) check = deMorgan
-- Let's play with agda. -- Am i having fun doing this? @KMx404 module intro where --load the file with C-c - like that data Bool: Set where true : Bool false : Bool data Empty: Set Empty Empty : Empty -- I'm gonna leave this here. Moving to tests
module Issue2858-nbe where open import Agda.Builtin.List data Ty : Set where α : Ty _↝_ : Ty → Ty → Ty variable σ τ : Ty Γ Δ Θ : List Ty Scoped : Set₁ Scoped = Ty → List Ty → Set data Var : Scoped where z : Var σ (σ ∷ Γ) s : Var σ Γ → Var σ (τ ∷ Γ) record Ren (Γ Δ : List Ty) : Set where field lookup...
{-# OPTIONS --without-K #-} -- Rending the Program Runner -- A proof of Lӧb′s theorem: quoted interpreters are inconsistent -- Jason Gross {- Title and some comments inspired by and drawn heavily from "Scooping the Loop Sniffer: A proof that the Halting Problem is undecidable", by Geoffrey K. Pullum (http://w...
open import Data.Product using ( _,_ ; proj₁ ; proj₂ ) open import Data.Sum using ( _⊎_ ; inj₁ ; inj₂ ) open import Relation.Binary.PropositionalEquality using ( refl ) open import Relation.Unary using ( _∈_ ) open import Web.Semantic.DL.ABox using ( ABox ; _,_ ; ⟨ABox⟩ ) open import Web.Semantic.DL.ABox.Interp using (...
open import Relation.Ternary.Separation module Relation.Ternary.Separation.Monad.CompleteUpdate {a} {A : Set a} {{r : RawSep A}} {u} {{ s : IsUnitalSep r u }} where open import Function open import Level hiding (Lift) open import Data.Product open import Data.Unit using (⊤) open import Relation.Unary open import...
--{-# OPTIONS --verbose 10 #-} open import ExtractSac as ES using () open import Extract (ES.kompile-fun) open import Data.Nat as N using (ℕ; zero; suc; _≤_; _≥_; _<_; s≤s; z≤n) import Data.Nat.DivMod as N open import Data.Nat.Properties as N open import Data.List as L using (List; []; _∷_) open import Data.Vec a...
module New.Unused where open import New.Changes module _ {ℓ₁} {ℓ₂} {A : Set ℓ₁} {B : Set ℓ₂} {{CA : ChAlg A}} {{CB : ChAlg B}} where open ≡-Reasoning open import Postulate.Extensionality module _ (f : A → B) where nil-is-derivative : IsDerivative f (nil f) nil-is-derivative a da v = begin ...
{-# OPTIONS --safe --without-K #-} open import Relation.Binary.PropositionalEquality using (refl) open import Relation.Nullary using (yes) open import Data.Unit using (⊤; tt) open import Data.Product using (_,_) open import Data.Sum using (inj₁) open import PiCalculus.LinearTypeSystem.Algebras module PiCalculus.Lin...
{-# OPTIONS --without-K #-} open import container.core module container.w.fibration {li la lb}(c : Container li la lb) where open import sum open import equality open import function open import container.w.core open import container.w.algebra c open import hott.level open Container c AlgFib : ∀ ℓ → Set _ AlgFib ...
open import FRP.JS.String using ( _≟_ ) open import FRP.JS.Bool using ( Bool ; true ; false ; if_then_else_ ; _∧_ ; _∨_ ; not ; _xor_ ) open import FRP.JS.QUnit using ( TestSuite ; ok ; test ; _,_ ) module FRP.JS.Test.Bool where tests : TestSuite tests = ( test "true" ( ok "true" true ) , test "false" ...
{-# OPTIONS --without-K --exact-split #-} import 05-identity-types open 05-identity-types public -- Inversion is uninteresting and comes from: inversion-proof : {i : Level} {A : UU i} (x : A) → (y : A) → Id x y → Id y x inversion-proof x y = ind-Id x (λ y' p' → Id y' x) refl y lemma-2-2-2-i : {i j : Level} {A : ...
module Semantics.Substitution where open import Semantics.Substitution.Kits public open import Semantics.Substitution.Traversal public open import Semantics.Substitution.Instances public open import Semantics.Substitution.Soundness public
{-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-# OPTIONS --without-K #-} module Verification.CorruptFormalisations where open import FOTC.Base open import FOTC.Base.List open import FOTC.Base.Loop open import FOTC.Progr...
{-# OPTIONS --without-K #-} open import lib.Basics open import lib.types.Span open import lib.types.Pointed open import lib.types.Pushout open import lib.types.PushoutFlattening open import lib.types.Unit open import lib.types.Paths open import lib.cubical.Square -- Suspension is defined as a particular case of pusho...
module BBHeap.Properties {A : Set}(_≤_ : A → A → Set) where open import BBHeap _≤_ open import BBHeap.Perfect _≤_ open import Bound.Lower A open import Bound.Lower.Order _≤_ open import Data.Empty sym≃ : {b b' : Bound}{h : BBHeap b}{h' : BBHeap b'} → h ≃ h' → h' ≃ h sym≃ ≃lf = ≃lf sym≃ (≃nd b≤x b'≤x' l⋘r l'⋘r' l≃r ...
module IncompletePatternMatching where data Nat : Set where zero : Nat suc : Nat -> Nat data True : Set where tt : True data False : Set where _==_ : Nat -> Nat -> Set zero == zero = True suc n == suc m = n == m thm : zero == suc zero thm = tt
-- Idiom bracket notation. module Syntax.Idiom where import Lvl open import Type private variable ℓ ℓ₁ ℓ₂ : Lvl.Level private variable A B : Type{ℓ} private variable F : Type{ℓ₁} → Type{ℓ₂} -- The notation `⦇ f x₁ x₂ x₃ ⦈` will automatically be translated to `((pure f <*> x₁) <*> x₂) <*> x₃`. record IdiomBracke...
open import Prelude open import Nat open import dynamics-core open import contexts open import lemmas-disjointness module exchange where -- exchanging just two disequal elements produces the same context swap-little : {A : Set} {x y : Nat} {τ1 τ2 : A} → (x ≠ y) → ((■ (x , τ1)) ,, (y , τ2)) == ((■ (y , τ2)) ,, ...
{-# OPTIONS --safe #-} module Cubical.Relation.Nullary where open import Cubical.Relation.Nullary.Base public open import Cubical.Relation.Nullary.Properties public
-- Andreas, 2018-10-16, erased lambda-arguments open import Agda.Builtin.List open import Common.Prelude sum : List Nat → Nat sum (x ∷ xs) = x + sum xs sum [] = 0 zipWith : {A B C : Set} (f : A → B → C) → List A → List B → List C zipWith f (x ∷ xs) (y ∷ ys) = f x y ∷ zipWith f xs ys zipWith _ _ _ = [] -- Shorten th...
-- Andreas, 2014-09-23 syntax bla (λ x → e) = blub e -- Should trigger error: -- malformed syntax declaration: syntax must use binding holes exactly once
------------------------------------------------------------------------ -- The Agda standard library -- -- Some unit types ------------------------------------------------------------------------ -- The definitions in this file are reexported by Data.Unit. module Data.Unit.Core where open import Level ------------...
{-# OPTIONS --warning=error #-} module UselessAbstractPrimitive where postulate Int : Set {-# BUILTIN INTEGER Int #-} abstract primitive primIntegerPlus : Int -> Int -> Int
------------------------------------------------------------------------------ -- Distributive laws properties ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} ...
module Data.Vec.All.Properties.Extra {a p}{A : Set a}{P : A → Set p} where open import Data.List using (List) import Data.List.Relation.Unary.All as All open import Data.Vec hiding (_[_]≔_) open import Data.Vec.Relation.Unary.All hiding (lookup) open import Data.Fin all-fromList : ∀ {xs : List A} → All.All P xs → All...
open import Relation.Unary using ( ∅ ; _∪_ ) open import Web.Semantic.DL.Concept using ( Concept ) open import Web.Semantic.DL.Role using ( Role ) open import Web.Semantic.DL.Signature using ( Signature ) open import Web.Semantic.Util using ( Subset ; ⁅_⁆ ) module Web.Semantic.DL.TBox where infixl 5 _⊑₁_ _⊑₂_ infixr ...
---------------------------------------------------------------------------------- -- Types for parse trees ---------------------------------------------------------------------------------- module cws-types where open import lib open import parse-tree posinfo = string {-# FOREIGN GHC import qualified CedilleCommen...
module Cats.Profunctor where open import Data.Product using (_,_) open import Level using (suc ; _⊔_) open import Cats.Category open import Cats.Category.Op using (_ᵒᵖ) open import Cats.Category.Product.Binary using (_×_) open import Cats.Category.Setoids using (Setoids) open import Cats.Functor import Cats.Category...
-- There was a rare bug in display form generation for with functions -- in local blocks. module WithInWhere where data Nat : Set where zero : Nat suc : Nat -> Nat data Z? : Nat -> Set where yes : Z? zero no : forall {n} -> Z? (suc n) z? : (n : Nat) -> Z? n z? zero = yes z? (suc n) = no bug : Nat -> N...
module Cats.Category.Preorder.Facts.PreorderAsCategory where open import Data.Bool using (true ; false) open import Relation.Binary using (Preorder) import Level open import Cats.Category open import Cats.Category.Preorder using (preorderAsCategory) open import Cats.Util.Logic.Constructive module _ {lc l≈ l≤} (P :...
{-# OPTIONS --safe #-} module Cubical.Data.FinType where open import Cubical.Data.FinType.Base public open import Cubical.Data.FinType.Properties public
{-# OPTIONS --cubical --safe --postfix-projections #-} open import Prelude open import Relation.Binary module Data.List.Mapping {kℓ} {K : Type kℓ} {r₁ r₂} (totalOrder : TotalOrder K r₁ r₂) where open import Relation.Binary.Construct.Decision totalOrder open import Relation.Binary.Construct.LowerBound dec-ord open im...
{-# OPTIONS --rewriting #-} module Interpreter where open import Agda.Builtin.IO using (IO) open import Agda.Builtin.Int using (pos) open import Agda.Builtin.Unit using (⊤) open import FFI.IO using (getContents; putStrLn; _>>=_; _>>_) open import FFI.Data.Aeson using (Value; eitherDecode) open import FFI.Data.Either...
{-# OPTIONS --without-K --rewriting #-} open import HoTT open import homotopy.PtdMapSequence module homotopy.CofiberSequence {i} where {- Useful abbreviations -} module _ {X Y : Ptd i} (f : X ⊙→ Y) where ⊙Cofiber² = ⊙Cofiber (⊙cfcod' f) ⊙cfcod²' = ⊙cfcod' (⊙cfcod' f) ⊙Cofiber³ = ⊙Cofiber ⊙cfcod²' ⊙cfcod³' ...
open import FRP.JS.Behaviour using ( Beh ; [_] ; hold ) open import FRP.JS.Event using ( tag ) open import FRP.JS.DOM using ( DOM ; text ; element ; listen ; click ; _++_ ) open import FRP.JS.RSet using ( ⟦_⟧ ) module FRP.JS.Demo.Button where main : ∀ {w} → ⟦ Beh (DOM w) ⟧ main = text lab ++ but where but = element...
module _ where module A where infixr 5 _∷_ data D : Set₂ where [] : D _∷_ : Set₁ → D → D module B where infix 5 _∷_ data D : Set₂ where _∷_ : Set₁ → Set₁ → D open A open B foo : A.D foo = Set ∷ [] bar : B.D bar = Set ∷ Set
{-# OPTIONS --without-K --exact-split --safe #-} module Basic_Types where -- Already in the builtin's of agda, there are Π types, which is ∀, and lambda -- abstraction, which is λ{ } and function types, which is →. -- ------------------------------------ -- Some operations for function types -- The curly brackts ∀{...
------------------------------------------------------------------------ -- The Agda standard library -- -- Properties of products ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Product.Properties where open import Data.Product open import Func...
module Options-in-right-order where data Unit : Set where unit : Unit postulate IO : Set → Set {-# COMPILE GHC IO = type IO #-} {-# BUILTIN IO IO #-} postulate return : {A : Set} → A → IO A {-# COMPILE GHC return = \_ -> return #-} main = return unit
{-# OPTIONS --without-K --safe #-} open import Categories.Category module Categories.Object.Subobject {o ℓ e} (𝒞 : Category o ℓ e) where open import Level open import Data.Product open import Data.Unit open import Relation.Binary using (Poset) open import Categories.Functor open import Categories.Category.Slice o...
{-# OPTIONS --cubical --save-metas #-} -- The code in this module should not be compiled. However, the -- following re-exported code should be compiled. open import Agda.Builtin.Bool public postulate easy : {A : Set} → A data Not-compiled : Set where
module Bee2.Crypto.Defs where open import Data.ByteString open import Data.ByteVec open import Agda.Builtin.Nat renaming (Nat to ℕ) {-# FOREIGN GHC import qualified Bee2.Defs #-} postulate SizeT : Set SizeFromℕ : ℕ → SizeT {-# COMPILE GHC SizeT = type (Bee2.Defs.Size) #-} {-# COMPILE GHC SizeFromℕ = ( Prel...
module std-reduction.Properties where open import std-reduction open import sn-calculus open import Relation.Binary.PropositionalEquality using (_≡_) open _≡_ {- std-redution-deterministic : ∀{p q r} → p ⇁ q → p ⇁ r → q ≡ r std-re...
open import Agda.Builtin.Size record R (A : Size → Set) (i : Size) : Set where field force : (j : Size< i) → A j data D (A : Size → Set) (i : Size) : Set where c : R A i → D A i postulate P : (A : Size → Set) → D A ∞ → D A ∞ → Set F : (Size → Set) → Set F A = (x : A ∞) (y : D A ∞) → P _ (c (record {...
module Screen where import Data.Nat import Data.Bool import Data.List import Logic.Base open Data.Bool open Data.List open Data.Nat open Logic.Base -- Ranges ----------------------------------------------------------------- data Range : Set where range : Nat -> Nat -> Range inRange : Range -> Nat -> Bool inRang...
{-# OPTIONS --without-K #-} -- Approx. 15-20 min are required to typecheck this file (for Agda 2.6.1) on -- my MacBook 13-inch 2017 with 3.5 GHz Core i7 CPU and 16 GB memory. -- -- Since most of the time was spent for termination analysis, please -- uncomment {-# TERMINATING #-} before evalR and eval to remove the -...
module Oscar.Data.Equality.properties where -- open import Relation.Binary.PropositionalEquality public using (cong; cong₂; cong-app; subst; subst₂; sym; trans) -- open import Oscar.Data.Equality -- open import Oscar.Function -- open import Oscar.Level -- open import Oscar.Relation -- -- ≡̇-refl : ∀ {a} {A : Set a}...
{-# OPTIONS --with-K #-} module Agda.Builtin.Equality.Erase where open import Agda.Builtin.Equality primitive primEraseEquality : ∀ {a} {A : Set a} {x y : A} → x ≡ y → x ≡ y
module Data.Num.Bounded where open import Data.Num.Core open import Data.Num.Maximum open import Data.Nat open import Data.Nat.Properties open import Data.Nat.Properties.Simple open import Data.Nat.Properties.Extra open import Data.Fin as Fin using (Fin; fromℕ≤; inject≤) renaming (zero to z; suc to s) open ...
------------------------------------------------------------------------ -- The Agda standard library -- -- Some derivable properties ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Algebra.Bundles module Algebra.Properties.DistributiveLattice ...
data ⊥ : Set where postulate M : Set → Set A : Set _>>=_ : ∀ {A B} → M A → (A → M B) → M B ma : M A f : A → M ⊥ pure : ∀ {A} → A → M A absurd-do : ∀ {A} → M A absurd-do = do x ← ma () ← f x atabsurd-do : ∀ {A} → M A atabsurd-do = do x ← ma (y@()) ← f x -- I don't know why you would do that...
-- Andreas, 2017-03-27, issue #2183 -- Better error message for splitting on non-visible dot pattern. open import Agda.Builtin.Equality open import Agda.Builtin.Nat data Fin : Nat → Set where fzero : ∀ n → Fin (suc n) test : ∀ n (i : Fin n) → Set test n (fzero m) = {!n!} -- C-c C-c -- Current error: -- Cannot s...
module Formalization.ClassicalPropositionalLogic.Place where open import Data.Boolean open import Data.Tuple as Tuple using (_,_ ; _⨯_) import Lvl open import Formalization.ClassicalPropositionalLogic.Syntax open import Functional as Fn using (_∘_ ; const) open import Sets.PredicateSet using (PredSet) open import...
--------------------------------------------------------------------------- -- Normalization by Evaluation for Intuitionistic Propositional Logic -- -- We employ a monadic interpreter for the soundness part, -- and a special class of monads, called cover monads, -- for the completeness part. -- -- Normalization is comp...
module M where Foo : Set Foo = Set
{-# OPTIONS --safe --without-K #-} module Data.List.Membership.Propositional.Distinct where open import Data.List using (List) import Relation.Binary.PropositionalEquality as P open import Data.List.Membership.Setoid.Distinct as D hiding (Distinct) public Distinct : ∀ {a} {A : Set a} → List A → Set a Distinct {A = A}...
module Inst (Gnd : Set)(U : Set)(El : U -> Set) where open import Basics open import Pr open import Nom import Kind open Kind Gnd U El import Cxt open Cxt Kind import Loc open Loc Kind import Term open Term Gnd U El import Shift open Shift Gnd U El mutual winst : {G : Cxt}{C : Kind}{L : Loc}{I : Kind} (x ...