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data Unit : Set where unit : Unit P : Unit β†’ Set P unit = Unit postulate Q : (u : Unit) β†’ P u β†’ Set variable u : Unit p : P u postulate q : P u β†’ Q u p q' : (u : Unit) (p : P u) β†’ P u β†’ Q u p q' u p = q {u} {p}
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data β„• : Set where zero : β„• suc : β„• β†’ β„• {-# BUILTIN NATURAL β„• #-} infixl 6 _+_ infix 6 _∸_ _+_ : β„• β†’ β„• β†’ β„• zero + n = n suc m + n = suc (m + n) _∸_ : β„• β†’ β„• β†’ β„• m ∸ zero = m zero ∸ suc n = zero suc m ∸ suc n = m ∸ n should-be-rejected : β„• should-be-rejected = 1 + 0 ∸ 1
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-- {-# OPTIONS -v term:20 #-} -- Andreas, 2011-04-19 (Agda list post by Leonard Rodriguez) module TerminationSubExpression where infixr 3 _⇨_ data Type : Set where int : Type _⇨_ : Type β†’ Type β†’ Type test : Type β†’ Type test int = int test (Ο† ⇨ int) = test Ο† test (Ο† ⇨ (Ο†β€² ⇨ Ο†β€³)) = test (Ο†β€² ⇨ Ο†β€³) -- this should ...
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{-# OPTIONS --safe --warning=error --without-K #-} open import Sets.EquivalenceRelations open import Setoids.Setoids open import Functions.Definition open import Groups.Definition open import Groups.Homomorphisms.Definition open import Groups.Subgroups.Definition open import Groups.Subgroups.Normal.Definition module ...
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{-# BUILTIN NATURAL β„• #-} module the-naturals where import Relation.Binary.PropositionalEquality as Eq open Eq using (_≑_; refl) open Eq.≑-Reasoning using (begin_; _β‰‘βŸ¨βŸ©_; _∎) infixl 6 _+_ _∸_ infixl 7 _*_ -- the naturals data β„• : Set where zero : β„• suc : β„• β†’ β„• -- addition _+_ : β„• β†’ β„• β†’ β„• zero + n = n (suc ...
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module Category.Functor.Arr where open import Agda.Primitive using (_βŠ”_) open import Category.Functor using (RawFunctor ; module RawFunctor ) open import Category.Applicative using (RawApplicative; module RawApplicative) open import Function using (_∘_) open import Category.Functor.Lawful open import Relation...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Universe levels ------------------------------------------------------------------------ module Level where -- Levels. open import Agda.Primitive public using (Level; _βŠ”_) renaming (lzero to zero; lsuc ...
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{-# OPTIONS --without-K #-} open import lib.Basics open import lib.NConnected open import lib.types.Nat open import lib.types.TLevel open import lib.types.Empty open import lib.types.Group open import lib.types.Pi open import lib.types.Pointed open import lib.types.Paths open import lib.types.Sigma open import lib.typ...
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open import Prelude module Implicits.Syntax.Term where open import Implicits.Syntax.Type infixl 9 _[_] _Β·_ data Term (Ξ½ n : β„•) : Set where var : (x : Fin n) β†’ Term Ξ½ n Ξ› : Term (suc Ξ½) n β†’ Term Ξ½ n Ξ»' : Type Ξ½ β†’ Term Ξ½ (suc n) β†’ Term Ξ½ n _[_] : Term Ξ½ n β†’ Type Ξ½ β†’ Term Ξ½ n _Β·_ : Term Ξ½ n β†’ Term Ξ½ n ...
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-} module Light.Library where module Literals where open import Light.Literals public module Data where module Empty where open import Light.Library.Data.Empty public module Either where open import Light.Library.Data.Either pub...
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{-# OPTIONS --safe #-} module Cubical.Algebra.CommRing.Instances.Polynomials where open import Cubical.Foundations.Prelude open import Cubical.Algebra.CommRing open import Cubical.Algebra.Polynomials private variable β„“ : Level Poly : (CommRing β„“) β†’ CommRing β„“ Poly R = (PolyMod.Poly R) , str where o...
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module empty where open import level ---------------------------------------------------------------------- -- datatypes ---------------------------------------------------------------------- data βŠ₯ {β„“ : Level} : Set β„“ where ---------------------------------------------------------------------- -- syntax ----------...
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-- Andreas, 2015-08-11, issue reported by G.Allais -- The `a` record field of `Pack` is identified as a function -- (coloured blue, put in a \AgdaFunction in the LaTeX backend) -- when it should be coloured pink. -- The problem does not show up when dropping the second record -- type or removing the module declaration...
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{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Data.Nat.GCD where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Function open import Cubical.Foundations.HLevels open import Cubical.Foundations.Equiv open import Cubical.Foundations.Isomorphism open import Cubical.Induction....
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{-# OPTIONS --prop --without-K --rewriting #-} module Calf.Types.Bool where open import Calf.Prelude open import Calf.Metalanguage open import Data.Bool public using (Bool; true; false; if_then_else_) bool : tp pos bool = U (meta Bool)
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{-# OPTIONS --safe #-} module MissingDefinition where T : Set -> Set
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{- Cubical Agda with K This file demonstrates the incompatibility of the --cubical and --with-K flags, relying on the well-known incosistency of K with univalence. The --safe flag can be used to prevent accidentally mixing such incompatible flags. -} {-# OPTIONS --with-K #-} module Cubical.WithK where open import...
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module WrongNamedArgument2 where postulate f : {A : Set₁} β†’ A test : Set test = f {B = Set} -- Unsolved meta. -- It is not an error since A could be instantiated to a function type -- accepting hidden argument with name B.
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------------------------------------------------------------------------ -- The Agda standard library -- -- Argument information used in the reflection machinery ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Reflection.Argument.Information where op...
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{-# OPTIONS --rewriting #-} module FFI.Data.Vector where open import Agda.Builtin.Equality using (_≑_) open import Agda.Builtin.Equality.Rewrite using () open import Agda.Builtin.Int using (Int; pos; negsuc) open import Agda.Builtin.Nat using (Nat) open import Agda.Builtin.Bool using (Bool; false; true) open import F...
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open import Function using (_∘_) open import Category.Functor open import Category.Monad open import Data.Empty using (βŠ₯; βŠ₯-elim) open import Data.Fin as Fin using (Fin; zero; suc) open import Data.Fin.Props as FinProps using () open import Data.Maybe as Maybe using (Maybe; maybe; just; nothing) open import Data.Nat us...
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{-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.ZCohomology.RingStructure.GradedCommutativity where open import Cubical.Foundations.HLevels open import Cubical.Foundations.Function open import Cubical.Foundations.Transport open import Cubical.Foundations.Prelude open import Cubical.Foundations.I...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Divisibility ------------------------------------------------------------------------ module Data.Nat.Divisibility where open import Data.Nat as Nat open import Data.Nat.DivMod import Data.Nat.Properties as Nat...
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------------------------------------------------------------------------ -- An alternative (non-standard) classical definition of weak -- bisimilarity ------------------------------------------------------------------------ -- This definition is based on the function "wb" in Section 6.5.1 of -- Pous and Sangiorgi's "E...
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------------------------------------------------------------------------------ -- Properties related with the group commutator ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-p...
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-- 2014-01-01 Andreas, test case constructed by Christian Sattler {-# OPTIONS --allow-unsolved-metas #-} -- unguarded recursive record record R : Set where constructor cons field r : R postulate F : (R β†’ Set) β†’ Set q : (βˆ€ P β†’ F P) β†’ (βˆ€ P β†’ F P) q h P = h (Ξ» {(cons x) β†’ {!!}}) -- ISSUE WAS: Bug in implement...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Examples of format strings and printf ------------------------------------------------------------------------ {-# OPTIONS --safe --without-K #-} module README.Text.Printf where open import Data.Nat.Base open ...
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module Inference-of-implicit-function-space where postulate _⇔_ : Set β†’ Set β†’ Set equivalence : {A B : Set} β†’ (A β†’ B) β†’ (B β†’ A) β†’ A ⇔ B A : Set P : Set P = {x : A} β†’ A ⇔ A works : P ⇔ P works = equivalence (Ξ» r {x} β†’ r {x = x}) (Ξ» r {x} β†’ r {x = x}) worksβ‚‚ : P ⇔ P worksβ‚‚ = equivalence {A = P...
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{-# OPTIONS --safe #-} open import Definition.Typed.EqualityRelation module Definition.LogicalRelation.Substitution.Introductions.Transp {{eqrel : EqRelSet}} where open EqRelSet {{...}} open import Definition.Untyped as U hiding (wk) open import Definition.Untyped.Properties open import Definition.Typed open import ...
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-------------------------------------------------------------------------------- -- This is part of Agda Inference Systems {-# OPTIONS --sized-types --guardedness #-} open import Data.Product open import Data.Vec open import Codata.Colist as Colist open import Agda.Builtin.Equality open import Size open import Codata...
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{-# OPTIONS --cubical-compatible #-} open import Common.Prelude open import Common.Equality open import Common.Product data _β‰…_ {A : Set} (a : A) : {B : Set} (b : B) β†’ Set₁ where refl : a β‰… a data D : Bool β†’ Set where x : D true y : D false P : Set -> Set₁ P S = Ξ£ S (\s β†’ s β‰… x) pbool : P (D true) pbool = _...
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