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  • RawApplicative to Applicative RawApplicative to Applicative id app f Applicative f id id app rawIApplicative where open Monad Id IdentityMonad a b A Set a n B Set b Set N ary level a b n A n B N ary n A B A Set n B Set Set A zero B B A suc n B A A n B A Set n B Set Set A zero

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Function.NP.html (2015-10-11)
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  • suc injective refl refl x y Bool zero zero true zero suc false suc zero false suc m suc n m n module where m n Set m n T m n subst Substitutive subst zero zero id subst P suc suc p subst P suc p subst zero suc subst suc zero sound m n T m n m n sound m n p subst m p refl refl Reflexive refl zero refl suc n refl n sym Symmetric sym m n eq rewrite sound m n eq refl n trans Transitive trans m n o m n n o rewrite sound m n m n sound n o n o refl o setoid Setoid setoid record Carrier isEquivalence record refl λ x refl x sym λ x y sym x y trans λ x y z trans x y z open Setoid setoid public hiding refl sym trans x y Bool zero true suc zero false suc m suc n m n module where sound m n T m n m n sound zero z n sound suc m suc n p s s sound m n p sound suc m zero complete m n m n T

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Data.Nat.NP.html (2015-10-11)
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  • A pure const an alias for pure K a A Set a Set K pure Cmp F Set i j Ix Set Cmp F i j F i F j Bool Π f g F Set f G i F i Set g Set Π F G i x F i G x i this version used to work type checking its uses better than that infixr 0 f g F Set f G Set g Set f g F G Π F const G expanded F G i F i G i infixr 0 f g F Set f G Set g Set F G F G id f F Set f F F id id f g h F Set f G Set g H Set h G H F G F H f g f g infixr 0 f g F Set f G i F i Set g Π F G Π F G id f g F Set f G Set g F G F G id infixl 4 a b A Set a B Set b Ix A B Ix A Ix B liftA a b A Set a B Set b A B Ix A Ix B liftA f x pure f x liftA liftA2 a b c A Set a B Set b C Set c A B C Ix A Ix B Ix C liftA2 f x y pure f x y List a Set a Set a List liftA List f F Set f List f F Agda could not infer this f f F Set f F List F List F Maybe a Set a Set a Maybe liftA Maybe nothing f F Set f Maybe f F Agda could not infer this f nothing nothing just f F

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Data.Indexed.html (2015-10-11)
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  • where open Pre preorder g i j begin where open Pre preorder open import Relation Binary module Relation Binary PreorderReasoning p p p P Preorder p p p where open Preorder P infix 4 IsRelatedTo infix 2 infixr 2 infix 1 begin This seemingly unnecessary type is used to make it possible to infer arguments even if the underlying equality evaluates data IsRelatedTo x y Carrier Set p where relTo

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Relation.Binary.PreorderReasoning.html (2015-10-11)
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  • Relation Binary PropositionalEquality module Relation Binary PropositionalEquality Core where open import Level open import Relation Binary Core open import Relation Binary Consequences Core Some properties sym a A Set a Symmetric A A sym refl refl trans a A Set a Transitive A A trans refl refl refl subst a p A Set a Substitutive A A p subst P refl p p resp a A Set a Rel A

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Relation.Binary.PropositionalEquality.Core.html (2015-10-11)
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  • currently the applicative functor laws are not included here module Category Applicative where open import Data Unit open import Category Applicative Indexed RawApplicative f Set f Set f Set RawApplicative F RawIApplicative I λ F module RawApplicative f F Set

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Category.Applicative.html (2015-10-11)
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  • a A Set a Rel A Rel A Substitutive Reflexive substitutive to reflexive subst refl x subst x refl substitutive a A Set a Rel A Substitutive a PropEq substitutive subst substitutive to reflexive PropEq subst PropEq refl record Equality a A Set a Rel A Set suc a where field isEquivalence IsEquivalence subst Substitutive a open IsEquivalence isEquivalence public to reflexive Reflexive to reflexive substitutive to reflexive subst to

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Relation.Binary.Extras.html (2015-10-11)
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  • a type which is analogous to the Rec type constructor used in the current version of ΠΣ data Rec a A Set a Set a where fold x A Rec A unfold a A Set a Rec A A unfold fold x x If guardedness preserving type constructors is enabled one can define types like by recursion open import Data Sum open import Data Unit Set Rec zero zero inj

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Coinduction.html (2015-10-11)
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