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  • Empty The Agda standard library Empty type module Data Empty where open import Level data Set where IMPORT Data FFI COMPILED DATA Data FFI AgdaEmpty elim w Whatever Set w

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Data.Empty.html (2015-10-11)
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  • Rel A Rel A Star flip Star flip evalStar a p q A Set a P Rel A p Q Rel A q idQ x Q x x Q x y z Q y z Q x y Q x

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Data.Star.NP.html (2015-10-11)
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  • Q Dec P True Q P toWitness Q yes p p toWitness Q no Establishes a truth given a witness fromWitness p P Set p Q Dec P P True Q fromWitness Q yes p const fromWitness Q no p p map p q P Set p Q Set q P Q Dec P Dec Q map P Q yes p yes Equivalence to P Q p map P Q

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Relation.Nullary.Decidable.html (2015-10-11)
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  • j k A B F i j A B F j k A F i k B rawFunctor i j RawFunctor F i j rawFunctor record λ g x pure g x private open module RF i j I RawFunctor rawFunctor i i j j public i j k A B F i j A F j k B F i k A x y const x y i j k A B F i j A F j k B F i k B x y flip const x y i j k A B F i j A F j k B F i k A B x y x y zipWith i j k A B C A B C F i j A F j k B F i k C zipWith f x y f x y Applicative functor morphisms specialised to propositional equality record Morphism i f I Set i F F IFun I f A RawIApplicative F A RawIApplicative F Set i suc f where module A RawIApplicative A module A RawIApplicative A field op i j X F i j X F i j X op pure i X x X op

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Category.Applicative.Indexed.html (2015-10-11)
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  • currently the functor laws are not included here module Category Functor where open import Function open import Level record RawFunctor F Set Set Set suc where infixl 4 field A B A B F A F B A B A

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Category.Functor.html (2015-10-11)
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  • import Category Monad Indexed open import Data Unit RawMonad f Set f Set f Set RawMonad M RawIMonad I λ M RawMonadZero f Set f Set f Set RawMonadZero M RawIMonadZero I λ M RawMonadPlus f Set f Set f Set RawMonadPlus M RawIMonadPlus I λ M module RawMonad f M Set f Set f Mon RawMonad M where open RawIMonad Mon public module RawMonadZero f M Set f Set

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Category.Monad.html (2015-10-11)
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  • The identity monad module Category Monad Identity where open import Category Monad Identity f Set f Set f Identity A A IdentityMonad f RawMonad Identity f IdentityMonad record return λ

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Category.Monad.Identity.html (2015-10-11)
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  • and operations are defined in Data Unit Core open import Data Unit Core public A unit type defined as a record type Note that the name of this type is top not T record Set where constructor tt record x y Set where Operations Decidable A yes refl Decidable yes total Total total inj Properties preorder Preorder preorder PropEq preorder setoid Setoid setoid PropEq setoid decTotalOrder DecTotalOrder decTotalOrder record Carrier

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