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  • Data Unit RawMonad Set Set Set RawMonad M RawIMonad λ M RawMonadZero Set Set Set RawMonadZero M RawIMonadZero λ M RawMonadPlus Set Set Set RawMonadPlus M RawIMonadPlus λ M module RawMonad M Set Set Mon RawMonad M where open RawIMonad

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Category.Monad.html (2015-10-11)
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  • m maybe f M return nothing where module M RawMonad M monad RawMonad Maybe monad monadT IdentityMonad monadZero RawMonadZero Maybe monadZero record monad monad nothing monadPlus RawMonadPlus Maybe monadPlus record monadZero monadZero where a Set Maybe a Maybe a Maybe a nothing y y just x y just x Equality open import Relation Nullary open import Relation Binary open import Relation Binary PropositionalEquality as PropEq using refl drop just A Set x y A just x just y x y drop just refl refl decSetoid A Set Decidable A A DecSetoid decSetoid A A PropEq decSetoid where Decidable A Maybe A just x just y with x A y just x just x yes refl yes refl just x just y no x y no x y drop just just x nothing no λ nothing just y no λ nothing nothing yes refl Any and All open import Data Empty using import Relation Nullary Decidable as Dec data Any a A Set a P A Set a Maybe A Set a where just x px P x Any P just x data All a A Set a P A Set a Maybe A Set a where just x px P

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Data.Maybe.html (2015-10-11)
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  • Set A Set b Set a b B λ x B x y B y x y Functions Sometimes the first component can be inferred a b A Set a B A Set b x B x B y y a b c A Set a B A Set b C x B x Set c f x A B x x A C f x x A Σ B x C f g x f x g x map a b p q A Set a B Set b P A Set p Q B Set q f A B x P x Q f x Σ A P Σ B Q map f g f proj g proj zip a b c p q r A Set a B Set b C Set c P A Set p Q B Set q R C Set r A B C x y P x Q y R x y Σ A P Σ B Q Σ C R zip p p proj p proj p proj p proj p swap a b A Set a B Set b A B B A swap proj proj a b i j

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Data.Product.html (2015-10-11)
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  • g x A B x x A C g x f g λ x f g x a b c A Set a B Set b C Set c B C A B A C f g f g id a A Set a A A id x x const a b A Set a B Set b A B A const x λ x flip a b c A Set a B Set b C A B Set c x A y B C x y y B x A C x y flip f λ x y f y x Note that is right associative like in Haskell If you want a left associative infix application operator use Category Functor available from Category Monad Identity IdentityMonad a b A Set a B A Set b x A B x x A B x f x f x a b c A Set a B Set b C Set c A A B C B C x f y f x y on a b c A Set a B Set b C Set c B B C A B A A C on f λ x y f

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Function.html (2015-10-11)
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  • x y x y f x f y cong f refl refl cong a b c A Set a B Set b C Set c f A B C x y u v x y u v f x u f y v cong f refl refl refl proof irrelevance a A Set a x y A p q x y p q proof irrelevance refl refl refl setoid a Set a Setoid setoid A record Carrier A isEquivalence isEquivalence decSetoid a A Set a Decidable A A DecSetoid decSetoid dec record isDecEquivalence record isEquivalence isEquivalence dec isPreorder a A Set a IsPreorder A A isPreorder record isEquivalence isEquivalence reflexive id trans trans preorder a Set a Preorder preorder A record Carrier A isPreorder isPreorder Pointwise equality infix 4 setoid a b A Set a B Set b Setoid A setoid B setoid A Setoid indexedSetoid setoid B a b A Set a B Set b f g A B Set A A B Setoid A setoid B to Π a b b A Set a B I Setoid b b x A I Setoid Carrier B x Π setoid A B to Π B B f record f cong cong where open I Setoid B using cong x y x y f x f y cong refl I Setoid refl B to a b b A Set a B Setoid b b A Setoid Carrier B setoid A B to to Π The inspect idiom The inspect idiom can be used when you want to pattern match on the result r of some expression e and you also need to remember that r e data Inspect a A Set a x A Set a where with y A eq x y Inspect x inspect a A Set a x

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Relation.Binary.PropositionalEquality.html (2015-10-11)
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  • not included here module Category Functor where open import Function record RawFunctor f Set Set Set where infixl 4 field a b a b f a f b a b

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Category.Functor.html (2015-10-11)
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  • that currently the applicative functor laws are not included here module Category Applicative where open import Data Unit open import Category Applicative Indexed RawApplicative Set Set Set RawApplicative F RawIApplicative I λ F module RawApplicative F Set Set app RawApplicative

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Category.Applicative.html (2015-10-11)
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  • Identity The identity monad module Category Monad Identity where open import Category Monad Identity Set Set Identity A A IdentityMonad RawMonad Identity IdentityMonad record return λ x x λ x

    Original URL path: http://nicolaspouillard.fr/publis/pouillard-pottier-fresh-look-agda-2010/html/Category.Monad.Identity.html (2015-10-11)
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