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  • import Data Product i f g Ix Set i F Ix Set f G Ix Set g Ix Set F G λ A F A G A i f g Ix Set i F Ix Set f G Ix Set

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Data.Indexed.html (2015-10-11)
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  • Set a b c C λ a λ b C a b a b A Set a B Set b Set a b A B Σ x A B a b A Set a B Set b A B A B Unique existence Parametrised on the underlying equality a b A Set a A A 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 x y f x g y 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 a p b q a b p q swap a b A Set a B Set b A B B A swap x y y x a b i j A Set a B Set b A B Set i A B Set j A B Set f g f g a b c d A Set a B Set b C Set c D Set d A B C A B D

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Data.Product.html (2015-10-11)
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  • 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 z P Q Star P Q evalStar idQ ε idQ evalStar idQ Q f x xs evalStar idQ Q f xs Q f x evalStar A Set P Q Rel A

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Data.Star.NP.html (2015-10-11)
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  • B M i j A M j k B M i k B m m m λ m i j k A B A M j k B M i j A M i k B f c c f join i j k A M i j M j k A M i k A join m m id rawIApplicative RawIApplicative M rawIApplicative record pure return λ f x

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Category.Monad.Indexed.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: http://nicolaspouillard.fr/publis/nameless-painless.agda/Category.Applicative.Indexed.html (2015-10-11)
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  • import Function Injection public open import Function Equality open import Relation Binary open import Data Product open import Level a a A A Setoid a a x Setoid Carrier A Setoid Carrier A inj Injection A A Set a A

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Function.Injection.NP.html (2015-10-11)
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  • A B f x y f x f y x y where open Setoid A renaming to open Setoid B renaming to The set of all injections between two setoids record Injection f f t t From Setoid f f To Setoid t t Set f f t t where field to From To injective Injective to Identity and composition infixr 9 id s s S Setoid s s Injection

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Function.Injection.html (2015-10-11)
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  • P Surjective functions record Surjective f f t t From Setoid f f To Setoid t t to From To Set f f t t where field from To From right inverse of from RightInverseOf to The set of all surjections from one setoid to another record Surjection f f t t From Setoid f f To Setoid t t Set f f t t where field to From To surjective Surjective to open Surjective surjective public right inverse RightInverse From To right inverse record to from from to left inverse of right inverse of injective Injective from injective LeftInverse injective right inverse injection Injection To From injection LeftInverse injection right inverse equivalent Equivalent From To equivalent record to to from from The set of all surjections from one set to another infix 3 f t Set f Set t Set From To Surjection P setoid From P setoid To Identity and composition id s s S Setoid s s Surjection S S id S S record to F id surjective record from LeftInverse to id right inverse of LeftInverse left inverse of id where id Left id S S infixr 9 f f m m t t F Setoid

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Function.Surjection.html (2015-10-11)
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