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  • Signatures.PLUGIN.Arch
    val dir pack string unit arch list unit arch val file string unit arch type info private current path string include dirs string list for pack string val annotate a arch info arch val print Format formatter a unit Format formatter a arch unit val print include dirs Format formatter string list unit val print info Format formatter info unit val iter info a unit a arch unit val fold

    Original URL path: http://nicolaspouillard.fr/ocamlbuild/html/Signatures.PLUGIN.Arch.html (2015-10-11)
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  • Level suc i Level Level BUILTIN LEVEL Level BUILTIN LEVELZERO zero BUILTIN LEVELSUC suc Maximum infixl 6 Level Level Level zero j j suc i zero suc i suc i suc j suc i j BUILTIN LEVELMAX Lifting record Lift

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Level.html (2015-10-11)
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  • Irrelevance OPTIONS universe polymorphism module Irrelevance where import Level record Irr a A Set a Set a where constructor irr field cert A open Irr public

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Irrelevance.html (2015-10-11)
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  • j i j refl refl refl a A Set a i j A Decidable A i j refl refl yes refl injective a A Set a InjectiveRel A injective refl refl refl surjective a A Set a SurjectiveRel A surjective refl refl refl bijective a A Set a BijectiveRel A bijective record injectiveREL injective surjectiveREL surjective module Reasoning a A Set a where infix 2 finally infixr 2 x y

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Relation.Binary.PropositionalEquality.NP.html (2015-10-11)
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  • 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 isEquivalence IsEquivalence isEquivalence record refl λ x refl x sym λ x y sym x y trans λ x y z trans x y z setoid Setoid setoid record Carrier isEquivalence isEquivalence data m n Dec m n Set where z n n zero n yes z n s z m suc m zero no λ s s yes m n m n m n yes m n suc m suc n yes s s m n s s no m n m n m n no m n suc m suc n no m n pred complete m n m n m n complete zero n z n complete suc n zero s z complete suc m suc n with m n complete m n yes q r s s yes r no q r

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Data.Nat.NP.html (2015-10-11)
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  • suc n with m n yes p yes suc p no p no p pred zero suc n no λ suc m zero no λ private refl Reflexive refl zero zero refl suc n suc refl n sym Symmetric sym zero zero sym suc n suc sym n trans Transitive trans zero zero zero trans suc m suc n suc trans m n subst Substitutive subst zero id subst P suc n subst P suc n isEquivalence IsEquivalence isEquivalence record refl refl sym sym trans trans isDecEquivalence IsDecEquivalence isDecEquivalence record isEquivalence isEquivalence equality Equality equality record isEquivalence isEquivalence subst subst PropEq Equality to reflexive equality PropEq PropEq refl setoid Setoid setoid record Carrier isEquivalence isEquivalence decSetoid DecSetoid decSetoid record Carrier isDecEquivalence isDecEquivalence cong f f cong zero refl cong f suc n cong f suc n module Reasoning Trans Reasoning trans data REL zero where z n m m m m m zero m z n z n s s m m n n m n m n m n m n m n m n m n m n m n suc m suc n s s m n s s m n pred m m n n m

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Data.Nat.Logical.html (2015-10-11)
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  • x C y 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

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Function.html (2015-10-11)
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  • To Identity and composition id a a A B Setoid a a A A id record Fun id cong Fun id infixr 9 a a A B Setoid a a b b B B Setoid b b c c C B Setoid c c B C A B A C f g record Fun f g cong Fun cong f cong g Constant equality preserving function const a a A B Setoid a a b b B B Setoid b b B Setoid Carrier B A B const B B b record Fun const b cong Fun const B Setoid refl B Function setoids Dependent setoid f f t t From B Setoid f f I Setoid B Setoid Carrier From t t B Setoid setoid From To record Carrier Π From To λ f g x y x y f x g y isEquivalence record refl λ f cong f sym λ f g x y To sym f g From sym x y trans λ f g g h x y To trans f g From refl g h x y where open module From B Setoid From using renaming to open module To I Setoid To using

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