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  • false Bool BUILTIN BOOL Bool BUILTIN TRUE true BUILTIN FALSE false COMPILED DATA Bool Bool True False Some operations not Bool Bool not true false not false true A function mapping true to an inhabited type and false to an empty type T Bool Set T true T false if then else a A Set a Bool A A A if true then t else f t if false then

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Data.Bool.html (2015-10-11)
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  • A 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

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Category.Monad.Indexed.html (2015-10-11)
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  • b A Set a B Set b A B A const x λ x The S combinator Written infix as in Conor McBride s paper Outrageous but Meaningful Coincidences Dependent type safe syntax and evaluation a b c A Set a B A Set b C x A B x Set c x A y B x C x y g x A B x x A C x g x f g λ x f x g 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 y x f x y 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

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Function.html (2015-10-11)
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  • Set c x A C inj x x B C inj x x A B C x f g inj x f x f g inj y g y a b c A Set a B Set b C Set c A C B C A B C map a b c d A Set a B Set b C Set c D Set d A C B D A

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Data.Sum.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: https://nicolaspouillard.fr/publis/NomPa.agda/Data.Product.html (2015-10-11)
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  • relations like negation and decidability Some operations on properties of nullary relations i e sets module Relation Nullary where import Relation Nullary Core as Core Negation open Core public using

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/Relation.Nullary.html (2015-10-11)
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  • 1 fromBool Bool World World fromBool true 1 fromBool false 1 fromBools List Bool World fromBools foldr fromBool ø module ListBoolSpecialized where infixl 6 World Set World List Bool World World α k replicate k false α i k j k i j α World World α k replicate k true α i i i 0 k 1 α k module where World Set World List WorldSymantics World record ø 1 λ α 0 map suc α 1 map suc open WorldSymantics public module ListBoolWorlds where World Set World List Bool listBoolWorlds WorldSymantics List Bool listBoolWorlds record ø ø 1 1 1 1 where ø World ø 1 World World α 1 false α 1 World World α 1 true α World Set zero false zero true suc n xs n xs World Set x α x α infix 2 uniq x α p q x α p q uniq uniq zero false xs uniq zero true xs refl uniq suc n xs p q uniq n xs p q infix 2 α β World Set α β x x α x β infix 2 α β World Set α β α β infix 2 record α β List Bool Set where constructor mk field coe x x α x β open public infix 2 α β World Set α β α β to List Bool List to to true bs 0 map suc to bs to false bs map suc to bs private module Unused where open WorldSymantics listBoolWorlds open WorldOps listBoolWorlds x ø x k x ø k x ø zero zero x ø suc zero x ø zero suc k x ø suc n suc k pf x ø n k pf false x xs x false xs pred x xs false zero λ false suc n

    Original URL path: https://nicolaspouillard.fr/publis/NomPa.agda/NomPa.Worlds.html (2015-10-11)
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  • definitions The definitions in this file are reexported by Relation Nullary module Relation Nullary Core where open import Data Empty open import Level Negation infix 3 Set Set P P Decidable relations data Dec p P Set p Set p

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