archive-fr.com » FR » N » NICOLASPOUILLARD.FR

Total: 307

Choose link from "Titles, links and description words view":

Or switch to "Titles and links view".

  • Relation Binary PropositionalEquality as PropEq using refl Types 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 isDecTotalOrder record isTotalOrder record isPartialOrder record isPreorder record isEquivalence PropEq isEquivalence reflexive λ trans

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Data.Unit.html (2015-10-11)
    Open archived version from archive



  • 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 Decidable relations

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Relation.Nullary.html (2015-10-11)
    Open archived version from archive


  • 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 Equivalent to P Q p map P Q

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Relation.Nullary.Decidable.html (2015-10-11)
    Open archived version from archive


  • injective inj fx fz fy fz f inj inj fx fz fy fz surjective Rel A SurjectiveRel A SurjectiveRel B on f surjective inj fx fz fy fz f inj inj fx fz fy fz bijective Rel A BijectiveRel A BijectiveRel B on f bijective bij record injectiveREL injective λ x y z inj x y z surjectiveREL surjective λ x y z sur x y z where open BijectiveREL

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Relation.Binary.On.NP.html (2015-10-11)
    Open archived version from archive


  • 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: http://nicolaspouillard.fr/publis/nameless-painless.agda/Category.Monad.html (2015-10-11)
    Open archived version from archive


  • 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/nameless-painless.agda/Data.Bool.html (2015-10-11)
    Open archived version from archive


  • 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 A Inspect x inspect x

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Relation.Binary.PropositionalEquality.html (2015-10-11)
    Open archived version from archive


  • Binary PropositionalEquality module Relation Binary PropositionalEquality Core where open import Level open import Relation Binary Core open import Relation Binary Consequences Core Some properties sym a A Set a Symmetric A A sym refl refl trans a A Set a Transitive A A trans refl refl refl subst a p A Set a Substitutive A A p subst P refl p p resp a A Set a Rel A Respects

    Original URL path: http://nicolaspouillard.fr/publis/nameless-painless.agda/Relation.Binary.PropositionalEquality.Core.html (2015-10-11)
    Open archived version from archive