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  • A A Set a b b b B A Set b B A Set b B x x x A x x B x B x Set b f x A B x f x A B x Set A B λ f f x x x A x x B x f x f x infixr 0 syntax A λ x f x A f infixr 1 a a a A Set a A Set a A A A Set a b b b B Set b B Set b B B B Set b f A B f A B Set A B Π A λ B infixr 0 e e a a a A Set a A Set a A A A Set a b b b B Set b B Set b B B B Set b f A B f A B Set e A B Π e A λ B open import Data Product open import Data Unit record x x Set where constructor tt open import Data Empty data x x Set where open import Relation Nullary infix 3 Set Set a a a A Set a A Set a A A A Set a A A Set A A A A World Set A α α World α α A α A α Set p A f A Set A λ p p Σ α World proj p proj p A α proj p proj p syntax λ α f α f Pred a A Set a Set a suc Pred A A Set Pred p p p a a a Set a a a Set Pred p Pred p Pred p p p A A Set p p p Pred p p p A λ f f x x x A

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Relation.Binary.Logical.html (2015-10-11)
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  • refl refl a A Set a i j A Decidable A i j refl refl yes refl a b c A Set a B Set b C Set c f g A B C Set f g x y f x y g x y 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

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Relation.Binary.PropositionalEquality.NP.html (2015-10-11)
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  • p s infixr 0 A B Parser A A Parser B Parser B pa f maybe uncurry f nothing pa infixl 0 A B A Parser B Parser A Parser B f pa pa f join A Parser Parser A Parser A join id map A B A B Parser A Parser B map f pa pa pure f infixl 4 A B Parser A B Parser A Parser B pf pa pf λ f pa λ a pure f a A B A B Parser A Parser B f x map f x A B C A B C Parser A Parser B Parser C f x y map f x y A B C D A B C D Parser A Parser B Parser C Parser D f x y z map f x y z A B Parser A Parser B Parser B p p p const p A B Parser A Parser B Parser A p p p λ x p pure x choices A List Parser A Parser A choices L foldr empty vec A n Parser A Parser Vec A n vec zero p pure vec suc n p p vec n p These are producing bounded vectors mainly for termination reasons manyBV A n Parser A Parser BoundedVec A n someBV A n Parser A Parser BoundedVec A suc n manyBV 0 empty manyBV suc n p someBV n p pure BV someBV n p BV p manyBV n p many A n Parser A Parser List A some A n Parser A Parser List A many 0 empty many suc n p some n p pure some n p p many n p manySat Char Bool Parser List Char manySat p pure manySat p x xs if p x then map first

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Text.Parser.html (2015-10-11)
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  • import Relation Nullary open import Relation Nullary Decidable ShowS Set ShowS String String Pr Set Set Pr A A ShowS String ShowS s tail Data String s tail parenBase ShowS ShowS parenBase doc doc record PrEnv Set where constructor mk

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Text.Printer.html (2015-10-11)
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  • Level Level Level Level Level MAlonzo compiles Level to This should be safe because it is not possible to pattern match on levels COMPILED TYPE Level COMPILED zero COMPILED suc COMPILED BUILTIN LEVEL Level BUILTIN LEVELZERO zero BUILTIN LEVELSUC suc

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Level.html (2015-10-11)
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  • s x s n Arithmetic pred pred zero zero pred suc n n infixl 6 zero n n suc m n suc m n BUILTIN NATPLUS Argument swapping addition Used by Data Vec zero n n suc m n suc n m m zero m zero suc n zero suc m suc n m n BUILTIN NATMINUS zero n zero suc m n n m n BUILTIN NATTIMES Max zero n n suc m zero suc m suc m suc n suc m n Min zero n zero suc m zero zero suc m suc n suc m n Division by 2 rounded downwards 2 0 2 0 1 2 0 suc suc n 2 suc n 2 Division by 2 rounded upwards 2 n 2 suc n 2 Queries infix 4 Decidable A zero zero yes refl suc m suc n with m n suc m suc m yes refl yes refl suc m suc n no prf no prf PropEq cong pred zero suc n no λ suc m zero no λ pred m n suc m suc n m n pred s s m n m n Decidable zero yes z n suc m zero no λ suc m suc n with m n yes m n yes s s m n no m n no m n pred A comparison view Taken from View from the left McBride McKinna details may differ data Ordering Rel Level zero where less m k Ordering m suc m k equal m Ordering m m greater m k Ordering suc m k m compare m n Ordering m n compare zero zero equal zero compare suc m zero greater zero m compare zero suc n less zero n compare suc m suc n with compare m n compare suc m

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Data.Nat.html (2015-10-11)
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  • Maybe type The definitions in this file are reexported by Data Maybe module Data Maybe Core where open import Level data Maybe a A Set a Set a where just x A Maybe A nothing Maybe A IMPORT Data FFI

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Data.Maybe.Core.html (2015-10-11)
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  • 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 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 B B C A B A A C on f λ x y f x f y a b c d e A Set a B Set b C Set c D Set d E Set e A B C C D E A B D A B E f g λ x y f x y g x y In Agda

    Original URL path: http://nicolaspouillard.fr/publis/lfmtp2012-talk/html/Function.html (2015-10-11)
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