category-extras-0.53.1: Various modules and constructs inspired by category theory Source code Contents Index

Control.Category.Cartesian.Closed Portability non-portable (class-associated types) Stability experimental Maintainer Edward Kmett <ehommett@gmail.com>

Contents Cartesian Closed Category Co-(Cartesian Closed Category)

Description

NB: Some rewrite rules are disabled pending resolution of: http://hackage.haskell.org/trac/ghc/ticket/2291

Synopsis

class (Monoidal hom prod i, Cartesian hom prod i) => CCC hom prod exp i | hom -> prod exp i where apply :: hom (prod (exp a b) a) b curry :: hom (prod a b) c -> hom a (exp b c) uncurry :: hom a (exp b c) -> hom (prod a b) c unitCCC :: CCC hom prod exp i => hom a (exp b (prod b a)) counitCCC :: CCC hom prod exp i => hom (prod b (exp b a)) a class (Comonoidal hom sum i, CoCartesian hom sum i) => CoCCC hom sum coexp i | hom -> sum coexp i where coapply :: hom b (sum (coexp hom a b) a) cocurry :: hom c (sum a b) -> hom (coexp hom b c) a uncocurry :: hom (coexp hom b c) a -> hom c (sum a b) unitCoCCC :: CoCCC hom sum coexp i => hom a (sum b (coexp hom b a)) counitCoCCC :: CoCCC hom sum coexp i => hom (coexp hom b (sum b a)) a

Cartesian Closed Category

class (Monoidal hom prod i, Cartesian hom prod i) => CCC hom prod exp i | hom -> prod exp i where Source

A CCC has full-fledged monoidal finite products and exponentials Methods apply :: hom (prod (exp a b) a) b Source curry :: hom (prod a b) c -> hom a (exp b c) Source uncurry :: hom a (exp b c) -> hom (prod a b) c Source

unitCCC :: CCC hom prod exp i => hom a (exp b (prod b a)) Source

counitCCC :: CCC hom prod exp i => hom (prod b (exp b a)) a Source

Co-(Cartesian Closed Category)

class (Comonoidal hom sum i, CoCartesian hom sum i) => CoCCC hom sum coexp i | hom -> sum coexp i where Source

A Co-CCC has full-fledged comonoidal finite coproducts and coexponentials Methods coapply :: hom b (sum (coexp hom a b) a) Source cocurry :: hom c (sum a b) -> hom (coexp hom b c) a Source uncocurry :: hom (coexp hom b c) a -> hom c (sum a b) Source

unitCoCCC :: CoCCC hom sum coexp i => hom a (sum b (coexp hom b a)) Source

counitCoCCC :: CoCCC hom sum coexp i => hom (coexp hom b (sum b a)) a Source

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