Copyright	2008 Edward Kmett
License	BSD
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable (class-associated types)
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Category.Cartesian.Closed

Contents

Description

Synopsis

Cartesian Closed Category

class Cartesian k => CCC k where Source

A CCC has full-fledged monoidal finite products and exponentials

Associated Types

type Exp k :: * -> * -> * Source

Methods

apply :: Product k (Exp k a b) a `k` b Source

curry :: (Product k a b `k` c) -> a `k` Exp k b c Source

uncurry :: (a `k` Exp k b c) -> Product k a b `k` c Source

Instances

CCC (->)

unitCCC :: CCC k => a `k` Exp k b (Product k b a) Source

counitCCC :: CCC k => Product k b (Exp k b a) `k` a Source

Co-(Cartesian Closed Category)

A Co-CCC has full-fledged comonoidal finite coproducts and coexponentials

Associated Types

type Coexp k :: * -> * -> * Source

Methods

coapply :: b `k` Sum k (Coexp k a b) a Source

cocurry :: (c `k` Sum k a b) -> Coexp k b c `k` a Source

uncocurry :: (Coexp k b c `k` a) -> c `k` Sum k a b Source

unitCoCCC :: CoCCC k => a `k` Sum k b (Coexp k b a) Source