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

class Cartesian k => CCC k where
- type Exp k :: * -> * -> *
- apply :: Product k (Exp k a b) a `k` b
- curry :: (Product k a b `k` c) -> a `k` Exp k b c
- uncurry :: (a `k` Exp k b c) -> Product k a b `k` c
unitCCC :: CCC k => a `k` Exp k b (Product k b a)
counitCCC :: CCC k => Product k b (Exp k b a) `k` a
class CoCartesian k => CoCCC k where
- type Coexp k :: * -> * -> *
- coapply :: b `k` Sum k (Coexp k a b) a
- cocurry :: (c `k` Sum k a b) -> Coexp k b c `k` a
- uncocurry :: (Coexp k b c `k` a) -> c `k` Sum k a b
unitCoCCC :: CoCCC k => a `k` Sum k b (Coexp k b a)
counitCoCCC :: CoCCC k => Coexp k b (Sum k b a) `k` a

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 details

CCC (->) Source #
Instance details Defined in Control.Category.Cartesian.Closed Associated Types type Exp (->) :: Type -> Type -> Type Source # Methods apply :: Product (->) (Exp (->) a b) a -> b Source # curry :: (Product (->) a b -> c) -> a -> Exp (->) b c Source # uncurry :: (a -> Exp (->) b c) -> Product (->) a b -> c Source #

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 #