Control.Category

base-4.11.0.0: Basic libraries

Copyright | (c) Ashley Yakeley 2007
License | BSD-style (see the LICENSE file in the distribution)
Maintainer | ashley@semantic.org
Stability | experimental
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Control.Category

Description

Synopsis

- class Category cat where
- (<<<) :: Category cat => cat b c -> cat a b -> cat a c
- (<<<) :: Category cat => cat b c -> cat a b -> cat a c
- (>>>) :: Category cat => cat a b -> cat b c -> cat a c
- (>>>) :: Category cat => cat a b -> cat b c -> cat a c

# Documentation

class Category cat where Source #

A class for categories. Instances should satisfy the laws

    f . id  =  f  -- (right identity)
    id . f  =  f  -- (left identity)
    f . (g . h)  =  (f . g) . h  -- (associativity)

Minimal complete definition

id, (.)

Methods

id :: cat a a Source #

the identity morphism

(.) :: cat b c -> cat a b -> cat a c infixr 9 Source #

morphism composition

Instances

Category (Coercion :: k -> k -> *) # | Since: 4.7.0.0
Instance details Methods id :: Coercion a a Source # (.) :: Coercion b c -> Coercion a b -> Coercion a c Source #
Category ((:~:) :: k -> k -> *) # | Since: 4.7.0.0
Instance details Methods id :: a :~: a Source # (.) :: (b :~: c) -> (a :~: b) -> a :~: c Source #
Category ((:~~:) :: k -> k -> *) # | Since: 4.10.0.0
Instance details Methods id :: a :~~: a Source # (.) :: (b :~~: c) -> (a :~~: b) -> a :~~: c Source #
Monad m => Category (Kleisli m :: * -> * -> *) # | Since: 3.0
Instance details Methods id :: Kleisli m a a Source # (.) :: Kleisli m b c -> Kleisli m a b -> Kleisli m a c Source #
Category ((->) :: * -> * -> *) # | Since: 3.0
Instance details Methods id :: a -> a Source # (.) :: (b -> c) -> (a -> b) -> a -> c Source #

(<<<) :: Category cat => cat b c -> cat a b -> cat a c infixr 1 Source #

Right-to-left composition

(<<<) :: Category cat => cat b c -> cat a b -> cat a c infixr 1 Source #

Right-to-left composition

(>>>) :: Category cat => cat a b -> cat b c -> cat a c infixr 1 Source #

Left-to-right composition

(>>>) :: Category cat => cat a b -> cat b c -> cat a c infixr 1 Source #

Left-to-right composition