Data.Cofunctor

Cofunctor is a structure from category theory dual to Functor

A Functor is defined by the operation fmap:

fmap :: (a -> b) -> (f a -> f b)

This means that its dual must be defined by the following operation:

cofmap :: (b -> a) -> (f b -> f a)

Since beginning his investigations, the author of this package has discovered that this pattern is at least as commonly used as Functor. In fact, many ubiquitous Haskell types (e.g. [], Maybe, ((->) a) turn out to have a Cofunctor instance.

Documentation

class Cofunctor f where

Cofunctor is a structure from category theory dual to Functor

Minimal complete definition

cofmap

Methods

cofmap :: (b -> a) -> f b -> f a

Instances

Cofunctor []

Methods

cofmap :: (b -> a) -> [b] -> [a]

Cofunctor Maybe

Methods

cofmap :: (b -> a) -> Maybe b -> Maybe a

Cofunctor IO

Methods

cofmap :: (b -> a) -> IO b -> IO a

Cofunctor ((->) a)

Methods

cofmap :: (b -> a) -> (a -> b) -> a -> a

Cofunctor (Either e)

Methods

cofmap :: (b -> a) -> Either e b -> Either e a

Cofunctor ((,) a)

Methods

cofmap :: (b -> a) -> (a, b) -> (a, a)

Cofunctor (Cocoyoneda f)

Methods

cofmap :: (b -> a) -> Cocoyoneda f b -> Cocoyoneda f a