semigroupoids-3.0.3: Haskell 98 semigroupoids: Category sans id

Copyright(C) 2011 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
Portabilityportable
Safe HaskellSafe
LanguageHaskell98

Data.Functor.Extend

Contents

Description

 

Synopsis

Extendable Functors

There are two ways to define an Extend instance:

I. Provide definitions for extend satisfying this law:

extended f . extended g = extended (f . extended g)

II. Alternately, you may choose to provide definitions for duplicate satisfying this law:

duplicated . duplicated = fmap duplicated . duplicated

These are both equivalent to the statement that (->-) is associative

(f ->- g) ->- h = f ->- (g ->- h)

You may of course, choose to define both duplicate and extend. In that case you must also satisfy these laws:

extended f = fmap f . duplicated
duplicated = extended id

These are the default definitions of extended and duplicated.

class Functor w => Extend w where

Minimal complete definition

Nothing

Methods

duplicated :: w a -> w (w a)

duplicated = extended id
fmap (fmap f) . duplicated = duplicated . fmap f

extended :: (w a -> b) -> w a -> w b

extended f  = fmap f . duplicated