Control.Comonad

(C) 2004 Dave Menendez License : BSD-style (see the file LICENSE)

Maintainer : Edward Kmett [e-mail] Stability : experimental Portability : portable

This module declares the Comonad class

Documentation

module Control.Functor.Pointed

class Copointed w => Comonad w where

There are two ways to define a comonad:

I. Provide definitions for fmap, extract, and duplicate satisfying these laws:

 extract . duplicate      == id
 fmap extract . duplicate == id
 duplicate . duplicate    == fmap duplicate . duplicate

II. Provide definitions for extract and extend satisfying these laws:

 extend extract      == id
 extract . extend f  == f
 extend f . extend g == extend (f . extend g)

(fmap cannot be defaulted, but a comonad which defines extend may simply set fmap equal to liftW.)

A comonad providing definitions for extend and duplicate, must also satisfy these laws:

 extend f  == fmap f . duplicate
 duplicate == extend id
 fmap f    == extend (f . duplicate)

(The first two are the defaults for extend and duplicate, and the third is the definition of liftW.)

Methods

duplicate :: w a -> w (w a)

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

Instances

Comonad Identity

Comonad Supply

Monoid m => Comonad ((->) m)

Comonad ((,) e)

Comonad (Context s)

Monoid m => Comonad (Exp m)

Ix i => Comonad (Pointer i)

Comonad (Coreader r)

(Bifunctor f Hask Hask Hask, PComonad f) => Comonad (Fix f)

Comonad (Density f)

ComonadCoideal w => Comonad (Coideal w)

Comonad w => Comonad (CoYoneda w)

Comonad f => Comonad (Yoneda f)

Comonad w => Comonad (ContextT b w)

Comonad w => Comonad (CoreaderT w b)

Adjunction f g => Comonad (ACompF f g)

(Comonad f, Comonad g, Distributes f g) => Comonad (DistCompF f g)

(Copointed f, Comonad w, PreUnfold f w) => Comonad (PreCompF f w)

(Comonad w, Copointed f, PostUnfold w f) => Comonad (PostCompF w f)

liftW :: Comonad w => (a -> b) -> w a -> w b

(=>>) :: Comonad w => w a -> (w a -> b) -> w b

extend with the arguments swapped. Dual to >>= for monads.

(.>>) :: Comonad w => w a -> b -> w b

Injects a value into the comonad.

liftCtx :: Comonad w => (a -> b) -> w a -> b

Transform a function into a comonadic action

mapW :: Comonad w => (w a -> b) -> w [a] -> [b]

parallelW :: Comonad w => w [a] -> [w a]

unfoldW :: Comonad w => (w b -> (a, b)) -> w b -> [a]

sequenceW :: Comonad w => [w a -> b] -> w a -> [b]

Converts a list of comonadic functions into a single function returning a list of values