comonad: Comonads

[ bsd3, comonads, control, library ] [ Propose Tags ]

Comonads.


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Versions [RSS] 0.1.0, 0.1.1, 0.3.0, 0.4.0, 0.5.0, 0.6.0, 0.6.1, 0.6.1.1, 0.6.1.2, 0.6.2, 0.6.2.1, 0.7.0, 0.9.0, 0.9.0.1, 1.0, 1.0.1, 1.0.2, 1.0.3, 1.1.0, 1.1.0.1, 1.1.0.2, 1.1.1, 1.1.1.1, 1.1.1.2, 1.1.1.3, 1.1.1.4, 1.1.1.5, 1.1.1.6, 3.0, 3.0.0.1, 3.0.0.2, 3.0.1.1, 3.0.2, 3.0.3, 3.1, 4.0, 4.0.1, 4.2, 4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.2.5, 4.2.6, 4.2.7, 4.2.7.1, 4.2.7.2, 4.3, 5, 5.0.1, 5.0.2, 5.0.3, 5.0.4, 5.0.5, 5.0.6, 5.0.7, 5.0.8
Change log CHANGELOG.markdown
Dependencies base (>=4 && <5), containers (>=0.3 && <0.8), distributive (>=0.5.2 && <1), indexed-traversable (>=0.1.1 && <0.2), semigroups (>=0.18.5 && <1), tagged (>=0.8.6.1 && <1), transformers (>=0.3 && <0.7), transformers-compat (>=0.5 && <1) [details]
License BSD-3-Clause
Copyright Copyright (C) 2008-2014 Edward A. Kmett, Copyright (C) 2004-2008 Dave Menendez
Author Edward A. Kmett
Maintainer Edward A. Kmett <ekmett@gmail.com>
Revised Revision 2 made by ryanglscott at 2023-09-30T12:22:30Z
Category Control, Comonads
Home page http://github.com/ekmett/comonad/
Bug tracker http://github.com/ekmett/comonad/issues
Source repo head: git clone git://github.com/ekmett/comonad.git
Uploaded by ryanglscott at 2020-12-30T12:48:43Z
Distributions Arch:5.0.8, Debian:5.0.6, Fedora:5.0.8, FreeBSD:4.2.7.2, LTSHaskell:5.0.8, NixOS:5.0.8, Stackage:5.0.8, openSUSE:5.0.8
Reverse Dependencies 163 direct, 8257 indirect [details]
Downloads 290389 total (408 in the last 30 days)
Rating 2.5 (votes: 5) [estimated by Bayesian average]
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Readme for comonad-5.0.8

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comonad

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This package provides comonads, the categorical dual of monads. The typeclass provides three methods: extract, duplicate, and extend.

class Functor w => Comonad w where
    extract :: w a -> a
    duplicate :: w a -> w (w a)
    extend :: (w a -> b) -> w a -> w b

There are two ways to define a comonad:

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

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

In this case, you may simply set fmap = liftW.

These laws are directly analogous to the laws for monads. The comonad laws can perhaps be made clearer by viewing them as stating that Cokleisli composition must be a) associative and b) have extract for a unit:

f =>= extract   = f
extract =>= f   = f
(f =>= g) =>= h = f =>= (g =>= h)

II. Alternately, you may choose to provide definitions for fmap, extract, and duplicate satisfying these laws:

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

In this case, you may not rely on the ability to define fmap in terms of liftW.

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

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

These implementations are the default definitions of extend andduplicate and the definition of liftW respectively.

Contact Information

Contributions and bug reports are welcome!

Please feel free to contact me through github or on the #haskell IRC channel on irc.freenode.net.

-Edward Kmett