comonad: Comonads

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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 && <4.15), containers (>=0.3 && <0.6), contravariant (>=0.2.0.1 && <1), distributive (>=0.2.2 && <1), semigroups (>=0.8.3.1 && <1), tagged (>=0.7 && <1), transformers (>=0.2 && <0.5) [details]
License BSD-3-Clause
Copyright Copyright (C) 2008-2013 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 2022-06-18T18:55:39Z
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 EdwardKmett at 2014-05-05T20:53:46Z
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 164 direct, 8417 indirect [details]
Downloads 292760 total (303 in the last 30 days)
Rating 2.5 (votes: 5) [estimated by Bayesian average]
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Status Docs available [build log]
Successful builds reported [all 1 reports]

Readme for comonad-4.2

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comonad

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This package provides comonads, the categorical dual of monads.

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 and perhaps can be made clearer by viewing them as laws stating that Cokleisli composition must be associative, and has 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 are the default definitions of 'extend' and'duplicate' 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