comonad: Comonads

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

Comonads


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Versions 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
Change log CHANGELOG.markdown
Dependencies base (>=4.5 && <5), containers (>=0.3 && <0.6), contravariant (>=0.2.0.1 && <2), distributive (>=0.2.2 && <1), semigroups (>=0.8.3.1 && <1), tagged (>=0.7 && <1), transformers (>=0.2 && <0.5), transformers-compat (>=0.3 && <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 4 made by phadej at Tue Jan 9 16:29:46 UTC 2018
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 Thu May 14 19:34:10 UTC 2015
Distributions Arch:5.0.3, Debian:4.2.7.2, Fedora:5.0.2, FreeBSD:4.2.7.2, LTSHaskell:5.0.3, NixOS:5.0.3, Stackage:5.0.3, openSUSE:5.0.3
Downloads 214212 total (434 in the last 30 days)
Rating 2.5 (votes: 4) [estimated by rule of succession]
Your Rating
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Status Docs available [build log]
Last success reported on 2015-05-14 [all 1 reports]
Hackage Matrix CI

Modules

[Index]

Flags

NameDescriptionDefaultType
test-doctestsEnabledManual
containers

You can disable the use of the containers package using -f-containers.

Disabing this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users.

EnabledManual
contravariant

You can disable the use of the contravariant package using -f-contravariant.

Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users.

If disabled we will not supply instances of Contravariant

EnabledManual
distributive

You can disable the use of the distributive package using -f-distributive.

Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users.

If disabled we will not supply instances of Distributive

EnabledManual

Use -f <flag> to enable a flag, or -f -<flag> to disable that flag. More info

Downloads

Note: This package has metadata revisions in the cabal description newer than included in the tarball. To unpack the package including the revisions, use 'cabal get'.

Maintainer's Corner

For package maintainers and hackage trustees


Readme for comonad-4.2.6

[back to package description]

comonad

Build Status

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