semigroupoids: Semigroupoids: Category sans id

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

Provides a wide array of (semi)groupoids and operations for working with them.

A Semigroupoid is a Category without the requirement of identity arrows for every object in the category.

A Category is any Semigroupoid for which the Yoneda lemma holds.

When working with comonads you often have the <*> portion of an Applicative, but not the pure. This was captured in Uustalu and Vene's "Essence of Dataflow Programming" in the form of the ComonadZip class in the days before Applicative. Apply provides a weaker invariant, but for the comonads used for data flow programming (found in the streams package), this invariant is preserved. Applicative function composition forms a semigroupoid.

Similarly many structures are nearly a comonad, but not quite, for instance lists provide a reasonable extend operation in the form of tails, but do not always contain a value.

Ideally the following relationships would hold:

Foldable ----> Traversable <--- Functor ------> Alt ---------> Plus           Semigroupoid
     |               |            |                              |                  |
     v               v            v                              v                  v
Foldable1 ---> Traversable1     Apply --------> Applicative -> Alternative      Category
                                  |               |              |                  |
                                  v               v              v                  v
                                Bind ---------> Monad -------> MonadPlus          Arrow

Apply, Bind, and Extend (not shown) give rise the Static, Kleisli and Cokleisli semigroupoids respectively.

This lets us remove many of the restrictions from various monad transformers as in many cases the binding operation or <*> operation does not require them.

Finally, to work with these weaker structures it is beneficial to have containers that can provide stronger guarantees about their contents, so versions of Traversable and Foldable that can be folded with just a Semigroup are added.


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Versions 1.0.0, 1.1.0, 1.1.1, 1.1.2, 1.1.3, 1.2.0, 1.2.1, 1.2.2, 1.2.2.1, 1.2.2.2, 1.2.2.3, 1.2.2.4, 1.2.4, 1.2.5, 1.2.6, 1.2.6.1, 1.2.6.2, 1.3, 1.3.1, 1.3.1.1, 1.3.1.2, 1.3.2, 1.3.2.1, 1.3.3, 1.3.4, 3.0, 3.0.0.1, 3.0.0.2, 3.0.1, 3.0.2, 3.0.3, 3.1, 4.0, 4.0.1, 4.0.2, 4.0.2.1, 4.0.3, 4.0.4, 4.2, 4.3, 4.5, 5, 5.0.0.1, 5.0.0.2, 5.0.0.3, 5.0.0.4, 5.0.1, 5.1, 5.2, 5.2.1, 5.2.2 (info)
Change log CHANGELOG.markdown
Dependencies base (>=4.5 && <5), base-orphans (>=0.3 && <1), bifunctors (==5.*), comonad (>=4.2.6 && <5), containers (>=0.3 && <0.6), contravariant (>=0.2.0.1 && <2), distributive (>=0.2.2 && <1), semigroups (>=0.8.3.1 && <1), tagged (>=0.8.5 && <1), transformers (>=0.2 && <0.6), transformers-compat (>=0.3 && <0.5) [details]
License BSD-3-Clause
Copyright Copyright (C) 2011-2015 Edward A. Kmett
Author Edward A. Kmett
Maintainer Edward A. Kmett <ekmett@gmail.com>
Revised Revision 2 made by ryanglscott at Sat Jan 6 17:55:55 UTC 2018
Category Control, Comonads
Home page http://github.com/ekmett/semigroupoids
Bug tracker http://github.com/ekmett/semigroupoids/issues
Source repo head: git clone git://github.com/ekmett/semigroupoids.git
Uploaded by EdwardKmett at Tue Jun 2 10:03:45 UTC 2015
Distributions Arch:5.2.2, Debian:5.0.0.4, Fedora:5.2.1, FreeBSD:5.0.0.3, LTSHaskell:5.2.2, NixOS:5.2.2, Stackage:5.2.2, openSUSE:5.2.2
Downloads 207960 total (456 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 2015-06-03 [all 1 reports]
Hackage Matrix CI

Modules

[Index]

Flags

NameDescriptionDefaultType
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
doctests

You can disable testing with doctests using -f-doctests.

EnabledManual
comonad

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

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 Comonad

EnabledManual
tagged

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

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

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 semigroupoids-5.0.0.2

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semigroupoids

Build Status

A semigroupoid is a Category without id.

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