semigroups: Anything that associates

[ algebra, bsd3, data, data-structures, library, math ] [ Propose Tags ]

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.


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Versions 0.1.0, 0.2.0, 0.3.0, 0.3.1, 0.3.2, 0.3.3, 0.3.4, 0.3.4.1, 0.3.4.2, 0.4.0, 0.5.0, 0.5.0.1, 0.5.0.2, 0.6, 0.6.1, 0.7.0, 0.7.1, 0.7.1.1, 0.7.1.2, 0.8, 0.8.0.1, 0.8.2, 0.8.3, 0.8.3.1, 0.8.3.2, 0.8.4, 0.8.4.1, 0.8.5, 0.9, 0.9.1, 0.9.2, 0.10, 0.11, 0.12, 0.12.0.1, 0.12.1, 0.12.2, 0.13, 0.13.0.1, 0.14, 0.15, 0.15.1, 0.15.2, 0.15.3, 0.15.4, 0.16, 0.16.0.1, 0.16.1, 0.16.2, 0.16.2.1, 0.16.2.2, 0.17, 0.17.0.1, 0.18, 0.18.0.1, 0.18.1, 0.18.2, 0.18.3, 0.18.4
Dependencies base (>=2 && <4.5 || >=4.6 && <5), bytestring (>=0.9 && <1), containers (>=0.3 && <0.6), hashable (>=1.1 && <1.3), nats (>=0.1 && <1), text (>=0.10 && <2), unordered-containers (==0.2.*) [details]
License BSD-3-Clause
Copyright Copyright (C) 2011-2014 Edward A. Kmett
Author Edward A. Kmett
Maintainer Edward A. Kmett <ekmett@gmail.com>
Revised Revision 1 made by HerbertValerioRiedel at Mon Dec 29 18:08:13 UTC 2014
Category Algebra, Data, Data Structures, Math
Home page http://github.com/ekmett/semigroups/
Bug tracker http://github.com/ekmett/semigroups/issues
Source repo head: git clone git://github.com/ekmett/semigroups.git
Uploaded by EdwardKmett at Wed Apr 9 14:02:14 UTC 2014
Distributions Arch:0.18.4, Debian:0.18.0.1, Fedora:0.18.3, FreeBSD:0.16.2.2, LTSHaskell:0.18.4, NixOS:0.18.4, Stackage:0.18.4, openSUSE:0.18.4
Downloads 384252 total (445 in the last 30 days)
Rating 2.75 (votes: 8) [estimated by rule of succession]
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Status Docs available [build log]
Successful builds reported [all 1 reports]
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Readme for semigroups-0.13

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semigroups

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Haskellers are usually familiar with monoids. A monoid has an appending operation <> or mappend and an identity element mempty. A Semigroup has an append <>, but does not require an mempty element. A Monoid can be made a Semigroup with just instance Semigroup MyMonoid

More formally, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.

Semigroups appear all over the place, except in the Haskell Prelude, so they are packaged here.

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