# 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 [RSS] 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, 0.18.5, 0.19, 0.19.1, 0.19.2, 0.20 base (>=2 && <5), bytestring (>=0.9 && <0.11), containers (>=0.3 && <0.6), hashable (>=1.1 && <1.3), nats (>=0.1 && <1), text (>=0.10 && <0.12), unordered-containers (>=0.2 && <0.3) [details] BSD-3-Clause Copyright (C) 2011-2013 Edward A. Kmett Edward A. Kmett Edward A. Kmett Algebra, Data, Data Structures, Math http://github.com/ekmett/semigroups/ http://github.com/ekmett/semigroups/issues head: git clone git://github.com/ekmett/semigroups.git by EdwardKmett at 2013-11-26T01:35:22Z Debian:0.19.1, Fedora:0.19.1, FreeBSD:0.16.2.2, LTSHaskell:0.19.2, NixOS:0.19.2, Stackage:0.20, openSUSE:0.20 473705 total (1345 in the last 30 days) 2.75 (votes: 9) [estimated by Bayesian average] λ λ λ Docs available Successful builds reported

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# semigroups

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.

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