# 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.

Versions [faq] 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 CHANGELOG.markdown base (>=2 && <5), binary, bytestring (>=0.9 && <1), bytestring-builder (>=0.10.4 && <1), containers (>=0.3 && <0.6), deepseq (>=1.1 && <1.5), ghc-prim, hashable (>=1.1.1.0 && <1.3), nats (>=0.1 && <2), tagged (>=0.4.4 && <1), text (>=0.10 && <2), transformers (>=0.2 && <0.6), unordered-containers (==0.2.*) [details] BSD-3-Clause Copyright (C) 2011-2015 Edward A. Kmett Edward A. Kmett Edward A. Kmett Revision 1 made by phadej at 2019-05-24T14:28:28Z 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 ryanglscott at 2016-06-23T12:54:05Z Arch:0.19.1, Debian:0.18.5, Fedora:0.19.1, FreeBSD:0.16.2.2, LTSHaskell:0.18.5, NixOS:0.19.1, Stackage:0.18.5, openSUSE:0.19.1 438232 total (2025 in the last 30 days) 2.75 (votes: 9) [estimated by Bayesian average] λ λ λ Docs available Last success reported on 2016-06-23

[Index]

## Flags

NameDescriptionDefaultType
hashable

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

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 Hashable

Note: -f-hashable implies -f-unordered-containers, as we are necessarily not able to supply those instances as well.

EnabledManual
binary

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

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

EnabledManual
bytestring

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

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

EnabledManual
bytestring-builder

You can disable the use of the bytestring-builder package using -f-bytestring-builder.

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

EnabledAutomatic
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
deepseq

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

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

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
text

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

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

EnabledManual
transformers

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

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

EnabledManual
unordered-containers

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

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

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

[back to package description]

# semigroups

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