# semirings: two monoids as one, in holy haskimony

Haskellers are usually familiar with monoids and semigroups. A monoid has an appending operation `<>`

(or `mappend`

),
and an identity element, `mempty`

. A semigroup has an appending `<>`

operation, but does not require a `mempty`

element.

A Semiring has two appending operations, `plus`

and `times`

, and two respective identity elements, `zero`

and `one`

.

More formally, a Semiring R is a set equipped with two binary relations `+`

and `*`

, such that:

(R,+) is a commutative monoid with identity element 0,

(R,*) is a monoid with identity element 1,

(*) left and right distributes over addition, and

multiplication by '0' annihilates R.

[Skip to Readme]

## Modules

[Index] [Quick Jump]

## Flags

### Manual Flags

Name | Description | Default |
---|---|---|

containers | You can disable the use of the Disabling this may be useful for accelerating builds in sandboxes for expert users. | Enabled |

unordered-containers | You can disable the use of the `unordered-containers` package using `-f-unordered-containers`. Disabling this may be useful for accelerating builds in sandboxes for expert users. | Enabled |

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

## Downloads

- semirings-0.7.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)

#### Maintainer's Corner

For package maintainers and hackage trustees

Candidates

Versions [RSS] | 0.0.0, 0.1.0, 0.1.1, 0.1.2, 0.1.3.0, 0.2.0.0, 0.2.0.1, 0.2.1.0, 0.2.1.1, 0.3.0.0, 0.3.1.0, 0.3.1.1, 0.3.1.2, 0.4, 0.4.1, 0.4.2, 0.5, 0.5.1, 0.5.2, 0.5.3, 0.5.4, 0.6, 0.7 |
---|---|

Change log | CHANGELOG.md |

Dependencies | base (>=4.8 && <5), containers (>=0.5.4), hashable (>=1.1), template-haskell (>=2.4.0.0), unordered-containers (>=0.2) [details] |

Tested with | ghc ==8.0, ghc ==8.2, ghc ==8.4, ghc ==8.6, ghc ==8.8, ghc ==8.10, ghc ==9.0, ghc ==9.2, ghc ==9.4, ghc ==9.6 |

License | BSD-3-Clause |

Copyright | Copyright (C) 2018 chessai |

Author | chessai |

Maintainer | chessai <chessai1996@gmail.com> |

Category | Algebra, Data, Data Structures, Math, Maths, Mathematics |

Home page | http://github.com/chessai/semirings |

Bug tracker | http://github.com/chessai/semirings/issues |

Source repo | head: git clone git://github.com/chessai/semirings.git |

Uploaded | by chessai at 2024-05-21T19:43:36Z |

Distributions | Arch:0.6, LTSHaskell:0.6, NixOS:0.6, Stackage:0.7 |

Reverse Dependencies | 18 direct, 7880 indirect [details] |

Downloads | 21267 total (256 in the last 30 days) |

Rating | 2.0 (votes: 1) [estimated by Bayesian average] |

Your Rating | |

Status | Docs uploaded by user Build status unknown [no reports yet] |