semirings

two monoids as one, in holy haskimony

Version0.7
CategoryAlgebra, Data, Data Structures, Math, Maths, Mathematics
LicenceBSD-3-Clause
Authorchessai
Maintainerchessai <chessai1996@gmail.com>
Homepagegithub.com/chessai/semirings
Pinned byhackage semirings 0.7
Sourcehackage.haskell.org/package/semirings-0.7

Modules

8 modules

Data.Euclidean6
Data.Field5A Field is a Ring in which all nonzero elements
Data.Ring.Ordered2An 'ordered ring' is a ring with a total order. Mathematical pedantry note Many (if not most) of the instances of the OrderedRing type cl…
Data.Semiring23A class for semirings (types with two binary operations, one commutative and one associative, and two respective identities), with variou…
Data.Semiring.Directed1A "directed semiring" refers to the semiring composed of the union of upwards
Data.Semiring.Generic9This module provides generic deriving tools for semirings and rings for
Data.Semiring.Tropical4A tropical semiring is an extension of another totally ordered
Data.Star1A class for *-semirings (pron. "star-semirings").

Description

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.

Depends on

4 packages

Modules

Description

Depends on

Used by in this set · 2