Overview

The Semiring class is for types that support an addition and multiplication operation.

Instances must satisfy the following laws:

  • Commutative monoid under addition:
    • Associativity: (a + b) + c = a + (b + c)
    • Identity: zero + a = a + zero = a
    • Commutative: a + b = b + a
  • Monoid under multiplication:
    • Associativity: (a * b) * c = a * (b * c)
    • Identity: one * a = a * one = a
  • Multiplication distributes over addition:
    • Left distributivity: a * (b + c) = (a * b) + (a * c)
    • Right distributivity: (a + b) * c = (a * c) + (b * c)
  • Annihilation: zero * a = a * zero = zero

Note: The number type is not fully law abiding members of this class hierarchy due to the potential for arithmetic overflows, and the presence of NaN and Infinity values. The behaviour is unspecified in these cases.


Table of contents


Semiring (interface)

Signature

export interface Semiring<A> {
  readonly add: (x: A, y: A) => A
  readonly zero: A
  readonly mul: (x: A, y: A) => A
  readonly one: A
}

Added in v2.0.0

getFunctionSemiring (function)

Signature

export function getFunctionSemiring<A, B>(S: Semiring<B>): Semiring<(a: A) => B> { ... }

Added in v2.0.0