Module

Data.Semiring

Package
prelude
Repository
purerl/purescript-prelude

#Semiring Source

class Semiring a  where

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 and Int types are not fully law abiding members of this class hierarchy due to the potential for arithmetic overflows, and in the case of Number, the presence of NaN and Infinity values. The behaviour is unspecified in these cases.

Members

Instances

#(+) Source

Operator alias for Data.Semiring.add (left-associative / precedence 6)

#(*) Source

Operator alias for Data.Semiring.mul (left-associative / precedence 7)

#SemiringRecord Source

class SemiringRecord :: RowList Type -> Row Type -> Row Type -> Constraintclass SemiringRecord rowlist row subrow | rowlist -> subrow where

A class for records where all fields have Semiring instances, used to implement the Semiring instance for records.

Members

Instances