Data.Semiring

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

• add :: a -> a -> a
• zero :: a
• mul :: a -> a -> a
• one :: a

Instances

• Semiring Int
• Semiring Number
• (Semiring b) => Semiring (a -> b)
• Semiring Unit

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

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