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
• (RowToList row list, SemiringRecord list row row) => Semiring (Record row)

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

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

class 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

• addRecord :: RLProxy rowlist -> Record row -> Record row -> Record subrow
• mulRecord :: RLProxy rowlist -> Record row -> Record row -> Record subrow
• oneRecord :: RLProxy rowlist -> RProxy row -> Record subrow
• zeroRecord :: RLProxy rowlist -> RProxy row -> Record subrow

Instances

• SemiringRecord Nil row ()
• (IsSymbol key, Cons key focus subrowTail subrow, SemiringRecord rowlistTail row subrowTail, Semiring focus) => SemiringRecord (Cons key focus rowlistTail) row subrow