Safe Haskell	None
Language	Haskell98

Semiring

Description

Semirings. Original: Agda.Terminatio.Semiring

Synopsis

class Eq a => HasZero a where
- zeroElement :: a
class (Eq a, Monoid a) => SemiRing a where
- multiply :: a -> a -> a
data Semiring a = Semiring {
- add :: a -> a -> a
- mul :: a -> a -> a
- zero :: a
}
integerSemiring :: Semiring Integer
boolSemiring :: Semiring Bool

Documentation

class Eq a => HasZero a where Source #

HasZero is needed for sparse matrices, to tell which is the element that does not have to be stored. It is a cut-down version of SemiRing which is definable without the implicit ?cutoff.

Methods

zeroElement :: a Source #

Instances

Instances details

HasZero Order Source #
Instance details Defined in Termination Methods zeroElement :: Order Source #
HasZero Integer Source #	Semiring invariant. The standard semiring on `Integer`s.
Instance details Defined in Semiring Methods zeroElement :: Integer Source #

class (Eq a, Monoid a) => SemiRing a where Source #

SemiRing type class. Additive monoid with multiplication operation. Inherit addition and zero from Monoid.

Methods

multiply :: a -> a -> a Source #

data Semiring a Source #

Semirings.

Constructors

Semiring
Fields add :: a -> a -> a Addition. mul :: a -> a -> a Multiplication. zero :: a Zero. The one is never used in matrix multiplication , one :: a -- ^ One.

integerSemiring :: Semiring Integer Source #

boolSemiring :: Semiring Bool Source #

The standard semiring on Bools.