Safe Haskell	Safe
Language	Haskell98

Agda.Termination.Semiring

Description

Semirings.

Synopsis

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.

Minimal complete definition

zeroElement

Methods

zeroElement :: a Source #

Instances

HasZero Int Source #	The standard semiring on `Int`s.
Methods zeroElement :: Int Source #
HasZero Integer Source #	The standard semiring on `Integer`s.
Methods zeroElement :: Integer Source #
HasZero Order Source #
Methods zeroElement :: Order Source #

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

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

Minimal complete definition

multiply

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.

semiringInvariant :: Eq a => Semiring a -> a -> a -> a -> Bool Source #

Semiring invariant.

integerSemiring :: Semiring Integer Source #

intSemiring :: Semiring Int Source #

boolSemiring :: Semiring Bool Source #

The standard semiring on Bools.

tests :: IO Bool Source #