Agda.Termination.Semiring

Semirings.

Documentation

class Eq a => HasZero a where

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

Instances

HasZero Int

The standard semiring on Ints.

HasZero Integer

The standard semiring on Integers.

HasZero Order

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

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

Methods

multiply :: a -> a -> a

Instances

SemiRing Int

SemiRing Integer

data Semiring a

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 :: (Arbitrary a, Eq a, Show a) => Semiring a -> a -> a -> a -> Bool

Semiring invariant.

integerSemiring :: Semiring Integer

intSemiring :: Semiring Int

boolSemiring :: Semiring Bool

The standard semiring on Bools.

tests :: IO Bool