Agda-2.5.1.2: A dependently typed functional programming language and proof assistant

Safe HaskellSafe
LanguageHaskell98

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 Ints.

HasZero Integer Source #

The standard semiring on Integers.

HasZero 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.

boolSemiring :: Semiring Bool Source #

The standard semiring on Bools.