{-# OPTIONS_GHC -Wall #-}
module NumHask.Algebra.Ring
( Semiring
, Ring
, CRing
, StarSemiring(..)
, KleeneAlgebra
) where
import Data.Complex (Complex(..))
import NumHask.Algebra.Additive
import NumHask.Algebra.Distribution
import NumHask.Algebra.Multiplicative
import Prelude (Bool(..), Double, Float, Int, Integer)
class (MultiplicativeAssociative a, MultiplicativeUnital a, Distribution a) =>
Semiring a
instance Semiring Double
instance Semiring Float
instance Semiring Int
instance Semiring Integer
instance Semiring Bool
instance (AdditiveGroup a, Semiring a) => Semiring (Complex a)
class ( Semiring a
, AdditiveGroup a
) =>
Ring a
instance Ring Double
instance Ring Float
instance Ring Int
instance Ring Integer
instance (Ring a) => Ring (Complex a)
class (Multiplicative a, Ring a) =>
CRing a
instance CRing Double
instance CRing Float
instance CRing Int
instance CRing Integer
instance (CRing a) => CRing (Complex a)
class (Semiring a) => StarSemiring a where
star :: a -> a
star a = one + plus' a
plus' :: a -> a
plus' a = a `times` star a
class (StarSemiring a, AdditiveIdempotent a) => KleeneAlgebra a