module NumHask.Algebra.Multiplicative (
MultiplicativeMagma(..)
, MultiplicativeUnital(..)
, MultiplicativeAssociative
, MultiplicativeCommutative
, MultiplicativeInvertible(..)
, MultiplicativeHomomorphic(..)
, MultiplicativeMonoidal
, Multiplicative(..)
, MultiplicativeRightCancellative(..)
, MultiplicativeLeftCancellative(..)
, MultiplicativeGroup(..)
) where
import qualified Protolude as P
import Protolude (Double, Float, Int, Integer, Bool(..))
import Data.Functor.Rep
class MultiplicativeMagma a where times :: a -> a -> a
instance MultiplicativeMagma Double where times = (P.*)
instance MultiplicativeMagma Float where times = (P.*)
instance MultiplicativeMagma Int where times = (P.*)
instance MultiplicativeMagma Integer where times = (P.*)
instance MultiplicativeMagma Bool where times = (P.&&)
instance (Representable r, MultiplicativeMagma a) => MultiplicativeMagma (r a) where
times = liftR2 times
class MultiplicativeMagma a => MultiplicativeUnital a where one :: a
instance MultiplicativeUnital Double where one = 1
instance MultiplicativeUnital Float where one = 1
instance MultiplicativeUnital Int where one = 1
instance MultiplicativeUnital Integer where one = 1
instance MultiplicativeUnital Bool where one = True
instance (Representable r, MultiplicativeUnital a) =>
MultiplicativeUnital (r a) where
one = pureRep one
class MultiplicativeMagma a => MultiplicativeCommutative a
instance MultiplicativeCommutative Double
instance MultiplicativeCommutative Float
instance MultiplicativeCommutative Int
instance MultiplicativeCommutative Integer
instance MultiplicativeCommutative Bool
instance (Representable r, MultiplicativeCommutative a) =>
MultiplicativeCommutative (r a)
class MultiplicativeMagma a => MultiplicativeAssociative a
instance MultiplicativeAssociative Double
instance MultiplicativeAssociative Float
instance MultiplicativeAssociative Int
instance MultiplicativeAssociative Integer
instance MultiplicativeAssociative Bool
instance (Representable r, MultiplicativeAssociative a) =>
MultiplicativeAssociative (r a)
class MultiplicativeMagma a => MultiplicativeInvertible a where recip :: a -> a
instance MultiplicativeInvertible Double where recip = P.recip
instance MultiplicativeInvertible Float where recip = P.recip
instance (Representable r, MultiplicativeInvertible a) =>
MultiplicativeInvertible (r a) where
recip = fmapRep recip
class ( MultiplicativeMagma b) =>
MultiplicativeHomomorphic a b where
timeshom :: a -> b
instance (Representable r, MultiplicativeMagma a) =>
MultiplicativeHomomorphic a (r a) where
timeshom a = pureRep a
instance MultiplicativeMagma a => MultiplicativeHomomorphic a a where
timeshom a = a
class ( MultiplicativeUnital a
, MultiplicativeAssociative a) =>
MultiplicativeMonoidal a
instance MultiplicativeMonoidal Double
instance MultiplicativeMonoidal Float
instance MultiplicativeMonoidal Int
instance MultiplicativeMonoidal Integer
instance MultiplicativeMonoidal Bool
instance (Representable r, MultiplicativeMonoidal a) =>
MultiplicativeMonoidal (r a)
class ( MultiplicativeCommutative a
, MultiplicativeUnital a
, MultiplicativeAssociative a) =>
Multiplicative a where
infixl 7 *
(*) :: a -> a -> a
a * b = times a b
instance Multiplicative Double
instance Multiplicative Float
instance Multiplicative Int
instance Multiplicative Integer
instance Multiplicative Bool
instance (Representable r, Multiplicative a) => Multiplicative (r a)
class ( MultiplicativeUnital a
, MultiplicativeAssociative a
, MultiplicativeInvertible a) =>
MultiplicativeLeftCancellative a where
infixl 7 ~/
(~/) :: a -> a -> a
a ~/ b = recip b `times` a
class ( MultiplicativeUnital a
, MultiplicativeAssociative a
, MultiplicativeInvertible a) =>
MultiplicativeRightCancellative a where
infixl 7 /~
(/~) :: a -> a -> a
a /~ b = a `times` recip b
class ( Multiplicative a
, MultiplicativeInvertible a) =>
MultiplicativeGroup a where
infixl 7 /
(/) :: a -> a -> a
(/) a b = a `times` recip b
instance MultiplicativeGroup Double
instance MultiplicativeGroup Float
instance (Representable r, MultiplicativeGroup a) => MultiplicativeGroup (r a)