Numeric.MixedTypes.Mul

Multiplication

type CanMul t1 t2 = (CanMulAsymmetric t1 t2, CanMulAsymmetric t2 t1, MulType t1 t2 ~ MulType t2 t1)

class CanMulAsymmetric t1 t2 where

A replacement for Prelude's *. If t1 = t2 and Num t1, then one can use the default implementation to mirror Prelude's *.

Minimal complete definition

Nothing

Associated Types

type MulType t1 t2

type MulType t1 t2 = t1

Methods

mul :: t1 -> t2 -> MulType t1 t2

default mul :: (MulType t1 t2 ~ t1, t1 ~ t2, Num t1) => t1 -> t2 -> MulType t1 t2

Instances

CanMulAsymmetric Rational Rational

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Rational Rational

Methods

mul :: Rational -> Rational -> MulType Rational Rational

CanMulAsymmetric Rational Integer

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Rational Integer

Methods

mul :: Rational -> Integer -> MulType Rational Integer

CanMulAsymmetric Rational Double

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Rational Double

Methods

mul :: Rational -> Double -> MulType Rational Double

CanMulAsymmetric Rational Int

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Rational Int

Methods

mul :: Rational -> Int -> MulType Rational Int

CanMulAsymmetric Integer Rational

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Integer Rational

Methods

mul :: Integer -> Rational -> MulType Integer Rational

CanMulAsymmetric Integer Integer

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Integer Integer

Methods

mul :: Integer -> Integer -> MulType Integer Integer

CanMulAsymmetric Integer Double

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Integer Double

Methods

mul :: Integer -> Double -> MulType Integer Double

CanMulAsymmetric Integer Int

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Integer Int

Methods

mul :: Integer -> Int -> MulType Integer Int

CanMulAsymmetric Double Rational

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Double Rational

Methods

mul :: Double -> Rational -> MulType Double Rational

CanMulAsymmetric Double Integer

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Double Integer

Methods

mul :: Double -> Integer -> MulType Double Integer

CanMulAsymmetric Double Double

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Double Double

Methods

mul :: Double -> Double -> MulType Double Double

CanMulAsymmetric Double Int

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Double Int

Methods

mul :: Double -> Int -> MulType Double Int

CanMulAsymmetric Int Rational

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Int Rational

Methods

mul :: Int -> Rational -> MulType Int Rational

CanMulAsymmetric Int Integer

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Int Integer

Methods

mul :: Int -> Integer -> MulType Int Integer

CanMulAsymmetric Int Double

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Int Double

Methods

mul :: Int -> Double -> MulType Int Double

CanMulAsymmetric Int Int

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Int Int

Methods

mul :: Int -> Int -> MulType Int Int

CanMulAsymmetric Rational b => CanMulAsymmetric Rational (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Rational (Complex b)

Methods

mul :: Rational -> Complex b -> MulType Rational (Complex b)

(CanMulAsymmetric Rational b, CanGiveUpIfVeryInaccurate (MulType Rational b)) => CanMulAsymmetric Rational (CN b)

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Rational (CN b)

Methods

mul :: Rational -> CN b -> MulType Rational (CN b)

CanMulAsymmetric Integer b => CanMulAsymmetric Integer (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Integer (Complex b)

Methods

mul :: Integer -> Complex b -> MulType Integer (Complex b)

(CanMulAsymmetric Integer b, CanGiveUpIfVeryInaccurate (MulType Integer b)) => CanMulAsymmetric Integer (CN b)

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Integer (CN b)

Methods

mul :: Integer -> CN b -> MulType Integer (CN b)

CanMulAsymmetric Double b => CanMulAsymmetric Double (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Double (Complex b)

Methods

mul :: Double -> Complex b -> MulType Double (Complex b)

(CanMulAsymmetric Double b, CanGiveUpIfVeryInaccurate (MulType Double b)) => CanMulAsymmetric Double (CN b)

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Double (CN b)

Methods

mul :: Double -> CN b -> MulType Double (CN b)

CanMulAsymmetric Int b => CanMulAsymmetric Int (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Int (Complex b)

Methods

mul :: Int -> Complex b -> MulType Int (Complex b)

(CanMulAsymmetric Int b, CanGiveUpIfVeryInaccurate (MulType Int b)) => CanMulAsymmetric Int (CN b)

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType Int (CN b)

Methods

mul :: Int -> CN b -> MulType Int (CN b)

CanMulAsymmetric a Rational => CanMulAsymmetric (Complex a) Rational

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Rational

Methods

mul :: Complex a -> Rational -> MulType (Complex a) Rational

CanMulAsymmetric a Integer => CanMulAsymmetric (Complex a) Integer

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Integer

Methods

mul :: Complex a -> Integer -> MulType (Complex a) Integer

CanMulAsymmetric a Double => CanMulAsymmetric (Complex a) Double

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Double

Methods

mul :: Complex a -> Double -> MulType (Complex a) Double

CanMulAsymmetric a Int => CanMulAsymmetric (Complex a) Int

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Int

Methods

mul :: Complex a -> Int -> MulType (Complex a) Int

(CanMulAsymmetric a Rational, CanGiveUpIfVeryInaccurate (MulType a Rational)) => CanMulAsymmetric (CN a) Rational

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType (CN a) Rational

Methods

mul :: CN a -> Rational -> MulType (CN a) Rational

(CanMulAsymmetric a Integer, CanGiveUpIfVeryInaccurate (MulType a Integer)) => CanMulAsymmetric (CN a) Integer

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType (CN a) Integer

Methods

mul :: CN a -> Integer -> MulType (CN a) Integer

(CanMulAsymmetric a Double, CanGiveUpIfVeryInaccurate (MulType a Double)) => CanMulAsymmetric (CN a) Double

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType (CN a) Double

Methods

mul :: CN a -> Double -> MulType (CN a) Double

(CanMulAsymmetric a Int, CanGiveUpIfVeryInaccurate (MulType a Int)) => CanMulAsymmetric (CN a) Int

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType (CN a) Int

Methods

mul :: CN a -> Int -> MulType (CN a) Int

(CanMulAsymmetric a b, CanAddSameType (MulType a b), CanSubSameType (MulType a b)) => CanMulAsymmetric (Complex a) (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) (Complex b)

Methods

mul :: Complex a -> Complex b -> MulType (Complex a) (Complex b)

(CanMulAsymmetric a b, CanGiveUpIfVeryInaccurate (MulType a b)) => CanMulAsymmetric (CN a) (CN b)

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType (CN a) (CN b)

Methods

mul :: CN a -> CN b -> MulType (CN a) (CN b)

CanMulAsymmetric a b => CanMulAsymmetric (Maybe a) (Maybe b)

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType (Maybe a) (Maybe b)

Methods

mul :: Maybe a -> Maybe b -> MulType (Maybe a) (Maybe b)

CanMulAsymmetric a b => CanMulAsymmetric [a] [b]

Defined in Numeric.MixedTypes.Mul

Associated Types

type MulType [a] [b]

Methods

mul :: [a] -> [b] -> MulType [a] [b]

type CanMulBy t1 t2 = (CanMul t1 t2, MulType t1 t2 ~ t1)

type CanMulSameType t = CanMulBy t t

(*) :: CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2 infixl 7

product :: (CanMulSameType t, ConvertibleExactly Integer t) => [t] -> t

productWithSample :: (CanMulSameType t, ConvertibleExactlyWithSample Integer t) => t -> [t] -> t

Tests

specCanMul :: _ => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of CanMul should satisfy.

specCanMulNotMixed :: _ => T t -> Spec

HSpec properties that each implementation of CanMul should satisfy.

specCanMulSameType :: (Show t, Arbitrary t, ConvertibleExactlyWithSample Integer t, CanTestCertainly (EqCompareType t t), HasEqAsymmetric t t, CanMulAsymmetric t t, MulType t t ~ t) => T t -> Spec

HSpec properties that each implementation of CanMulSameType should satisfy.