mixed-types-num-0.6.2: Alternative Prelude with numeric and logic expressions typed bottom-up
Copyright(c) Michal Konecny
LicenseBSD3
Maintainer[email protected]
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell2010

Numeric.MixedTypes.Div

Description

 
Synopsis

Division

class CanDiv t1 t2 where Source #

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

Associated Types

type DivType t1 t2 Source #

type DivType t1 t2 = t1

Methods

divide :: t1 -> t2 -> DivType t1 t2 Source #

Instances

Instances details
CanDiv Rational Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Rational Rational 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Rational Rational = Rational

Methods

divide :: Rational -> Rational -> DivType Rational Rational Source #

CanDiv Rational Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Rational Integer 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Rational Integer = Rational

Methods

divide :: Rational -> Integer -> DivType Rational Integer Source #

CanDiv Rational Double Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Rational Double 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Rational Double = Double

Methods

divide :: Rational -> Double -> DivType Rational Double Source #

CanDiv Rational Int Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Rational Int 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Rational Int = Rational

Methods

divide :: Rational -> Int -> DivType Rational Int Source #

CanDiv Integer Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Integer Rational 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Integer Rational = Rational

Methods

divide :: Integer -> Rational -> DivType Integer Rational Source #

CanDiv Integer Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Integer Integer 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Integer Integer = Rational

Methods

divide :: Integer -> Integer -> DivType Integer Integer Source #

CanDiv Integer Double Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Integer Double 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Integer Double = Double

Methods

divide :: Integer -> Double -> DivType Integer Double Source #

CanDiv Integer Int Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Integer Int 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Integer Int = Rational

Methods

divide :: Integer -> Int -> DivType Integer Int Source #

CanDiv Double Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Double Rational 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Double Rational = Double

Methods

divide :: Double -> Rational -> DivType Double Rational Source #

CanDiv Double Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Double Integer 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Double Integer = Double

Methods

divide :: Double -> Integer -> DivType Double Integer Source #

CanDiv Double Double Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Double Double 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Double Double = Double

Methods

divide :: Double -> Double -> DivType Double Double Source #

CanDiv Double Int Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Double Int 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Double Int = Double

Methods

divide :: Double -> Int -> DivType Double Int Source #

CanDiv Int Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Int Rational 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Int Rational = Rational

Methods

divide :: Int -> Rational -> DivType Int Rational Source #

CanDiv Int Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Int Integer 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Int Integer = Rational

Methods

divide :: Int -> Integer -> DivType Int Integer Source #

CanDiv Int Double Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Int Double 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Int Double = Double

Methods

divide :: Int -> Double -> DivType Int Double Source #

CanDiv Int Int Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Int Int 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Int Int = Rational

Methods

divide :: Int -> Int -> DivType Int Int Source #

(CanMulAsymmetric Rational b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Rational b) (MulType b b)) => CanDiv Rational (Complex b) Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType Rational (Complex b) 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType Rational (Complex b) = Complex (DivType (MulType Rational b) (MulType b b))

Methods

divide :: Rational -> Complex b -> DivType Rational (Complex b) Source #

(CanDiv Rational b, CanTestZero b) => CanDiv Rational (CN b) Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Rational (CN b) 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Rational (CN b) = CN (DivType Rational b)

Methods

divide :: Rational -> CN b -> DivType Rational (CN b) Source #

(CanMulAsymmetric Integer b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Integer b) (MulType b b)) => CanDiv Integer (Complex b) Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType Integer (Complex b) 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType Integer (Complex b) = Complex (DivType (MulType Integer b) (MulType b b))

Methods

divide :: Integer -> Complex b -> DivType Integer (Complex b) Source #

(CanDiv Integer b, CanTestZero b) => CanDiv Integer (CN b) Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Integer (CN b) 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Integer (CN b) = CN (DivType Integer b)

Methods

divide :: Integer -> CN b -> DivType Integer (CN b) Source #

(CanMulAsymmetric Double b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Double b) (MulType b b)) => CanDiv Double (Complex b) Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType Double (Complex b) 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType Double (Complex b) = Complex (DivType (MulType Double b) (MulType b b))

Methods

divide :: Double -> Complex b -> DivType Double (Complex b) Source #

(CanDiv Double b, CanTestZero b) => CanDiv Double (CN b) Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Double (CN b) 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Double (CN b) = CN (DivType Double b)

Methods

divide :: Double -> CN b -> DivType Double (CN b) Source #

(CanMulAsymmetric Int b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Int b) (MulType b b)) => CanDiv Int (Complex b) Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType Int (Complex b) 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType Int (Complex b) = Complex (DivType (MulType Int b) (MulType b b))

Methods

divide :: Int -> Complex b -> DivType Int (Complex b) Source #

(CanDiv Int b, CanTestZero b) => CanDiv Int (CN b) Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType Int (CN b) 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType Int (CN b) = CN (DivType Int b)

Methods

divide :: Int -> CN b -> DivType Int (CN b) Source #

CanDiv a Rational => CanDiv (Complex a) Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType (Complex a) Rational 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType (Complex a) Rational = Complex (DivType a Rational)

Methods

divide :: Complex a -> Rational -> DivType (Complex a) Rational Source #

CanDiv a Integer => CanDiv (Complex a) Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType (Complex a) Integer 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType (Complex a) Integer = Complex (DivType a Integer)

Methods

divide :: Complex a -> Integer -> DivType (Complex a) Integer Source #

CanDiv a Double => CanDiv (Complex a) Double Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType (Complex a) Double 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType (Complex a) Double = Complex (DivType a Double)

Methods

divide :: Complex a -> Double -> DivType (Complex a) Double Source #

CanDiv a Int => CanDiv (Complex a) Int Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType (Complex a) Int 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType (Complex a) Int = Complex (DivType a Int)

Methods

divide :: Complex a -> Int -> DivType (Complex a) Int Source #

CanDiv a Rational => CanDiv (CN a) Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType (CN a) Rational 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType (CN a) Rational = CN (DivType a Rational)

Methods

divide :: CN a -> Rational -> DivType (CN a) Rational Source #

CanDiv a Integer => CanDiv (CN a) Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType (CN a) Integer 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType (CN a) Integer = CN (DivType a Integer)

Methods

divide :: CN a -> Integer -> DivType (CN a) Integer Source #

CanDiv a Double => CanDiv (CN a) Double Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType (CN a) Double 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType (CN a) Double = CN (DivType a Double)

Methods

divide :: CN a -> Double -> DivType (CN a) Double Source #

CanDiv a Int => CanDiv (CN a) Int Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType (CN a) Int 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType (CN a) Int = CN (DivType a Int)

Methods

divide :: CN a -> Int -> DivType (CN a) Int Source #

(CanMulAsymmetric a b, CanAddSameType (MulType a b), CanSubSameType (MulType a b), CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType a b) (MulType b b)) => CanDiv (Complex a) (Complex b) Source # 
Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type DivType (Complex a) (Complex b) 
Instance details

Defined in Numeric.MixedTypes.Complex

type DivType (Complex a) (Complex b) = Complex (DivType (MulType a b) (MulType b b))

Methods

divide :: Complex a -> Complex b -> DivType (Complex a) (Complex b) Source #

(CanDiv a b, CanTestZero b) => CanDiv (CN a) (CN b) Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType (CN a) (CN b) 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType (CN a) (CN b) = CN (DivType a b)

Methods

divide :: CN a -> CN b -> DivType (CN a) (CN b) Source #

CanDiv a b => CanDiv (Maybe a) (Maybe b) Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType (Maybe a) (Maybe b) 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType (Maybe a) (Maybe b) = Maybe (DivType a b)

Methods

divide :: Maybe a -> Maybe b -> DivType (Maybe a) (Maybe b) Source #

CanDiv a b => CanDiv [a] [b] Source # 
Instance details

Defined in Numeric.MixedTypes.Div

Associated Types

type DivType [a] [b] 
Instance details

Defined in Numeric.MixedTypes.Div

type DivType [a] [b] = [DivType a b]

Methods

divide :: [a] -> [b] -> DivType [a] [b] Source #

type CanDivBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ t1) Source #

type CanDivSameType t = CanDivBy t t Source #

type CanRecip t = CanDiv Integer t Source #

type CanRecipSameType t = (CanDiv Integer t, DivType Integer t ~ t) Source #

(/) :: CanDiv t1 t2 => t1 -> t2 -> DivType t1 t2 infixl 7 Source #

recip :: CanRecip t => t -> DivType Integer t Source #

Tests

specCanDiv :: (Arbitrary t1, Arbitrary t2, Arbitrary (DivType t1 t1), CanDiv t1 t2, CanDiv t1 t1, CanRecip t1, CanRecip (DivType Integer t1), CanTestZero t1, CanTestZero t2, CanTestZero (DivType Integer t1), HasEqAsymmetric (DivType t1 t1) (DivType t1 t1), HasEqAsymmetric (DivType t1 t2) t1, HasEqAsymmetric (DivType t1 t2) (MulType t1 (DivType t1 t2)), HasEqAsymmetric (DivType Integer (DivType Integer t1)) t1, CanTestCertainly (EqCompareType (DivType t1 t1) (DivType t1 t1)), CanTestCertainly (EqCompareType (DivType t1 t2) t1), CanTestCertainly (EqCompareType (DivType t1 t2) (MulType t1 (DivType t1 t2))), CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t1)) t1), Show t1, Show t2, Show (DivType t1 t2), Show (DivType t1 t1), Show (DivType Integer (DivType Integer t1)), Show (MulType t1 (DivType t1 t2)), CanMulAsymmetric t1 (DivType t1 t2), ConvertibleExactlyWithSample Integer t2, ConvertibleExactlyWithSample Integer t1, ConvertibleExactlyWithSample Integer (DivType t1 t1)) => T t1 -> T t2 -> Spec Source #

HSpec properties that each implementation of CanDiv should satisfy.

specCanDivNotMixed :: (Arbitrary t, Arbitrary (DivType t t), CanDiv t t, CanRecip t, CanRecip (DivType Integer t), CanTestZero t, CanTestZero (DivType Integer t), HasEqAsymmetric (DivType t t) t, HasEqAsymmetric (DivType t t) (DivType t t), HasEqAsymmetric (DivType t t) (MulType t (DivType t t)), HasEqAsymmetric (DivType Integer (DivType Integer t)) t, CanTestCertainly (EqCompareType (DivType t t) t), CanTestCertainly (EqCompareType (DivType t t) (DivType t t)), CanTestCertainly (EqCompareType (DivType t t) (MulType t (DivType t t))), CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t)) t), Show t, Show (DivType t t), Show (DivType Integer (DivType Integer t)), Show (MulType t (DivType t t)), CanMulAsymmetric t (DivType t t), ConvertibleExactlyWithSample Integer t, ConvertibleExactlyWithSample Integer (DivType t t)) => T t -> Spec Source #

HSpec properties that each implementation of CanDiv should satisfy.