Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

Numeric.MixedTypes.MinMaxAbs

Contents

Minimum and maximum
- Tests
Absolute value
- Tests
Orphan instances

Description

Synopsis

type CanMinMax t1 t2 = (CanMinMaxAsymmetric t1 t2, CanMinMaxAsymmetric t2 t1, MinMaxType t1 t2 ~ MinMaxType t2 t1)
class CanMinMaxAsymmetric t1 t2 where
- type MinMaxType t1 t2
- min :: t1 -> t2 -> MinMaxType t1 t2
- max :: t1 -> t2 -> MinMaxType t1 t2
type CanMinMaxThis t1 t2 = (CanMinMax t1 t2, MinMaxType t1 t2 ~ t1)
type CanMinMaxSameType t = CanMinMaxThis t t
minimum :: CanMinMaxSameType t => [t] -> t
maximum :: CanMinMaxSameType t => [t] -> t
specCanMinMax :: (Show t1, Show t2, Show t3, Show (MinMaxType t1 t2), Show (MinMaxType t1 t1), Show (MinMaxType t2 t1), Show (MinMaxType t1 (MinMaxType t2 t3)), Show (MinMaxType (MinMaxType t1 t2) t3), Arbitrary t1, Arbitrary t2, Arbitrary t3, CanTestCertainly (EqCompareType t1 t1), CanTestCertainly (EqCompareType t2 t2), CanTestCertainly (OrderCompareType (MinMaxType t1 t2) t2), CanTestCertainly (OrderCompareType (MinMaxType t1 t2) t1), CanTestCertainly (EqCompareType (MinMaxType t1 t1) t1), CanTestCertainly (EqCompareType (MinMaxType t1 t2) (MinMaxType t2 t1)), CanTestCertainly (EqCompareType t3 t3), CanTestCertainly (EqCompareType (MinMaxType t1 (MinMaxType t2 t3)) (MinMaxType (MinMaxType t1 t2) t3)), CanTestFinite t1, CanTestFinite t2, CanTestFinite t3, HasEqAsymmetric t1 t1, HasEqAsymmetric t2 t2, HasEqAsymmetric t3 t3, HasEqAsymmetric (MinMaxType t1 t2) (MinMaxType t2 t1), HasEqAsymmetric (MinMaxType t1 t1) t1, HasEqAsymmetric (MinMaxType t1 (MinMaxType t2 t3)) (MinMaxType (MinMaxType t1 t2) t3), HasOrderAsymmetric (MinMaxType t1 t2) t1, HasOrderAsymmetric (MinMaxType t1 t2) t2, CanMinMaxAsymmetric t1 t1, CanMinMaxAsymmetric t1 t2, CanMinMaxAsymmetric t1 (MinMaxType t2 t3), CanMinMaxAsymmetric t2 t1, CanMinMaxAsymmetric t2 t3, CanMinMaxAsymmetric (MinMaxType t1 t2) t3) => T t1 -> T t2 -> T t3 -> Spec
specCanMinMaxNotMixed :: (Show t, Show (MinMaxType t t), Show (MinMaxType t (MinMaxType t t)), Show (MinMaxType (MinMaxType t t) t), Arbitrary t, CanTestCertainly (EqCompareType t t), CanTestCertainly (OrderCompareType (MinMaxType t t) t), CanTestCertainly (EqCompareType (MinMaxType t t) t), CanTestCertainly (EqCompareType (MinMaxType t t) (MinMaxType t t)), CanTestCertainly (EqCompareType (MinMaxType t (MinMaxType t t)) (MinMaxType (MinMaxType t t) t)), CanTestFinite t, HasEqAsymmetric t t, HasEqAsymmetric (MinMaxType t t) t, HasEqAsymmetric (MinMaxType t t) (MinMaxType t t), HasEqAsymmetric (MinMaxType t (MinMaxType t t)) (MinMaxType (MinMaxType t t) t), HasOrderAsymmetric (MinMaxType t t) t, CanMinMaxAsymmetric t t, CanMinMaxAsymmetric t (MinMaxType t t), CanMinMaxAsymmetric (MinMaxType t t) t) => T t -> Spec
class CanAbs t where
- type AbsType t
- abs :: t -> AbsType t
type CanAbsSameType t = (CanAbs t, AbsType t ~ t)
specCanNegNum :: (CanNegX t, CanNegX (NegType t), HasEqCertainly t (NegType (NegType t)), ConvertibleExactly Integer t, HasEqCertainly t t, HasEqCertainly t (NegType t), CanTestFinite t, CanTestPosNeg t, CanTestPosNeg (NegType t)) => T t -> Spec
specCanAbs :: (CanAbsX t, CanAbsX (AbsType t), CanTestFinite t) => T t -> Spec

Minimum and maximum

type CanMinMax t1 t2 = (CanMinMaxAsymmetric t1 t2, CanMinMaxAsymmetric t2 t1, MinMaxType t1 t2 ~ MinMaxType t2 t1) Source #

class CanMinMaxAsymmetric t1 t2 where Source #

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

Minimal complete definition

Nothing

Associated Types

type MinMaxType t1 t2 Source #

Methods

min :: t1 -> t2 -> MinMaxType t1 t2 Source #

max :: t1 -> t2 -> MinMaxType t1 t2 Source #

min :: (MinMaxType t1 t2 ~ t1, t1 ~ t2, Ord t1) => t1 -> t2 -> MinMaxType t1 t2 Source #

max :: (MinMaxType t1 t2 ~ t1, t1 ~ t2, Ord t1) => t1 -> t2 -> MinMaxType t1 t2 Source #

Instances

CanMinMaxAsymmetric Double Double Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Double Double :: Type Source # Methods min :: Double -> Double -> MinMaxType Double Double Source # max :: Double -> Double -> MinMaxType Double Double Source #
CanMinMaxAsymmetric Int Int Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Int Int :: Type Source # Methods min :: Int -> Int -> MinMaxType Int Int Source # max :: Int -> Int -> MinMaxType Int Int Source #
CanMinMaxAsymmetric Int Integer Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Int Integer :: Type Source # Methods min :: Int -> Integer -> MinMaxType Int Integer Source # max :: Int -> Integer -> MinMaxType Int Integer Source #
CanMinMaxAsymmetric Int Rational Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Int Rational :: Type Source # Methods min :: Int -> Rational -> MinMaxType Int Rational Source # max :: Int -> Rational -> MinMaxType Int Rational Source #
CanMinMaxAsymmetric Integer Int Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Integer Int :: Type Source # Methods min :: Integer -> Int -> MinMaxType Integer Int Source # max :: Integer -> Int -> MinMaxType Integer Int Source #
CanMinMaxAsymmetric Integer Integer Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Integer Integer :: Type Source # Methods min :: Integer -> Integer -> MinMaxType Integer Integer Source # max :: Integer -> Integer -> MinMaxType Integer Integer Source #
CanMinMaxAsymmetric Integer Rational Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Integer Rational :: Type Source # Methods min :: Integer -> Rational -> MinMaxType Integer Rational Source # max :: Integer -> Rational -> MinMaxType Integer Rational Source #
CanMinMaxAsymmetric Rational Int Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Rational Int :: Type Source # Methods min :: Rational -> Int -> MinMaxType Rational Int Source # max :: Rational -> Int -> MinMaxType Rational Int Source #
CanMinMaxAsymmetric Rational Integer Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Rational Integer :: Type Source # Methods min :: Rational -> Integer -> MinMaxType Rational Integer Source # max :: Rational -> Integer -> MinMaxType Rational Integer Source #
CanMinMaxAsymmetric Rational Rational Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Rational Rational :: Type Source # Methods min :: Rational -> Rational -> MinMaxType Rational Rational Source # max :: Rational -> Rational -> MinMaxType Rational Rational Source #
(CanMinMaxAsymmetric Double b, CanEnsureCE es b, CanEnsureCE es (MinMaxType Double b), SuitableForCE es) => CanMinMaxAsymmetric Double (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Double (CollectErrors es b) :: Type Source # Methods min :: Double -> CollectErrors es b -> MinMaxType Double (CollectErrors es b) Source # max :: Double -> CollectErrors es b -> MinMaxType Double (CollectErrors es b) Source #
(CanMinMaxAsymmetric Int b, CanEnsureCE es b, CanEnsureCE es (MinMaxType Int b), SuitableForCE es) => CanMinMaxAsymmetric Int (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Int (CollectErrors es b) :: Type Source # Methods min :: Int -> CollectErrors es b -> MinMaxType Int (CollectErrors es b) Source # max :: Int -> CollectErrors es b -> MinMaxType Int (CollectErrors es b) Source #
(CanMinMaxAsymmetric Integer b, CanEnsureCE es b, CanEnsureCE es (MinMaxType Integer b), SuitableForCE es) => CanMinMaxAsymmetric Integer (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Integer (CollectErrors es b) :: Type Source # Methods min :: Integer -> CollectErrors es b -> MinMaxType Integer (CollectErrors es b) Source # max :: Integer -> CollectErrors es b -> MinMaxType Integer (CollectErrors es b) Source #
(CanMinMaxAsymmetric Rational b, CanEnsureCE es b, CanEnsureCE es (MinMaxType Rational b), SuitableForCE es) => CanMinMaxAsymmetric Rational (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType Rational (CollectErrors es b) :: Type Source # Methods min :: Rational -> CollectErrors es b -> MinMaxType Rational (CollectErrors es b) Source # max :: Rational -> CollectErrors es b -> MinMaxType Rational (CollectErrors es b) Source #
CanMinMaxAsymmetric a b => CanMinMaxAsymmetric [a] [b] Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType [a] [b] :: Type Source # Methods min :: [a] -> [b] -> MinMaxType [a] [b] Source # max :: [a] -> [b] -> MinMaxType [a] [b] Source #
CanMinMaxAsymmetric a b => CanMinMaxAsymmetric (Maybe a) (Maybe b) Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType (Maybe a) (Maybe b) :: Type Source # Methods min :: Maybe a -> Maybe b -> MinMaxType (Maybe a) (Maybe b) Source # max :: Maybe a -> Maybe b -> MinMaxType (Maybe a) (Maybe b) Source #
(CanMinMaxAsymmetric a Integer, CanEnsureCE es a, CanEnsureCE es (MinMaxType a Integer), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) Integer Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType (CollectErrors es a) Integer :: Type Source # Methods min :: CollectErrors es a -> Integer -> MinMaxType (CollectErrors es a) Integer Source # max :: CollectErrors es a -> Integer -> MinMaxType (CollectErrors es a) Integer Source #
(CanMinMaxAsymmetric a Int, CanEnsureCE es a, CanEnsureCE es (MinMaxType a Int), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) Int Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType (CollectErrors es a) Int :: Type Source # Methods min :: CollectErrors es a -> Int -> MinMaxType (CollectErrors es a) Int Source # max :: CollectErrors es a -> Int -> MinMaxType (CollectErrors es a) Int Source #
(CanMinMaxAsymmetric a Rational, CanEnsureCE es a, CanEnsureCE es (MinMaxType a Rational), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) Rational Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType (CollectErrors es a) Rational :: Type Source # Methods min :: CollectErrors es a -> Rational -> MinMaxType (CollectErrors es a) Rational Source # max :: CollectErrors es a -> Rational -> MinMaxType (CollectErrors es a) Rational Source #
(CanMinMaxAsymmetric a Double, CanEnsureCE es a, CanEnsureCE es (MinMaxType a Double), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) Double Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType (CollectErrors es a) Double :: Type Source # Methods min :: CollectErrors es a -> Double -> MinMaxType (CollectErrors es a) Double Source # max :: CollectErrors es a -> Double -> MinMaxType (CollectErrors es a) Double Source #
(CanMinMaxAsymmetric a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (MinMaxType a b), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type MinMaxType (CollectErrors es a) (CollectErrors es b) :: Type Source # Methods min :: CollectErrors es a -> CollectErrors es b -> MinMaxType (CollectErrors es a) (CollectErrors es b) Source # max :: CollectErrors es a -> CollectErrors es b -> MinMaxType (CollectErrors es a) (CollectErrors es b) Source #

type CanMinMaxThis t1 t2 = (CanMinMax t1 t2, MinMaxType t1 t2 ~ t1) Source #

type CanMinMaxSameType t = CanMinMaxThis t t Source #

minimum :: CanMinMaxSameType t => [t] -> t Source #

maximum :: CanMinMaxSameType t => [t] -> t Source #

Tests

specCanMinMax :: (Show t1, Show t2, Show t3, Show (MinMaxType t1 t2), Show (MinMaxType t1 t1), Show (MinMaxType t2 t1), Show (MinMaxType t1 (MinMaxType t2 t3)), Show (MinMaxType (MinMaxType t1 t2) t3), Arbitrary t1, Arbitrary t2, Arbitrary t3, CanTestCertainly (EqCompareType t1 t1), CanTestCertainly (EqCompareType t2 t2), CanTestCertainly (OrderCompareType (MinMaxType t1 t2) t2), CanTestCertainly (OrderCompareType (MinMaxType t1 t2) t1), CanTestCertainly (EqCompareType (MinMaxType t1 t1) t1), CanTestCertainly (EqCompareType (MinMaxType t1 t2) (MinMaxType t2 t1)), CanTestCertainly (EqCompareType t3 t3), CanTestCertainly (EqCompareType (MinMaxType t1 (MinMaxType t2 t3)) (MinMaxType (MinMaxType t1 t2) t3)), CanTestFinite t1, CanTestFinite t2, CanTestFinite t3, HasEqAsymmetric t1 t1, HasEqAsymmetric t2 t2, HasEqAsymmetric t3 t3, HasEqAsymmetric (MinMaxType t1 t2) (MinMaxType t2 t1), HasEqAsymmetric (MinMaxType t1 t1) t1, HasEqAsymmetric (MinMaxType t1 (MinMaxType t2 t3)) (MinMaxType (MinMaxType t1 t2) t3), HasOrderAsymmetric (MinMaxType t1 t2) t1, HasOrderAsymmetric (MinMaxType t1 t2) t2, CanMinMaxAsymmetric t1 t1, CanMinMaxAsymmetric t1 t2, CanMinMaxAsymmetric t1 (MinMaxType t2 t3), CanMinMaxAsymmetric t2 t1, CanMinMaxAsymmetric t2 t3, CanMinMaxAsymmetric (MinMaxType t1 t2) t3) => T t1 -> T t2 -> T t3 -> Spec Source #

HSpec properties that each implementation of CanMinMax should satisfy.

specCanMinMaxNotMixed :: (Show t, Show (MinMaxType t t), Show (MinMaxType t (MinMaxType t t)), Show (MinMaxType (MinMaxType t t) t), Arbitrary t, CanTestCertainly (EqCompareType t t), CanTestCertainly (OrderCompareType (MinMaxType t t) t), CanTestCertainly (EqCompareType (MinMaxType t t) t), CanTestCertainly (EqCompareType (MinMaxType t t) (MinMaxType t t)), CanTestCertainly (EqCompareType (MinMaxType t (MinMaxType t t)) (MinMaxType (MinMaxType t t) t)), CanTestFinite t, HasEqAsymmetric t t, HasEqAsymmetric (MinMaxType t t) t, HasEqAsymmetric (MinMaxType t t) (MinMaxType t t), HasEqAsymmetric (MinMaxType t (MinMaxType t t)) (MinMaxType (MinMaxType t t) t), HasOrderAsymmetric (MinMaxType t t) t, CanMinMaxAsymmetric t t, CanMinMaxAsymmetric t (MinMaxType t t), CanMinMaxAsymmetric (MinMaxType t t) t) => T t -> Spec Source #

HSpec properties that each implementation of CanMinMax should satisfy.

Absolute value

class CanAbs t where Source #

A replacement for Prelude's abs. If Num t, then one can use the default implementation to mirror Prelude's abs.

Minimal complete definition

Nothing

Associated Types

type AbsType t Source #

Methods

abs :: t -> AbsType t Source #

abs :: (AbsType t ~ t, Num t) => t -> AbsType t Source #

Instances

CanAbs Double Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type AbsType Double :: Type Source # Methods abs :: Double -> AbsType Double Source #
CanAbs Int Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type AbsType Int :: Type Source # Methods abs :: Int -> AbsType Int Source #
CanAbs Integer Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type AbsType Integer :: Type Source # Methods abs :: Integer -> AbsType Integer Source #
CanAbs Rational Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type AbsType Rational :: Type Source # Methods abs :: Rational -> AbsType Rational Source #
(CanMulAsymmetric t t, CanAddSameType (MulType t t), CanSqrt (MulType t t)) => CanAbs (Complex t) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AbsType (Complex t) :: Type Source # Methods abs :: Complex t -> AbsType (Complex t) Source #
(CanAbs a, CanEnsureCE es a, CanEnsureCE es (AbsType a), SuitableForCE es) => CanAbs (CollectErrors es a) Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type AbsType (CollectErrors es a) :: Type Source # Methods abs :: CollectErrors es a -> AbsType (CollectErrors es a) Source #

type CanAbsSameType t = (CanAbs t, AbsType t ~ t) Source #

Tests

specCanNegNum :: (CanNegX t, CanNegX (NegType t), HasEqCertainly t (NegType (NegType t)), ConvertibleExactly Integer t, HasEqCertainly t t, HasEqCertainly t (NegType t), CanTestFinite t, CanTestPosNeg t, CanTestPosNeg (NegType t)) => T t -> Spec Source #

HSpec properties that each numeric implementation of CanNeg should satisfy.

specCanAbs :: (CanAbsX t, CanAbsX (AbsType t), CanTestFinite t) => T t -> Spec Source #

HSpec properties that each implementation of CanAbs should satisfy.

Orphan instances

CanNeg Double Source #
Instance details Associated Types type NegType Double :: Type Source # Methods negate :: Double -> NegType Double Source #
CanNeg Int Source #
Instance details Associated Types type NegType Int :: Type Source # Methods negate :: Int -> NegType Int Source #
CanNeg Integer Source #
Instance details Associated Types type NegType Integer :: Type Source # Methods negate :: Integer -> NegType Integer Source #
CanNeg Rational Source #
Instance details Associated Types type NegType Rational :: Type Source # Methods negate :: Rational -> NegType Rational Source #