Numeric.MixedTypes.MinMaxAbs

Minimum and maximum

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

class CanMinMaxAsymmetric t1 t2 where

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.

Associated Types

type MinMaxType t1 t2

Methods

min :: t1 -> t2 -> MinMaxType t1 t2

max :: t1 -> t2 -> MinMaxType t1 t2

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

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

Instances

CanMinMaxAsymmetric Double Double

Associated Types

type MinMaxType Double Double :: *

Methods

min :: Double -> Double -> MinMaxType Double Double

max :: Double -> Double -> MinMaxType Double Double

CanMinMaxAsymmetric Int Int

Associated Types

type MinMaxType Int Int :: *

Methods

min :: Int -> Int -> MinMaxType Int Int

max :: Int -> Int -> MinMaxType Int Int

CanMinMaxAsymmetric Int Integer

Associated Types

type MinMaxType Int Integer :: *

Methods

min :: Int -> Integer -> MinMaxType Int Integer

max :: Int -> Integer -> MinMaxType Int Integer

CanMinMaxAsymmetric Int Rational

Associated Types

type MinMaxType Int Rational :: *

Methods

min :: Int -> Rational -> MinMaxType Int Rational

max :: Int -> Rational -> MinMaxType Int Rational

CanMinMaxAsymmetric Integer Int

Associated Types

type MinMaxType Integer Int :: *

Methods

min :: Integer -> Int -> MinMaxType Integer Int

max :: Integer -> Int -> MinMaxType Integer Int

CanMinMaxAsymmetric Integer Integer

Associated Types

type MinMaxType Integer Integer :: *

Methods

min :: Integer -> Integer -> MinMaxType Integer Integer

max :: Integer -> Integer -> MinMaxType Integer Integer

CanMinMaxAsymmetric Integer Rational

Associated Types

type MinMaxType Integer Rational :: *

Methods

min :: Integer -> Rational -> MinMaxType Integer Rational

max :: Integer -> Rational -> MinMaxType Integer Rational

CanMinMaxAsymmetric Rational Int

Associated Types

type MinMaxType Rational Int :: *

Methods

min :: Rational -> Int -> MinMaxType Rational Int

max :: Rational -> Int -> MinMaxType Rational Int

CanMinMaxAsymmetric Rational Integer

Associated Types

type MinMaxType Rational Integer :: *

Methods

min :: Rational -> Integer -> MinMaxType Rational Integer

max :: Rational -> Integer -> MinMaxType Rational Integer

CanMinMaxAsymmetric Rational Rational

Associated Types

type MinMaxType Rational Rational :: *

Methods

min :: Rational -> Rational -> MinMaxType Rational Rational

max :: Rational -> Rational -> MinMaxType Rational Rational

(CanMinMaxAsymmetric Double b0, CanEnsureCE es0 (MinMaxType Double b0), SuitableForCE es0) => CanMinMaxAsymmetric Double (CollectErrors es0 b0)

Associated Types

type MinMaxType Double (CollectErrors es0 b0) :: *

Methods

min :: Double -> CollectErrors es0 b0 -> MinMaxType Double (CollectErrors es0 b0)

max :: Double -> CollectErrors es0 b0 -> MinMaxType Double (CollectErrors es0 b0)

(CanMinMaxAsymmetric Int b0, CanEnsureCE es0 (MinMaxType Int b0), SuitableForCE es0) => CanMinMaxAsymmetric Int (CollectErrors es0 b0)

Associated Types

type MinMaxType Int (CollectErrors es0 b0) :: *

Methods

min :: Int -> CollectErrors es0 b0 -> MinMaxType Int (CollectErrors es0 b0)

max :: Int -> CollectErrors es0 b0 -> MinMaxType Int (CollectErrors es0 b0)

(CanMinMaxAsymmetric Integer b0, CanEnsureCE es0 (MinMaxType Integer b0), SuitableForCE es0) => CanMinMaxAsymmetric Integer (CollectErrors es0 b0)

Associated Types

type MinMaxType Integer (CollectErrors es0 b0) :: *

Methods

min :: Integer -> CollectErrors es0 b0 -> MinMaxType Integer (CollectErrors es0 b0)

max :: Integer -> CollectErrors es0 b0 -> MinMaxType Integer (CollectErrors es0 b0)

(CanMinMaxAsymmetric Rational b0, CanEnsureCE es0 (MinMaxType Rational b0), SuitableForCE es0) => CanMinMaxAsymmetric Rational (CollectErrors es0 b0)

Associated Types

type MinMaxType Rational (CollectErrors es0 b0) :: *

Methods

min :: Rational -> CollectErrors es0 b0 -> MinMaxType Rational (CollectErrors es0 b0)

max :: Rational -> CollectErrors es0 b0 -> MinMaxType Rational (CollectErrors es0 b0)

CanMinMaxAsymmetric a b => CanMinMaxAsymmetric [a] [b]

Associated Types

type MinMaxType [a] [b] :: *

Methods

min :: [a] -> [b] -> MinMaxType [a] [b]

max :: [a] -> [b] -> MinMaxType [a] [b]

CanMinMaxAsymmetric a b => CanMinMaxAsymmetric (Maybe a) (Maybe b)

Associated Types

type MinMaxType (Maybe a) (Maybe b) :: *

Methods

min :: Maybe a -> Maybe b -> MinMaxType (Maybe a) (Maybe b)

max :: Maybe a -> Maybe b -> MinMaxType (Maybe a) (Maybe b)

(CanMinMaxAsymmetric a0 Double, CanEnsureCE es0 (MinMaxType a0 Double), SuitableForCE es0) => CanMinMaxAsymmetric (CollectErrors es0 a0) Double

Associated Types

type MinMaxType (CollectErrors es0 a0) Double :: *

Methods

min :: CollectErrors es0 a0 -> Double -> MinMaxType (CollectErrors es0 a0) Double

max :: CollectErrors es0 a0 -> Double -> MinMaxType (CollectErrors es0 a0) Double

(CanMinMaxAsymmetric a0 Rational, CanEnsureCE es0 (MinMaxType a0 Rational), SuitableForCE es0) => CanMinMaxAsymmetric (CollectErrors es0 a0) Rational

Associated Types

type MinMaxType (CollectErrors es0 a0) Rational :: *

Methods

min :: CollectErrors es0 a0 -> Rational -> MinMaxType (CollectErrors es0 a0) Rational

max :: CollectErrors es0 a0 -> Rational -> MinMaxType (CollectErrors es0 a0) Rational

(CanMinMaxAsymmetric a0 Int, CanEnsureCE es0 (MinMaxType a0 Int), SuitableForCE es0) => CanMinMaxAsymmetric (CollectErrors es0 a0) Int

Associated Types

type MinMaxType (CollectErrors es0 a0) Int :: *

Methods

min :: CollectErrors es0 a0 -> Int -> MinMaxType (CollectErrors es0 a0) Int

max :: CollectErrors es0 a0 -> Int -> MinMaxType (CollectErrors es0 a0) Int

(CanMinMaxAsymmetric a0 Integer, CanEnsureCE es0 (MinMaxType a0 Integer), SuitableForCE es0) => CanMinMaxAsymmetric (CollectErrors es0 a0) Integer

Associated Types

type MinMaxType (CollectErrors es0 a0) Integer :: *

Methods

min :: CollectErrors es0 a0 -> Integer -> MinMaxType (CollectErrors es0 a0) Integer

max :: CollectErrors es0 a0 -> Integer -> MinMaxType (CollectErrors es0 a0) Integer

(CanMinMaxAsymmetric a b, CanEnsureCE es (MinMaxType a b), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) (CollectErrors es b)

Associated Types

type MinMaxType (CollectErrors es a) (CollectErrors es b) :: *

Methods

min :: CollectErrors es a -> CollectErrors es b -> MinMaxType (CollectErrors es a) (CollectErrors es b)

max :: CollectErrors es a -> CollectErrors es b -> MinMaxType (CollectErrors es a) (CollectErrors es b)

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

Tests

specCanMinMax :: (CanMinMaxXX t1 t1, CanMinMaxXX t1 t2, CanMinMaxXX t1 t3, CanMinMaxXX t2 t3, CanMinMaxXX t1 (MinMaxType t2 t3), CanMinMaxXX (MinMaxType t1 t2) t3, HasEqCertainly (MinMaxType t1 (MinMaxType t2 t3)) (MinMaxType (MinMaxType t1 t2) t3)) => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of CanMinMax should satisfy.

specCanMinMaxNotMixed :: (CanMinMaxXX t t, CanMinMaxXX t (MinMaxType t t), HasEq (MinMaxType (MinMaxType t t) t) (MinMaxType t (MinMaxType t t))) => T t -> Spec

HSpec properties that each implementation of CanMinMax should satisfy.

type CanMinMaxX t1 t2 = (CanMinMax t1 t2, Show t1, Arbitrary t1, Show t2, Arbitrary t2, Show (MinMaxType t1 t2), HasEqCertainly t1 t1, HasEqCertainly t2 t2, HasEqCertainly t1 (MinMaxType t1 t2), HasEqCertainly t2 (MinMaxType t1 t2), HasEqCertainly (MinMaxType t1 t2) (MinMaxType t1 t2), HasOrderCertainly t1 (MinMaxType t1 t2), HasOrderCertainly t2 (MinMaxType t1 t2), HasOrderCertainly (MinMaxType t1 t2) (MinMaxType t1 t2))

Compound type constraint useful for test definition.

type CanMinMaxXX t1 t2 = (CanMinMaxX t1 t2, HasEqCertainly (MinMaxType t1 t2) (MinMaxType t2 t1))

Compound type constraint useful for test definition.

Absolute value

class CanAbs t where

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

Associated Types

type AbsType t

Methods

abs :: t -> AbsType t

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

Instances

CanAbs Double

Associated Types

type AbsType Double :: *

Methods

abs :: Double -> AbsType Double

CanAbs Int

Associated Types

type AbsType Int :: *

Methods

abs :: Int -> AbsType Int

CanAbs Integer

Associated Types

type AbsType Integer :: *

Methods

abs :: Integer -> AbsType Integer

CanAbs Rational

Associated Types

type AbsType Rational :: *

Methods

abs :: Rational -> AbsType Rational

(CanAbs a, CanEnsureCE es (AbsType a), SuitableForCE es) => CanAbs (CollectErrors es a)

Associated Types

type AbsType (CollectErrors es a) :: *

Methods

abs :: CollectErrors es a -> AbsType (CollectErrors es a)

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

Tests

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

HSpec properties that each numeric implementation of CanNeg should satisfy.

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

HSpec properties that each implementation of CanAbs should satisfy.

Orphan instances

CanNeg Double

Associated Types

type NegType Double :: *

Methods

negate :: Double -> NegType Double

CanNeg Int

Associated Types

type NegType Int :: *

Methods

negate :: Int -> NegType Int

CanNeg Integer

Associated Types

type NegType Integer :: *

Methods

negate :: Integer -> NegType Integer

CanNeg Rational

Associated Types

type NegType Rational :: *

Methods

negate :: Rational -> NegType Rational