Numeric.MixedTypes.Ord

Comparisons in numeric order

type HasOrder t1 t2 = (HasOrderAsymmetric t1 t2, HasOrderAsymmetric t2 t1, OrderCompareType t1 t2 ~ OrderCompareType t2 t1)

class IsBool (OrderCompareType a b) => HasOrderAsymmetric a b where

Associated Types

type OrderCompareType a b

Methods

lessThan :: a -> b -> OrderCompareType a b

lessThan :: (OrderCompareType a b ~ Bool, a ~ b, Ord a) => a -> b -> Bool

greaterThan :: a -> b -> OrderCompareType a b

greaterThan :: (HasOrder b a, OrderCompareType b a ~ OrderCompareType a b) => a -> b -> OrderCompareType a b

leq :: a -> b -> OrderCompareType a b

leq :: (OrderCompareType a b ~ Bool, a ~ b, Ord a) => a -> b -> Bool

geq :: a -> b -> OrderCompareType a b

geq :: (HasOrder b a, OrderCompareType b a ~ OrderCompareType a b) => a -> b -> OrderCompareType a b

Instances

HasOrderAsymmetric Double Double

Associated Types

type OrderCompareType Double Double :: *

Methods

lessThan :: Double -> Double -> OrderCompareType Double Double

greaterThan :: Double -> Double -> OrderCompareType Double Double

leq :: Double -> Double -> OrderCompareType Double Double

geq :: Double -> Double -> OrderCompareType Double Double

HasOrderAsymmetric Double Int

Associated Types

type OrderCompareType Double Int :: *

Methods

lessThan :: Double -> Int -> OrderCompareType Double Int

greaterThan :: Double -> Int -> OrderCompareType Double Int

leq :: Double -> Int -> OrderCompareType Double Int

geq :: Double -> Int -> OrderCompareType Double Int

HasOrderAsymmetric Double Integer

Associated Types

type OrderCompareType Double Integer :: *

Methods

lessThan :: Double -> Integer -> OrderCompareType Double Integer

greaterThan :: Double -> Integer -> OrderCompareType Double Integer

leq :: Double -> Integer -> OrderCompareType Double Integer

geq :: Double -> Integer -> OrderCompareType Double Integer

HasOrderAsymmetric Int Double

Associated Types

type OrderCompareType Int Double :: *

Methods

lessThan :: Int -> Double -> OrderCompareType Int Double

greaterThan :: Int -> Double -> OrderCompareType Int Double

leq :: Int -> Double -> OrderCompareType Int Double

geq :: Int -> Double -> OrderCompareType Int Double

HasOrderAsymmetric Int Int

Associated Types

type OrderCompareType Int Int :: *

Methods

lessThan :: Int -> Int -> OrderCompareType Int Int

greaterThan :: Int -> Int -> OrderCompareType Int Int

leq :: Int -> Int -> OrderCompareType Int Int

geq :: Int -> Int -> OrderCompareType Int Int

HasOrderAsymmetric Int Integer

Associated Types

type OrderCompareType Int Integer :: *

Methods

lessThan :: Int -> Integer -> OrderCompareType Int Integer

greaterThan :: Int -> Integer -> OrderCompareType Int Integer

leq :: Int -> Integer -> OrderCompareType Int Integer

geq :: Int -> Integer -> OrderCompareType Int Integer

HasOrderAsymmetric Int Rational

Associated Types

type OrderCompareType Int Rational :: *

Methods

lessThan :: Int -> Rational -> OrderCompareType Int Rational

greaterThan :: Int -> Rational -> OrderCompareType Int Rational

leq :: Int -> Rational -> OrderCompareType Int Rational

geq :: Int -> Rational -> OrderCompareType Int Rational

HasOrderAsymmetric Integer Double

Associated Types

type OrderCompareType Integer Double :: *

Methods

lessThan :: Integer -> Double -> OrderCompareType Integer Double

greaterThan :: Integer -> Double -> OrderCompareType Integer Double

leq :: Integer -> Double -> OrderCompareType Integer Double

geq :: Integer -> Double -> OrderCompareType Integer Double

HasOrderAsymmetric Integer Int

Associated Types

type OrderCompareType Integer Int :: *

Methods

lessThan :: Integer -> Int -> OrderCompareType Integer Int

greaterThan :: Integer -> Int -> OrderCompareType Integer Int

leq :: Integer -> Int -> OrderCompareType Integer Int

geq :: Integer -> Int -> OrderCompareType Integer Int

HasOrderAsymmetric Integer Integer

Associated Types

type OrderCompareType Integer Integer :: *

Methods

lessThan :: Integer -> Integer -> OrderCompareType Integer Integer

greaterThan :: Integer -> Integer -> OrderCompareType Integer Integer

leq :: Integer -> Integer -> OrderCompareType Integer Integer

geq :: Integer -> Integer -> OrderCompareType Integer Integer

HasOrderAsymmetric Integer Rational

Associated Types

type OrderCompareType Integer Rational :: *

Methods

lessThan :: Integer -> Rational -> OrderCompareType Integer Rational

greaterThan :: Integer -> Rational -> OrderCompareType Integer Rational

leq :: Integer -> Rational -> OrderCompareType Integer Rational

geq :: Integer -> Rational -> OrderCompareType Integer Rational

HasOrderAsymmetric Rational Int

Associated Types

type OrderCompareType Rational Int :: *

Methods

lessThan :: Rational -> Int -> OrderCompareType Rational Int

greaterThan :: Rational -> Int -> OrderCompareType Rational Int

leq :: Rational -> Int -> OrderCompareType Rational Int

geq :: Rational -> Int -> OrderCompareType Rational Int

HasOrderAsymmetric Rational Integer

Associated Types

type OrderCompareType Rational Integer :: *

Methods

lessThan :: Rational -> Integer -> OrderCompareType Rational Integer

greaterThan :: Rational -> Integer -> OrderCompareType Rational Integer

leq :: Rational -> Integer -> OrderCompareType Rational Integer

geq :: Rational -> Integer -> OrderCompareType Rational Integer

HasOrderAsymmetric Rational Rational

Associated Types

type OrderCompareType Rational Rational :: *

Methods

lessThan :: Rational -> Rational -> OrderCompareType Rational Rational

greaterThan :: Rational -> Rational -> OrderCompareType Rational Rational

leq :: Rational -> Rational -> OrderCompareType Rational Rational

geq :: Rational -> Rational -> OrderCompareType Rational Rational

(>) :: HasOrderAsymmetric a b => a -> b -> OrderCompareType a b infix 4

(<) :: HasOrderAsymmetric a b => a -> b -> OrderCompareType a b infix 4

(<=) :: HasOrderAsymmetric a b => a -> b -> OrderCompareType a b infix 4

(>=) :: HasOrderAsymmetric a b => a -> b -> OrderCompareType a b infix 4

type HasOrderCertainlyAsymmetric t1 t2 = (HasOrderAsymmetric t1 t2, CanTestCertainly (OrderCompareType t1 t2))

type HasOrderCertainly t1 t2 = (HasOrder t1 t2, CanTestCertainly (OrderCompareType t1 t2))

(?<=?) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

(?<?) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

(?>=?) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

(?>?) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

(!<=!) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

(!<!) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

(!>=!) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

(!>!) :: HasOrderCertainlyAsymmetric a b => a -> b -> Bool infix 4

Tests

specHasOrder :: (HasOrderX t1 t1, HasOrderX t1 t2, HasOrderX t1 t3, HasOrderX t2 t3, CanAndOrX (OrderCompareType t1 t2) (OrderCompareType t2 t3)) => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of HasOrder should satisfy.

specHasOrderNotMixed :: (HasOrderX t t, CanAndOrX (OrderCompareType t t) (OrderCompareType t t)) => T t -> Spec

HSpec properties that each implementation of HasOrder should satisfy.

type HasOrderX t1 t2 = (HasOrderCertainly t1 t2, Show t1, Arbitrary t1, Show t2, Arbitrary t2)

Compound type constraint useful for test definition.

Specific comparisons

class CanTestPosNeg t where

Methods

isCertainlyPositive :: t -> Bool

isCertainlyNonNegative :: t -> Bool

isCertainlyNegative :: t -> Bool

isCertainlyNonPositive :: t -> Bool

isCertainlyPositive :: HasOrderCertainly t Integer => t -> Bool

isCertainlyNonNegative :: HasOrderCertainly t Integer => t -> Bool

isCertainlyNegative :: HasOrderCertainly t Integer => t -> Bool

isCertainlyNonPositive :: HasOrderCertainly t Integer => t -> Bool

Instances

CanTestPosNeg Double

Methods

isCertainlyPositive :: Double -> Bool

isCertainlyNonNegative :: Double -> Bool

isCertainlyNegative :: Double -> Bool

isCertainlyNonPositive :: Double -> Bool

CanTestPosNeg Int

Methods

isCertainlyPositive :: Int -> Bool

isCertainlyNonNegative :: Int -> Bool

isCertainlyNegative :: Int -> Bool

isCertainlyNonPositive :: Int -> Bool

CanTestPosNeg Integer

Methods

isCertainlyPositive :: Integer -> Bool

isCertainlyNonNegative :: Integer -> Bool

isCertainlyNegative :: Integer -> Bool

isCertainlyNonPositive :: Integer -> Bool

CanTestPosNeg Rational

Methods

isCertainlyPositive :: Rational -> Bool

isCertainlyNonNegative :: Rational -> Bool

isCertainlyNegative :: Rational -> Bool

isCertainlyNonPositive :: Rational -> Bool