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

Minimal complete definition

Nothing

Associated Types

type OrderCompareType a b

Methods

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

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

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 -> OrderCompareType a b

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Double Double :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Double Int :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Double Integer :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Int Double :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Int Int :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Int Integer :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Int Rational :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Integer Double :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Integer Int :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Integer Integer :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Integer Rational :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Rational Int :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Rational Integer :: Type

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

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Rational Rational :: Type

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 () ()

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType () () :: Type

Methods

lessThan :: () -> () -> OrderCompareType () ()

greaterThan :: () -> () -> OrderCompareType () ()

leq :: () -> () -> OrderCompareType () ()

geq :: () -> () -> OrderCompareType () ()

(HasOrderAsymmetric Double b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType Double b), IsBool (EnsureCE es (OrderCompareType Double b)), SuitableForCE es) => HasOrderAsymmetric Double (CollectErrors es b)

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Double (CollectErrors es b) :: Type

Methods

lessThan :: Double -> CollectErrors es b -> OrderCompareType Double (CollectErrors es b)

greaterThan :: Double -> CollectErrors es b -> OrderCompareType Double (CollectErrors es b)

leq :: Double -> CollectErrors es b -> OrderCompareType Double (CollectErrors es b)

geq :: Double -> CollectErrors es b -> OrderCompareType Double (CollectErrors es b)

(HasOrderAsymmetric Int b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType Int b), IsBool (EnsureCE es (OrderCompareType Int b)), SuitableForCE es) => HasOrderAsymmetric Int (CollectErrors es b)

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Int (CollectErrors es b) :: Type

Methods

lessThan :: Int -> CollectErrors es b -> OrderCompareType Int (CollectErrors es b)

greaterThan :: Int -> CollectErrors es b -> OrderCompareType Int (CollectErrors es b)

leq :: Int -> CollectErrors es b -> OrderCompareType Int (CollectErrors es b)

geq :: Int -> CollectErrors es b -> OrderCompareType Int (CollectErrors es b)

(HasOrderAsymmetric Integer b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType Integer b), IsBool (EnsureCE es (OrderCompareType Integer b)), SuitableForCE es) => HasOrderAsymmetric Integer (CollectErrors es b)

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Integer (CollectErrors es b) :: Type

Methods

lessThan :: Integer -> CollectErrors es b -> OrderCompareType Integer (CollectErrors es b)

greaterThan :: Integer -> CollectErrors es b -> OrderCompareType Integer (CollectErrors es b)

leq :: Integer -> CollectErrors es b -> OrderCompareType Integer (CollectErrors es b)

geq :: Integer -> CollectErrors es b -> OrderCompareType Integer (CollectErrors es b)

(HasOrderAsymmetric Rational b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType Rational b), IsBool (EnsureCE es (OrderCompareType Rational b)), SuitableForCE es) => HasOrderAsymmetric Rational (CollectErrors es b)

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType Rational (CollectErrors es b) :: Type

Methods

lessThan :: Rational -> CollectErrors es b -> OrderCompareType Rational (CollectErrors es b)

greaterThan :: Rational -> CollectErrors es b -> OrderCompareType Rational (CollectErrors es b)

leq :: Rational -> CollectErrors es b -> OrderCompareType Rational (CollectErrors es b)

geq :: Rational -> CollectErrors es b -> OrderCompareType Rational (CollectErrors es b)

(HasOrderAsymmetric a Integer, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a Integer), IsBool (EnsureCE es (OrderCompareType a Integer)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) Integer

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType (CollectErrors es a) Integer :: Type

Methods

lessThan :: CollectErrors es a -> Integer -> OrderCompareType (CollectErrors es a) Integer

greaterThan :: CollectErrors es a -> Integer -> OrderCompareType (CollectErrors es a) Integer

leq :: CollectErrors es a -> Integer -> OrderCompareType (CollectErrors es a) Integer

geq :: CollectErrors es a -> Integer -> OrderCompareType (CollectErrors es a) Integer

(HasOrderAsymmetric a Int, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a Int), IsBool (EnsureCE es (OrderCompareType a Int)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) Int

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType (CollectErrors es a) Int :: Type

Methods

lessThan :: CollectErrors es a -> Int -> OrderCompareType (CollectErrors es a) Int

greaterThan :: CollectErrors es a -> Int -> OrderCompareType (CollectErrors es a) Int

leq :: CollectErrors es a -> Int -> OrderCompareType (CollectErrors es a) Int

geq :: CollectErrors es a -> Int -> OrderCompareType (CollectErrors es a) Int

(HasOrderAsymmetric a Rational, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a Rational), IsBool (EnsureCE es (OrderCompareType a Rational)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) Rational

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType (CollectErrors es a) Rational :: Type

Methods

lessThan :: CollectErrors es a -> Rational -> OrderCompareType (CollectErrors es a) Rational

greaterThan :: CollectErrors es a -> Rational -> OrderCompareType (CollectErrors es a) Rational

leq :: CollectErrors es a -> Rational -> OrderCompareType (CollectErrors es a) Rational

geq :: CollectErrors es a -> Rational -> OrderCompareType (CollectErrors es a) Rational

(HasOrderAsymmetric a Double, CanEnsureCE es a, CanEnsureCE es (OrderCompareType a Double), IsBool (EnsureCE es (OrderCompareType a Double)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) Double

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType (CollectErrors es a) Double :: Type

Methods

lessThan :: CollectErrors es a -> Double -> OrderCompareType (CollectErrors es a) Double

greaterThan :: CollectErrors es a -> Double -> OrderCompareType (CollectErrors es a) Double

leq :: CollectErrors es a -> Double -> OrderCompareType (CollectErrors es a) Double

geq :: CollectErrors es a -> Double -> OrderCompareType (CollectErrors es a) Double

(HasOrderAsymmetric a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (OrderCompareType a b), IsBool (EnsureCE es (OrderCompareType a b)), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) (CollectErrors es b)

Defined in Numeric.MixedTypes.Ord

Associated Types

type OrderCompareType (CollectErrors es a) (CollectErrors es b) :: Type

Methods

lessThan :: CollectErrors es a -> CollectErrors es b -> OrderCompareType (CollectErrors es a) (CollectErrors es b)

greaterThan :: CollectErrors es a -> CollectErrors es b -> OrderCompareType (CollectErrors es a) (CollectErrors es b)

leq :: CollectErrors es a -> CollectErrors es b -> OrderCompareType (CollectErrors es a) (CollectErrors es b)

geq :: CollectErrors es a -> CollectErrors es b -> OrderCompareType (CollectErrors es a) (CollectErrors es b)

(>) :: 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))

type HasOrderCertainlyCE es t1 t2 = (HasOrderCertainly t1 t2, HasOrderCertainly (EnsureCE es t1) (EnsureCE es t2))

type HasOrderCertainlyCN t1 t2 = HasOrderCertainlyCE NumErrors 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 :: (Show t1, Show t2, Show t3, Arbitrary t1, Arbitrary t2, Arbitrary t3, CanTestCertainly (OrderCompareType t1 t1), CanTestCertainly (OrderCompareType t1 t2), CanTestCertainly (OrderCompareType t2 t1), CanTestCertainly (OrderCompareType t2 t3), CanTestCertainly (AndOrType (OrderCompareType t1 t2) (OrderCompareType t2 t3)), CanAndOrAsymmetric (OrderCompareType t1 t2) (OrderCompareType t2 t3), HasOrderAsymmetric t1 t1, HasOrderAsymmetric t1 t2, HasOrderAsymmetric t2 t1, HasOrderAsymmetric t2 t3) => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of HasOrder should satisfy.

specHasOrderNotMixed :: (Show t, Arbitrary t, CanTestCertainly (OrderCompareType t t), CanTestCertainly (AndOrType (OrderCompareType t t) (OrderCompareType t t)), HasOrderAsymmetric t t) => T t -> Spec

HSpec properties that each implementation of HasOrder should satisfy.

Specific comparisons

class CanTestPosNeg t where

Minimal complete definition

Nothing

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

Defined in Numeric.MixedTypes.Ord

Methods

isCertainlyPositive :: Double -> Bool

isCertainlyNonNegative :: Double -> Bool

isCertainlyNegative :: Double -> Bool

isCertainlyNonPositive :: Double -> Bool

CanTestPosNeg Int

Defined in Numeric.MixedTypes.Ord

Methods

isCertainlyPositive :: Int -> Bool

isCertainlyNonNegative :: Int -> Bool

isCertainlyNegative :: Int -> Bool

isCertainlyNonPositive :: Int -> Bool

CanTestPosNeg Integer

Defined in Numeric.MixedTypes.Ord

Methods

isCertainlyPositive :: Integer -> Bool

isCertainlyNonNegative :: Integer -> Bool

isCertainlyNegative :: Integer -> Bool

isCertainlyNonPositive :: Integer -> Bool

CanTestPosNeg Rational

Defined in Numeric.MixedTypes.Ord

Methods

isCertainlyPositive :: Rational -> Bool

isCertainlyNonNegative :: Rational -> Bool

isCertainlyNegative :: Rational -> Bool

isCertainlyNonPositive :: Rational -> Bool

(CanTestPosNeg t, SuitableForCE es) => CanTestPosNeg (CollectErrors es t)

Defined in Numeric.MixedTypes.Ord

Methods

isCertainlyPositive :: CollectErrors es t -> Bool

isCertainlyNonNegative :: CollectErrors es t -> Bool

isCertainlyNegative :: CollectErrors es t -> Bool

isCertainlyNonPositive :: CollectErrors es t -> Bool