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 -> 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

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 () ()

Associated Types

type OrderCompareType () () :: *

Methods

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

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

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

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

(HasOrderAsymmetric Double b0, CanEnsureCE es0 b0, CanEnsureCE es0 (OrderCompareType Double b0), IsBool (EnsureCE es0 (OrderCompareType Double b0)), SuitableForCE es0) => HasOrderAsymmetric Double (CollectErrors es0 b0)

Associated Types

type OrderCompareType Double (CollectErrors es0 b0) :: *

Methods

lessThan :: Double -> CollectErrors es0 b0 -> OrderCompareType Double (CollectErrors es0 b0)

greaterThan :: Double -> CollectErrors es0 b0 -> OrderCompareType Double (CollectErrors es0 b0)

leq :: Double -> CollectErrors es0 b0 -> OrderCompareType Double (CollectErrors es0 b0)

geq :: Double -> CollectErrors es0 b0 -> OrderCompareType Double (CollectErrors es0 b0)

(HasOrderAsymmetric Int b0, CanEnsureCE es0 b0, CanEnsureCE es0 (OrderCompareType Int b0), IsBool (EnsureCE es0 (OrderCompareType Int b0)), SuitableForCE es0) => HasOrderAsymmetric Int (CollectErrors es0 b0)

Associated Types

type OrderCompareType Int (CollectErrors es0 b0) :: *

Methods

lessThan :: Int -> CollectErrors es0 b0 -> OrderCompareType Int (CollectErrors es0 b0)

greaterThan :: Int -> CollectErrors es0 b0 -> OrderCompareType Int (CollectErrors es0 b0)

leq :: Int -> CollectErrors es0 b0 -> OrderCompareType Int (CollectErrors es0 b0)

geq :: Int -> CollectErrors es0 b0 -> OrderCompareType Int (CollectErrors es0 b0)

(HasOrderAsymmetric Integer b0, CanEnsureCE es0 b0, CanEnsureCE es0 (OrderCompareType Integer b0), IsBool (EnsureCE es0 (OrderCompareType Integer b0)), SuitableForCE es0) => HasOrderAsymmetric Integer (CollectErrors es0 b0)

Associated Types

type OrderCompareType Integer (CollectErrors es0 b0) :: *

Methods

lessThan :: Integer -> CollectErrors es0 b0 -> OrderCompareType Integer (CollectErrors es0 b0)

greaterThan :: Integer -> CollectErrors es0 b0 -> OrderCompareType Integer (CollectErrors es0 b0)

leq :: Integer -> CollectErrors es0 b0 -> OrderCompareType Integer (CollectErrors es0 b0)

geq :: Integer -> CollectErrors es0 b0 -> OrderCompareType Integer (CollectErrors es0 b0)

(HasOrderAsymmetric Rational b0, CanEnsureCE es0 b0, CanEnsureCE es0 (OrderCompareType Rational b0), IsBool (EnsureCE es0 (OrderCompareType Rational b0)), SuitableForCE es0) => HasOrderAsymmetric Rational (CollectErrors es0 b0)

Associated Types

type OrderCompareType Rational (CollectErrors es0 b0) :: *

Methods

lessThan :: Rational -> CollectErrors es0 b0 -> OrderCompareType Rational (CollectErrors es0 b0)

greaterThan :: Rational -> CollectErrors es0 b0 -> OrderCompareType Rational (CollectErrors es0 b0)

leq :: Rational -> CollectErrors es0 b0 -> OrderCompareType Rational (CollectErrors es0 b0)

geq :: Rational -> CollectErrors es0 b0 -> OrderCompareType Rational (CollectErrors es0 b0)

(HasOrderAsymmetric a0 Double, CanEnsureCE es0 a0, CanEnsureCE es0 (OrderCompareType a0 Double), IsBool (EnsureCE es0 (OrderCompareType a0 Double)), SuitableForCE es0) => HasOrderAsymmetric (CollectErrors es0 a0) Double

Associated Types

type OrderCompareType (CollectErrors es0 a0) Double :: *

Methods

lessThan :: CollectErrors es0 a0 -> Double -> OrderCompareType (CollectErrors es0 a0) Double

greaterThan :: CollectErrors es0 a0 -> Double -> OrderCompareType (CollectErrors es0 a0) Double

leq :: CollectErrors es0 a0 -> Double -> OrderCompareType (CollectErrors es0 a0) Double

geq :: CollectErrors es0 a0 -> Double -> OrderCompareType (CollectErrors es0 a0) Double

(HasOrderAsymmetric a0 Rational, CanEnsureCE es0 a0, CanEnsureCE es0 (OrderCompareType a0 Rational), IsBool (EnsureCE es0 (OrderCompareType a0 Rational)), SuitableForCE es0) => HasOrderAsymmetric (CollectErrors es0 a0) Rational

Associated Types

type OrderCompareType (CollectErrors es0 a0) Rational :: *

Methods

lessThan :: CollectErrors es0 a0 -> Rational -> OrderCompareType (CollectErrors es0 a0) Rational

greaterThan :: CollectErrors es0 a0 -> Rational -> OrderCompareType (CollectErrors es0 a0) Rational

leq :: CollectErrors es0 a0 -> Rational -> OrderCompareType (CollectErrors es0 a0) Rational

geq :: CollectErrors es0 a0 -> Rational -> OrderCompareType (CollectErrors es0 a0) Rational

(HasOrderAsymmetric a0 Int, CanEnsureCE es0 a0, CanEnsureCE es0 (OrderCompareType a0 Int), IsBool (EnsureCE es0 (OrderCompareType a0 Int)), SuitableForCE es0) => HasOrderAsymmetric (CollectErrors es0 a0) Int

Associated Types

type OrderCompareType (CollectErrors es0 a0) Int :: *

Methods

lessThan :: CollectErrors es0 a0 -> Int -> OrderCompareType (CollectErrors es0 a0) Int

greaterThan :: CollectErrors es0 a0 -> Int -> OrderCompareType (CollectErrors es0 a0) Int

leq :: CollectErrors es0 a0 -> Int -> OrderCompareType (CollectErrors es0 a0) Int

geq :: CollectErrors es0 a0 -> Int -> OrderCompareType (CollectErrors es0 a0) Int

(HasOrderAsymmetric a0 Integer, CanEnsureCE es0 a0, CanEnsureCE es0 (OrderCompareType a0 Integer), IsBool (EnsureCE es0 (OrderCompareType a0 Integer)), SuitableForCE es0) => HasOrderAsymmetric (CollectErrors es0 a0) Integer

Associated Types

type OrderCompareType (CollectErrors es0 a0) Integer :: *

Methods

lessThan :: CollectErrors es0 a0 -> Integer -> OrderCompareType (CollectErrors es0 a0) Integer

greaterThan :: CollectErrors es0 a0 -> Integer -> OrderCompareType (CollectErrors es0 a0) Integer

leq :: CollectErrors es0 a0 -> Integer -> OrderCompareType (CollectErrors es0 a0) Integer

geq :: CollectErrors es0 a0 -> Integer -> OrderCompareType (CollectErrors es0 a0) Integer

(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)

Associated Types

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

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

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

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

Methods

isCertainlyPositive :: CollectErrors es t -> Bool

isCertainlyNonNegative :: CollectErrors es t -> Bool

isCertainlyNegative :: CollectErrors es t -> Bool

isCertainlyNonPositive :: CollectErrors es t -> Bool