Numeric.MixedTypes.AddSub

Addition

type CanAdd t1 t2 = (CanAddAsymmetric t1 t2, CanAddAsymmetric t2 t1, AddType t1 t2 ~ AddType t2 t1)

class CanAddAsymmetric t1 t2 where

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

Associated Types

type AddType t1 t2

Methods

add :: t1 -> t2 -> AddType t1 t2

add :: (AddType t1 t2 ~ t1, t1 ~ t2, Num t1) => t1 -> t2 -> AddType t1 t2

Instances

CanAddAsymmetric Double Double

Associated Types

type AddType Double Double :: *

Methods

add :: Double -> Double -> AddType Double Double

CanAddAsymmetric Double Int

Associated Types

type AddType Double Int :: *

Methods

add :: Double -> Int -> AddType Double Int

CanAddAsymmetric Double Integer

Associated Types

type AddType Double Integer :: *

Methods

add :: Double -> Integer -> AddType Double Integer

CanAddAsymmetric Double Rational

Associated Types

type AddType Double Rational :: *

Methods

add :: Double -> Rational -> AddType Double Rational

CanAddAsymmetric Int Double

Associated Types

type AddType Int Double :: *

Methods

add :: Int -> Double -> AddType Int Double

CanAddAsymmetric Int Int

Associated Types

type AddType Int Int :: *

Methods

add :: Int -> Int -> AddType Int Int

CanAddAsymmetric Int Integer

Associated Types

type AddType Int Integer :: *

Methods

add :: Int -> Integer -> AddType Int Integer

CanAddAsymmetric Int Rational

Associated Types

type AddType Int Rational :: *

Methods

add :: Int -> Rational -> AddType Int Rational

CanAddAsymmetric Integer Double

Associated Types

type AddType Integer Double :: *

Methods

add :: Integer -> Double -> AddType Integer Double

CanAddAsymmetric Integer Int

Associated Types

type AddType Integer Int :: *

Methods

add :: Integer -> Int -> AddType Integer Int

CanAddAsymmetric Integer Integer

Associated Types

type AddType Integer Integer :: *

Methods

add :: Integer -> Integer -> AddType Integer Integer

CanAddAsymmetric Integer Rational

Associated Types

type AddType Integer Rational :: *

Methods

add :: Integer -> Rational -> AddType Integer Rational

CanAddAsymmetric Rational Double

Associated Types

type AddType Rational Double :: *

Methods

add :: Rational -> Double -> AddType Rational Double

CanAddAsymmetric Rational Int

Associated Types

type AddType Rational Int :: *

Methods

add :: Rational -> Int -> AddType Rational Int

CanAddAsymmetric Rational Integer

Associated Types

type AddType Rational Integer :: *

Methods

add :: Rational -> Integer -> AddType Rational Integer

CanAddAsymmetric Rational Rational

Associated Types

type AddType Rational Rational :: *

Methods

add :: Rational -> Rational -> AddType Rational Rational

(CanAddAsymmetric Double b0, CanEnsureCE es0 b0, CanEnsureCE es0 (AddType Double b0), SuitableForCE es0) => CanAddAsymmetric Double (CollectErrors es0 b0)

Associated Types

type AddType Double (CollectErrors es0 b0) :: *

Methods

add :: Double -> CollectErrors es0 b0 -> AddType Double (CollectErrors es0 b0)

(CanAddAsymmetric Int b0, CanEnsureCE es0 b0, CanEnsureCE es0 (AddType Int b0), SuitableForCE es0) => CanAddAsymmetric Int (CollectErrors es0 b0)

Associated Types

type AddType Int (CollectErrors es0 b0) :: *

Methods

add :: Int -> CollectErrors es0 b0 -> AddType Int (CollectErrors es0 b0)

(CanAddAsymmetric Integer b0, CanEnsureCE es0 b0, CanEnsureCE es0 (AddType Integer b0), SuitableForCE es0) => CanAddAsymmetric Integer (CollectErrors es0 b0)

Associated Types

type AddType Integer (CollectErrors es0 b0) :: *

Methods

add :: Integer -> CollectErrors es0 b0 -> AddType Integer (CollectErrors es0 b0)

(CanAddAsymmetric Rational b0, CanEnsureCE es0 b0, CanEnsureCE es0 (AddType Rational b0), SuitableForCE es0) => CanAddAsymmetric Rational (CollectErrors es0 b0)

Associated Types

type AddType Rational (CollectErrors es0 b0) :: *

Methods

add :: Rational -> CollectErrors es0 b0 -> AddType Rational (CollectErrors es0 b0)

CanAddAsymmetric a b => CanAddAsymmetric [a] [b]

Associated Types

type AddType [a] [b] :: *

Methods

add :: [a] -> [b] -> AddType [a] [b]

CanAddAsymmetric a b => CanAddAsymmetric (Maybe a) (Maybe b)

Associated Types

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

Methods

add :: Maybe a -> Maybe b -> AddType (Maybe a) (Maybe b)

(CanAddAsymmetric a0 Double, CanEnsureCE es0 a0, CanEnsureCE es0 (AddType a0 Double), SuitableForCE es0) => CanAddAsymmetric (CollectErrors es0 a0) Double

Associated Types

type AddType (CollectErrors es0 a0) Double :: *

Methods

add :: CollectErrors es0 a0 -> Double -> AddType (CollectErrors es0 a0) Double

(CanAddAsymmetric a0 Rational, CanEnsureCE es0 a0, CanEnsureCE es0 (AddType a0 Rational), SuitableForCE es0) => CanAddAsymmetric (CollectErrors es0 a0) Rational

Associated Types

type AddType (CollectErrors es0 a0) Rational :: *

Methods

add :: CollectErrors es0 a0 -> Rational -> AddType (CollectErrors es0 a0) Rational

(CanAddAsymmetric a0 Int, CanEnsureCE es0 a0, CanEnsureCE es0 (AddType a0 Int), SuitableForCE es0) => CanAddAsymmetric (CollectErrors es0 a0) Int

Associated Types

type AddType (CollectErrors es0 a0) Int :: *

Methods

add :: CollectErrors es0 a0 -> Int -> AddType (CollectErrors es0 a0) Int

(CanAddAsymmetric a0 Integer, CanEnsureCE es0 a0, CanEnsureCE es0 (AddType a0 Integer), SuitableForCE es0) => CanAddAsymmetric (CollectErrors es0 a0) Integer

Associated Types

type AddType (CollectErrors es0 a0) Integer :: *

Methods

add :: CollectErrors es0 a0 -> Integer -> AddType (CollectErrors es0 a0) Integer

(CanAddAsymmetric a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (AddType a b), SuitableForCE es) => CanAddAsymmetric (CollectErrors es a) (CollectErrors es b)

Associated Types

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

Methods

add :: CollectErrors es a -> CollectErrors es b -> AddType (CollectErrors es a) (CollectErrors es b)

type CanAddThis t1 t2 = (CanAdd t1 t2, AddType t1 t2 ~ t1)

type CanAddSameType t = CanAddThis t t

(+) :: CanAddAsymmetric t1 t2 => t1 -> t2 -> AddType t1 t2 infixl 6

sum :: (CanAddSameType t, ConvertibleExactly Integer t) => [t] -> t

Tests

specCanAdd :: (Show t1, Show t2, Show t3, Show (AddType t1 t1), Show (AddType t1 t2), Show (AddType t2 t1), Show (AddType t1 (AddType t2 t3)), Show (AddType (AddType t1 t2) t3), Arbitrary t1, Arbitrary t2, Arbitrary t3, ConvertibleExactly Integer t1, CanTestCertainly (EqCompareType (AddType t1 t1) t1), CanTestCertainly (EqCompareType (AddType t1 t2) (AddType t2 t1)), CanTestCertainly (EqCompareType (AddType t1 (AddType t2 t3)) (AddType (AddType t1 t2) t3)), CanTestCertainly (OrderCompareType (AddType t1 t2) t2), HasEqAsymmetric (AddType t1 t1) t1, HasEqAsymmetric (AddType t1 t2) (AddType t2 t1), HasEqAsymmetric (AddType t1 (AddType t2 t3)) (AddType (AddType t1 t2) t3), HasOrderAsymmetric (AddType t1 t2) t2, CanTestPosNeg t1, CanAddAsymmetric t1 t1, CanAddAsymmetric t1 t2, CanAddAsymmetric t1 (AddType t2 t3), CanAddAsymmetric t2 t1, CanAddAsymmetric t2 t3, CanAddAsymmetric (AddType t1 t2) t3) => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of CanAdd should satisfy.

specCanAddNotMixed :: (Show t, Show (AddType t t), Show (AddType t (AddType t t)), Show (AddType (AddType t t) t), Arbitrary t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType (AddType t t) t), CanTestCertainly (EqCompareType (AddType t t) (AddType t t)), CanTestCertainly (EqCompareType (AddType t (AddType t t)) (AddType (AddType t t) t)), CanTestCertainly (OrderCompareType (AddType t t) t), HasEqAsymmetric (AddType t t) t, HasEqAsymmetric (AddType t t) (AddType t t), HasEqAsymmetric (AddType t (AddType t t)) (AddType (AddType t t) t), HasOrderAsymmetric (AddType t t) t, CanTestPosNeg t, CanAddAsymmetric t t, CanAddAsymmetric t (AddType t t), CanAddAsymmetric (AddType t t) t) => T t -> Spec

HSpec properties that each implementation of CanAdd should satisfy.

specCanAddSameType :: (ConvertibleExactly Integer t, Show t, HasEqCertainly t t, CanAddSameType t) => T t -> Spec

HSpec properties that each implementation of CanAddSameType should satisfy.

Subtraction

class CanSub t1 t2 where

A replacement for Prelude's binary -.

If CanNeg t2 and CanAdd t1 (NegType t2), then one can use the default implementation via a-b = a + (-b).

Associated Types

type SubType t1 t2

Methods

sub :: t1 -> t2 -> SubType t1 t2

sub :: (SubType t1 t2 ~ AddType t1 (NegType t2), CanNeg t2, CanAdd t1 (NegType t2)) => t1 -> t2 -> SubType t1 t2

Instances

CanSub Double Double

Associated Types

type SubType Double Double :: *

Methods

sub :: Double -> Double -> SubType Double Double

CanSub Double Int

Associated Types

type SubType Double Int :: *

Methods

sub :: Double -> Int -> SubType Double Int

CanSub Double Integer

Associated Types

type SubType Double Integer :: *

Methods

sub :: Double -> Integer -> SubType Double Integer

CanSub Double Rational

Associated Types

type SubType Double Rational :: *

Methods

sub :: Double -> Rational -> SubType Double Rational

CanSub Int Double

Associated Types

type SubType Int Double :: *

Methods

sub :: Int -> Double -> SubType Int Double

CanSub Int Int

Associated Types

type SubType Int Int :: *

Methods

sub :: Int -> Int -> SubType Int Int

CanSub Int Integer

Associated Types

type SubType Int Integer :: *

Methods

sub :: Int -> Integer -> SubType Int Integer

CanSub Int Rational

Associated Types

type SubType Int Rational :: *

Methods

sub :: Int -> Rational -> SubType Int Rational

CanSub Integer Double

Associated Types

type SubType Integer Double :: *

Methods

sub :: Integer -> Double -> SubType Integer Double

CanSub Integer Int

Associated Types

type SubType Integer Int :: *

Methods

sub :: Integer -> Int -> SubType Integer Int

CanSub Integer Integer

Associated Types

type SubType Integer Integer :: *

Methods

sub :: Integer -> Integer -> SubType Integer Integer

CanSub Integer Rational

Associated Types

type SubType Integer Rational :: *

Methods

sub :: Integer -> Rational -> SubType Integer Rational

CanSub Rational Double

Associated Types

type SubType Rational Double :: *

Methods

sub :: Rational -> Double -> SubType Rational Double

CanSub Rational Int

Associated Types

type SubType Rational Int :: *

Methods

sub :: Rational -> Int -> SubType Rational Int

CanSub Rational Integer

Associated Types

type SubType Rational Integer :: *

Methods

sub :: Rational -> Integer -> SubType Rational Integer

CanSub Rational Rational

Associated Types

type SubType Rational Rational :: *

Methods

sub :: Rational -> Rational -> SubType Rational Rational

(CanSub Double b0, CanEnsureCE es0 b0, CanEnsureCE es0 (SubType Double b0), SuitableForCE es0) => CanSub Double (CollectErrors es0 b0)

Associated Types

type SubType Double (CollectErrors es0 b0) :: *

Methods

sub :: Double -> CollectErrors es0 b0 -> SubType Double (CollectErrors es0 b0)

(CanSub Int b0, CanEnsureCE es0 b0, CanEnsureCE es0 (SubType Int b0), SuitableForCE es0) => CanSub Int (CollectErrors es0 b0)

Associated Types

type SubType Int (CollectErrors es0 b0) :: *

Methods

sub :: Int -> CollectErrors es0 b0 -> SubType Int (CollectErrors es0 b0)

(CanSub Integer b0, CanEnsureCE es0 b0, CanEnsureCE es0 (SubType Integer b0), SuitableForCE es0) => CanSub Integer (CollectErrors es0 b0)

Associated Types

type SubType Integer (CollectErrors es0 b0) :: *

Methods

sub :: Integer -> CollectErrors es0 b0 -> SubType Integer (CollectErrors es0 b0)

(CanSub Rational b0, CanEnsureCE es0 b0, CanEnsureCE es0 (SubType Rational b0), SuitableForCE es0) => CanSub Rational (CollectErrors es0 b0)

Associated Types

type SubType Rational (CollectErrors es0 b0) :: *

Methods

sub :: Rational -> CollectErrors es0 b0 -> SubType Rational (CollectErrors es0 b0)

CanSub a b => CanSub [a] [b]

Associated Types

type SubType [a] [b] :: *

Methods

sub :: [a] -> [b] -> SubType [a] [b]

CanSub a b => CanSub (Maybe a) (Maybe b)

Associated Types

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

Methods

sub :: Maybe a -> Maybe b -> SubType (Maybe a) (Maybe b)

(CanSub a0 Double, CanEnsureCE es0 a0, CanEnsureCE es0 (SubType a0 Double), SuitableForCE es0) => CanSub (CollectErrors es0 a0) Double

Associated Types

type SubType (CollectErrors es0 a0) Double :: *

Methods

sub :: CollectErrors es0 a0 -> Double -> SubType (CollectErrors es0 a0) Double

(CanSub a0 Rational, CanEnsureCE es0 a0, CanEnsureCE es0 (SubType a0 Rational), SuitableForCE es0) => CanSub (CollectErrors es0 a0) Rational

Associated Types

type SubType (CollectErrors es0 a0) Rational :: *

Methods

sub :: CollectErrors es0 a0 -> Rational -> SubType (CollectErrors es0 a0) Rational

(CanSub a0 Int, CanEnsureCE es0 a0, CanEnsureCE es0 (SubType a0 Int), SuitableForCE es0) => CanSub (CollectErrors es0 a0) Int

Associated Types

type SubType (CollectErrors es0 a0) Int :: *

Methods

sub :: CollectErrors es0 a0 -> Int -> SubType (CollectErrors es0 a0) Int

(CanSub a0 Integer, CanEnsureCE es0 a0, CanEnsureCE es0 (SubType a0 Integer), SuitableForCE es0) => CanSub (CollectErrors es0 a0) Integer

Associated Types

type SubType (CollectErrors es0 a0) Integer :: *

Methods

sub :: CollectErrors es0 a0 -> Integer -> SubType (CollectErrors es0 a0) Integer

(CanSub a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (SubType a b), SuitableForCE es) => CanSub (CollectErrors es a) (CollectErrors es b)

Associated Types

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

Methods

sub :: CollectErrors es a -> CollectErrors es b -> SubType (CollectErrors es a) (CollectErrors es b)

type CanSubThis t1 t2 = (CanSub t1 t2, SubType t1 t2 ~ t1)

type CanSubSameType t = CanSubThis t t

(-) :: CanSub t1 t2 => t1 -> t2 -> SubType t1 t2 infixl 6

Tests

specCanSub :: (Show t1, Show t2, Show (SubType t1 t1), Show (SubType t1 t2), Show (AddType t1 (NegType t2)), Arbitrary t1, Arbitrary t2, ConvertibleExactly Integer t1, CanTestCertainly (EqCompareType (SubType t1 t1) t1), CanTestCertainly (EqCompareType (SubType t1 t2) (AddType t1 (NegType t2))), CanNeg t2, HasEqAsymmetric (SubType t1 t1) t1, HasEqAsymmetric (SubType t1 t2) (AddType t1 (NegType t2)), CanSub t1 t1, CanSub t1 t2, CanAddAsymmetric t1 (NegType t2)) => T t1 -> T t2 -> Spec

HSpec properties that each implementation of CanSub should satisfy.

specCanSubNotMixed :: (Show t, Show (SubType t t), Show (AddType t (NegType t)), Arbitrary t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType (SubType t t) t), CanTestCertainly (EqCompareType (SubType t t) (AddType t (NegType t))), CanNeg t, HasEqAsymmetric (SubType t t) t, HasEqAsymmetric (SubType t t) (AddType t (NegType t)), CanSub t t, CanAddAsymmetric t (NegType t)) => T t -> Spec

HSpec properties that each implementation of CanSub should satisfy.