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 +.

Minimal complete definition

Nothing

Associated Types

type AddType t1 t2

type AddType t1 t2 = t1

Methods

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

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

Instances

CanAddAsymmetric Double Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Double Double

Methods

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

CanAddAsymmetric Double Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Double Int

Methods

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

CanAddAsymmetric Double Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Double Integer

Methods

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

CanAddAsymmetric Double Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Double Rational

Methods

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

CanAddAsymmetric Int Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Int Double

Methods

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

CanAddAsymmetric Int Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Int Int

Methods

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

CanAddAsymmetric Int Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Int Integer

Methods

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

CanAddAsymmetric Int Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Int Rational

Methods

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

CanAddAsymmetric Integer Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Integer Double

Methods

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

CanAddAsymmetric Integer Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Integer Int

Methods

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

CanAddAsymmetric Integer Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Integer Integer

Methods

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

CanAddAsymmetric Integer Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Integer Rational

Methods

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

CanAddAsymmetric Rational Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Rational Double

Methods

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

CanAddAsymmetric Rational Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Rational Int

Methods

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

CanAddAsymmetric Rational Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Rational Integer

Methods

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

CanAddAsymmetric Rational Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Rational Rational

Methods

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

CanAddAsymmetric Double b => CanAddAsymmetric Double (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType Double (Complex b)

Methods

add :: Double -> Complex b -> AddType Double (Complex b)

CanAddAsymmetric Int b => CanAddAsymmetric Int (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType Int (Complex b)

Methods

add :: Int -> Complex b -> AddType Int (Complex b)

CanAddAsymmetric Integer b => CanAddAsymmetric Integer (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType Integer (Complex b)

Methods

add :: Integer -> Complex b -> AddType Integer (Complex b)

CanAddAsymmetric Rational b => CanAddAsymmetric Rational (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType Rational (Complex b)

Methods

add :: Rational -> Complex b -> AddType Rational (Complex b)

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Double (CollectErrors es b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Int (CollectErrors es b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Integer (CollectErrors es b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Rational (CollectErrors es b)

Methods

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

CanAddAsymmetric a Integer => CanAddAsymmetric (Complex a) Integer

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType (Complex a) Integer

Methods

add :: Complex a -> Integer -> AddType (Complex a) Integer

CanAddAsymmetric a Int => CanAddAsymmetric (Complex a) Int

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType (Complex a) Int

Methods

add :: Complex a -> Int -> AddType (Complex a) Int

CanAddAsymmetric a Rational => CanAddAsymmetric (Complex a) Rational

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType (Complex a) Rational

Methods

add :: Complex a -> Rational -> AddType (Complex a) Rational

CanAddAsymmetric a Double => CanAddAsymmetric (Complex a) Double

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType (Complex a) Double

Methods

add :: Complex a -> Double -> AddType (Complex a) Double

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType [a] [b]

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType (Maybe a) (Maybe b)

Methods

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

CanAddAsymmetric a b => CanAddAsymmetric (Complex a) (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type AddType (Complex a) (Complex b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType (CollectErrors es a) Integer

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType (CollectErrors es a) Int

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType (CollectErrors es a) Rational

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType (CollectErrors es a) Double

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

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).

Minimal complete definition

Nothing

Associated Types

type SubType t1 t2

type SubType t1 t2 = AddType t1 (NegType t2)

Methods

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

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

Instances

CanSub Double Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Double Double

Methods

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

CanSub Double Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Double Int

Methods

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

CanSub Double Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Double Integer

Methods

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

CanSub Double Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Double Rational

Methods

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

CanSub Int Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Int Double

Methods

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

CanSub Int Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Int Int

Methods

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

CanSub Int Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Int Integer

Methods

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

CanSub Int Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Int Rational

Methods

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

CanSub Integer Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Integer Double

Methods

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

CanSub Integer Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Integer Int

Methods

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

CanSub Integer Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Integer Integer

Methods

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

CanSub Integer Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Integer Rational

Methods

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

CanSub Rational Double

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Rational Double

Methods

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

CanSub Rational Int

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Rational Int

Methods

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

CanSub Rational Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Rational Integer

Methods

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

CanSub Rational Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Rational Rational

Methods

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

CanSub Double b => CanSub Double (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType Double (Complex b)

Methods

sub :: Double -> Complex b -> SubType Double (Complex b)

CanSub Int b => CanSub Int (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType Int (Complex b)

Methods

sub :: Int -> Complex b -> SubType Int (Complex b)

CanSub Integer b => CanSub Integer (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType Integer (Complex b)

Methods

sub :: Integer -> Complex b -> SubType Integer (Complex b)

CanSub Rational b => CanSub Rational (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType Rational (Complex b)

Methods

sub :: Rational -> Complex b -> SubType Rational (Complex b)

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Double (CollectErrors es b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Int (CollectErrors es b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Integer (CollectErrors es b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Rational (CollectErrors es b)

Methods

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

CanSub a Integer => CanSub (Complex a) Integer

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType (Complex a) Integer

Methods

sub :: Complex a -> Integer -> SubType (Complex a) Integer

CanSub a Int => CanSub (Complex a) Int

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType (Complex a) Int

Methods

sub :: Complex a -> Int -> SubType (Complex a) Int

CanSub a Rational => CanSub (Complex a) Rational

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType (Complex a) Rational

Methods

sub :: Complex a -> Rational -> SubType (Complex a) Rational

CanSub a Double => CanSub (Complex a) Double

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType (Complex a) Double

Methods

sub :: Complex a -> Double -> SubType (Complex a) Double

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType [a] [b]

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType (Maybe a) (Maybe b)

Methods

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

CanSub a b => CanSub (Complex a) (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type SubType (Complex a) (Complex b)

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType (CollectErrors es a) Integer

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType (CollectErrors es a) Int

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType (CollectErrors es a) Rational

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType (CollectErrors es a) Double

Methods

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

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

Defined in Numeric.MixedTypes.AddSub

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.