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 -> t1 -> t1

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 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)

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 :: (CanAddXX t1 t1, CanAddXX t1 t2, CanAddXX t1 t3, CanAddXX t2 t3, CanAddXX t1 (AddType t2 t3), CanAddXX (AddType t1 t2) t3, ConvertibleExactly Integer t1, CanTestPosNeg t1, HasEqCertainly (AddType t1 (AddType t2 t3)) (AddType (AddType t1 t2) t3)) => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of CanAdd should satisfy.

specCanAddNotMixed :: (CanAddXX t t, CanAddXX t (AddType t t), ConvertibleExactly Integer t, CanTestPosNeg 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.

type CanAddX t1 t2 = (CanAdd t1 t2, Show t1, Arbitrary t1, Show t2, Arbitrary t2, Show (AddType t1 t2), HasEqCertainly t1 (AddType t1 t2), HasEqCertainly t2 (AddType t1 t2), HasEqCertainly (AddType t1 t2) (AddType t1 t2), HasOrderCertainly t1 (AddType t1 t2), HasOrderCertainly t2 (AddType t1 t2), HasOrderCertainly (AddType t1 t2) (AddType t1 t2))

Compound type constraint useful for test definition.

type CanAddXX t1 t2 = (CanAddX t1 t2, HasEqCertainly (AddType t1 t2) (AddType t2 t1))

Compound type constraint useful for test definition.

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 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)

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 :: (CanSubX t1 t1, CanSubX t1 t2, CanNeg t2, CanAdd t1 (NegType t2), HasEqCertainly (SubType t1 t2) (AddType t1 (NegType t2)), Show (AddType t1 (NegType t2)), ConvertibleExactly Integer t1) => T t1 -> T t2 -> Spec

HSpec properties that each implementation of CanSub should satisfy.

specCanSubNotMixed :: (CanSubX t t, CanSubX t (SubType t t), CanNeg t, CanAdd t (NegType t), Show (AddType t (NegType t)), HasEqCertainly (SubType t t) (AddType t (NegType t)), ConvertibleExactly Integer t) => T t -> Spec

HSpec properties that each implementation of CanSub should satisfy.

type CanSubX t1 t2 = (CanSub t1 t2, HasEqCertainly t1 (SubType t1 t2), CanAddXX t1 t2, Show (SubType t1 t2))

Compound type constraint useful for test definition.