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 Rational Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Rational Rational

Methods

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

CanAddAsymmetric Rational Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Rational Integer

Methods

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

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 Integer Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Integer Rational

Methods

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

CanAddAsymmetric Integer Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Integer Integer

Methods

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

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 Double Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Double Rational

Methods

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

CanAddAsymmetric Double Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Double Integer

Methods

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

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 Int Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Int Rational

Methods

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

CanAddAsymmetric Int Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType Int Integer

Methods

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

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 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 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 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 Rational b, CanBeErrors 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 Integer b, CanBeErrors 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 Double b, CanBeErrors 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, CanBeErrors 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 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 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 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 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 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 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 [a] [b]

Defined in Numeric.MixedTypes.AddSub

Associated Types

type AddType [a] [b]

Methods

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

(CanAddAsymmetric a Rational, CanBeErrors 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 Integer, CanBeErrors 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 Double, CanBeErrors 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 Int, CanBeErrors 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 b, CanBeErrors 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 :: _ => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of CanAdd should satisfy.

specCanAddNotMixed :: _ => 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 Rational Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Rational Rational

Methods

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

CanSub Rational Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Rational Integer

Methods

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

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 Integer Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Integer Rational

Methods

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

CanSub Integer Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Integer Integer

Methods

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

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 Double Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Double Rational

Methods

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

CanSub Double Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Double Integer

Methods

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

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 Int Rational

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Int Rational

Methods

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

CanSub Int Integer

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType Int Integer

Methods

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

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 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 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 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 Rational b, CanBeErrors 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 Integer b, CanBeErrors 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 Double b, CanBeErrors 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, CanBeErrors 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 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 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 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 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 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 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 [a] [b]

Defined in Numeric.MixedTypes.AddSub

Associated Types

type SubType [a] [b]

Methods

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

(CanSub a Rational, CanBeErrors 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 Integer, CanBeErrors 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 Double, CanBeErrors 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 Int, CanBeErrors 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 b, CanBeErrors 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 :: _ => T t1 -> T t2 -> Spec

HSpec properties that each implementation of CanSub should satisfy.

specCanSubNotMixed :: _ => T t -> Spec

HSpec properties that each implementation of CanSub should satisfy.