Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Numeric.MixedTypes.AddSub

Contents

Addition
- Tests
Subtraction
- Tests

Description

Synopsis

type CanAdd t1 t2 = (CanAddAsymmetric t1 t2, CanAddAsymmetric t2 t1, AddType t1 t2 ~ AddType t2 t1)
class CanAddAsymmetric t1 t2 where
- type AddType t1 t2
- add :: t1 -> t2 -> AddType t1 t2
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
sum :: (CanAddSameType t, ConvertibleExactly Integer t) => [t] -> t
specCanAdd :: _ => T t1 -> T t2 -> T t3 -> Spec
specCanAddNotMixed :: _ => T t -> Spec
specCanAddSameType :: (ConvertibleExactly Integer t, Show t, HasEqCertainly t t, CanAddSameType t) => T t -> Spec
class CanSub t1 t2 where
- type SubType t1 t2
- sub :: t1 -> t2 -> SubType t1 t2
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
specCanSub :: _ => T t1 -> T t2 -> Spec
specCanSubNotMixed :: _ => T t -> Spec

Addition

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

class CanAddAsymmetric t1 t2 where Source #

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 Source #

type AddType t1 t2 = t1

Methods

add :: t1 -> t2 -> AddType t1 t2 Source #

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

Instances

Instances details

CanAddAsymmetric Double Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Double Double Source # Methods add :: Double -> Double -> AddType Double Double Source #
CanAddAsymmetric Double Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Double Int Source # Methods add :: Double -> Int -> AddType Double Int Source #
CanAddAsymmetric Double Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Double Integer Source # Methods add :: Double -> Integer -> AddType Double Integer Source #
CanAddAsymmetric Double Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Double Rational Source # Methods add :: Double -> Rational -> AddType Double Rational Source #
CanAddAsymmetric Int Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Int Double Source # Methods add :: Int -> Double -> AddType Int Double Source #
CanAddAsymmetric Int Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Int Int Source # Methods add :: Int -> Int -> AddType Int Int Source #
CanAddAsymmetric Int Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Int Integer Source # Methods add :: Int -> Integer -> AddType Int Integer Source #
CanAddAsymmetric Int Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Int Rational Source # Methods add :: Int -> Rational -> AddType Int Rational Source #
CanAddAsymmetric Integer Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Integer Double Source # Methods add :: Integer -> Double -> AddType Integer Double Source #
CanAddAsymmetric Integer Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Integer Int Source # Methods add :: Integer -> Int -> AddType Integer Int Source #
CanAddAsymmetric Integer Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Integer Integer Source # Methods add :: Integer -> Integer -> AddType Integer Integer Source #
CanAddAsymmetric Integer Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Integer Rational Source # Methods add :: Integer -> Rational -> AddType Integer Rational Source #
CanAddAsymmetric Rational Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Rational Double Source # Methods add :: Rational -> Double -> AddType Rational Double Source #
CanAddAsymmetric Rational Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Rational Int Source # Methods add :: Rational -> Int -> AddType Rational Int Source #
CanAddAsymmetric Rational Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Rational Integer Source # Methods add :: Rational -> Integer -> AddType Rational Integer Source #
CanAddAsymmetric Rational Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Rational Rational Source # Methods add :: Rational -> Rational -> AddType Rational Rational Source #
CanAddAsymmetric Double b => CanAddAsymmetric Double (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType Double (Complex b) Source # Methods add :: Double -> Complex b -> AddType Double (Complex b) Source #
CanAddAsymmetric Int b => CanAddAsymmetric Int (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType Int (Complex b) Source # Methods add :: Int -> Complex b -> AddType Int (Complex b) Source #
CanAddAsymmetric Integer b => CanAddAsymmetric Integer (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType Integer (Complex b) Source # Methods add :: Integer -> Complex b -> AddType Integer (Complex b) Source #
CanAddAsymmetric Rational b => CanAddAsymmetric Rational (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType Rational (Complex b) Source # Methods add :: Rational -> Complex b -> AddType Rational (Complex b) Source #
(CanAddAsymmetric Double b, CanBeErrors es) => CanAddAsymmetric Double (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Double (CollectErrors es b) Source # Methods add :: Double -> CollectErrors es b -> AddType Double (CollectErrors es b) Source #
(CanAddAsymmetric Int b, CanBeErrors es) => CanAddAsymmetric Int (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Int (CollectErrors es b) Source # Methods add :: Int -> CollectErrors es b -> AddType Int (CollectErrors es b) Source #
(CanAddAsymmetric Integer b, CanBeErrors es) => CanAddAsymmetric Integer (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Integer (CollectErrors es b) Source # Methods add :: Integer -> CollectErrors es b -> AddType Integer (CollectErrors es b) Source #
(CanAddAsymmetric Rational b, CanBeErrors es) => CanAddAsymmetric Rational (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType Rational (CollectErrors es b) Source # Methods add :: Rational -> CollectErrors es b -> AddType Rational (CollectErrors es b) Source #
CanAddAsymmetric a Integer => CanAddAsymmetric (Complex a) Integer Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType (Complex a) Integer Source # Methods add :: Complex a -> Integer -> AddType (Complex a) Integer Source #
CanAddAsymmetric a Int => CanAddAsymmetric (Complex a) Int Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType (Complex a) Int Source # Methods add :: Complex a -> Int -> AddType (Complex a) Int Source #
CanAddAsymmetric a Rational => CanAddAsymmetric (Complex a) Rational Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType (Complex a) Rational Source # Methods add :: Complex a -> Rational -> AddType (Complex a) Rational Source #
CanAddAsymmetric a Double => CanAddAsymmetric (Complex a) Double Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType (Complex a) Double Source # Methods add :: Complex a -> Double -> AddType (Complex a) Double Source #
CanAddAsymmetric a b => CanAddAsymmetric [a] [b] Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType [a] [b] Source # Methods add :: [a] -> [b] -> AddType [a] [b] Source #
CanAddAsymmetric a b => CanAddAsymmetric (Maybe a) (Maybe b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType (Maybe a) (Maybe b) Source # Methods add :: Maybe a -> Maybe b -> AddType (Maybe a) (Maybe b) Source #
CanAddAsymmetric a b => CanAddAsymmetric (Complex a) (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type AddType (Complex a) (Complex b) Source # Methods add :: Complex a -> Complex b -> AddType (Complex a) (Complex b) Source #
(CanAddAsymmetric a Integer, CanBeErrors es) => CanAddAsymmetric (CollectErrors es a) Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType (CollectErrors es a) Integer Source # Methods add :: CollectErrors es a -> Integer -> AddType (CollectErrors es a) Integer Source #
(CanAddAsymmetric a Int, CanBeErrors es) => CanAddAsymmetric (CollectErrors es a) Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType (CollectErrors es a) Int Source # Methods add :: CollectErrors es a -> Int -> AddType (CollectErrors es a) Int Source #
(CanAddAsymmetric a Rational, CanBeErrors es) => CanAddAsymmetric (CollectErrors es a) Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType (CollectErrors es a) Rational Source # Methods add :: CollectErrors es a -> Rational -> AddType (CollectErrors es a) Rational Source #
(CanAddAsymmetric a Double, CanBeErrors es) => CanAddAsymmetric (CollectErrors es a) Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType (CollectErrors es a) Double Source # Methods add :: CollectErrors es a -> Double -> AddType (CollectErrors es a) Double Source #
(CanAddAsymmetric a b, CanBeErrors es) => CanAddAsymmetric (CollectErrors es a) (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type AddType (CollectErrors es a) (CollectErrors es b) Source # Methods add :: CollectErrors es a -> CollectErrors es b -> AddType (CollectErrors es a) (CollectErrors es b) Source #

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

type CanAddSameType t = CanAddThis t t Source #

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

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

Tests

specCanAdd :: _ => T t1 -> T t2 -> T t3 -> Spec Source #

HSpec properties that each implementation of CanAdd should satisfy.

specCanAddNotMixed :: _ => T t -> Spec Source #

HSpec properties that each implementation of CanAdd should satisfy.

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

HSpec properties that each implementation of CanAddSameType should satisfy.

Subtraction

class CanSub t1 t2 where Source #

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 Source #

type SubType t1 t2 = AddType t1 (NegType t2)

Methods

sub :: t1 -> t2 -> SubType t1 t2 Source #

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

Instances

Instances details

CanSub Double Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Double Double Source # Methods sub :: Double -> Double -> SubType Double Double Source #
CanSub Double Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Double Int Source # Methods sub :: Double -> Int -> SubType Double Int Source #
CanSub Double Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Double Integer Source # Methods sub :: Double -> Integer -> SubType Double Integer Source #
CanSub Double Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Double Rational Source # Methods sub :: Double -> Rational -> SubType Double Rational Source #
CanSub Int Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Int Double Source # Methods sub :: Int -> Double -> SubType Int Double Source #
CanSub Int Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Int Int Source # Methods sub :: Int -> Int -> SubType Int Int Source #
CanSub Int Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Int Integer Source # Methods sub :: Int -> Integer -> SubType Int Integer Source #
CanSub Int Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Int Rational Source # Methods sub :: Int -> Rational -> SubType Int Rational Source #
CanSub Integer Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Integer Double Source # Methods sub :: Integer -> Double -> SubType Integer Double Source #
CanSub Integer Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Integer Int Source # Methods sub :: Integer -> Int -> SubType Integer Int Source #
CanSub Integer Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Integer Integer Source # Methods sub :: Integer -> Integer -> SubType Integer Integer Source #
CanSub Integer Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Integer Rational Source # Methods sub :: Integer -> Rational -> SubType Integer Rational Source #
CanSub Rational Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Rational Double Source # Methods sub :: Rational -> Double -> SubType Rational Double Source #
CanSub Rational Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Rational Int Source # Methods sub :: Rational -> Int -> SubType Rational Int Source #
CanSub Rational Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Rational Integer Source # Methods sub :: Rational -> Integer -> SubType Rational Integer Source #
CanSub Rational Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Rational Rational Source # Methods sub :: Rational -> Rational -> SubType Rational Rational Source #
CanSub Double b => CanSub Double (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType Double (Complex b) Source # Methods sub :: Double -> Complex b -> SubType Double (Complex b) Source #
CanSub Int b => CanSub Int (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType Int (Complex b) Source # Methods sub :: Int -> Complex b -> SubType Int (Complex b) Source #
CanSub Integer b => CanSub Integer (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType Integer (Complex b) Source # Methods sub :: Integer -> Complex b -> SubType Integer (Complex b) Source #
CanSub Rational b => CanSub Rational (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType Rational (Complex b) Source # Methods sub :: Rational -> Complex b -> SubType Rational (Complex b) Source #
(CanSub Double b, CanBeErrors es) => CanSub Double (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Double (CollectErrors es b) Source # Methods sub :: Double -> CollectErrors es b -> SubType Double (CollectErrors es b) Source #
(CanSub Int b, CanBeErrors es) => CanSub Int (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Int (CollectErrors es b) Source # Methods sub :: Int -> CollectErrors es b -> SubType Int (CollectErrors es b) Source #
(CanSub Integer b, CanBeErrors es) => CanSub Integer (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Integer (CollectErrors es b) Source # Methods sub :: Integer -> CollectErrors es b -> SubType Integer (CollectErrors es b) Source #
(CanSub Rational b, CanBeErrors es) => CanSub Rational (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType Rational (CollectErrors es b) Source # Methods sub :: Rational -> CollectErrors es b -> SubType Rational (CollectErrors es b) Source #
CanSub a Integer => CanSub (Complex a) Integer Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType (Complex a) Integer Source # Methods sub :: Complex a -> Integer -> SubType (Complex a) Integer Source #
CanSub a Int => CanSub (Complex a) Int Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType (Complex a) Int Source # Methods sub :: Complex a -> Int -> SubType (Complex a) Int Source #
CanSub a Rational => CanSub (Complex a) Rational Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType (Complex a) Rational Source # Methods sub :: Complex a -> Rational -> SubType (Complex a) Rational Source #
CanSub a Double => CanSub (Complex a) Double Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType (Complex a) Double Source # Methods sub :: Complex a -> Double -> SubType (Complex a) Double Source #
CanSub a b => CanSub [a] [b] Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType [a] [b] Source # Methods sub :: [a] -> [b] -> SubType [a] [b] Source #
CanSub a b => CanSub (Maybe a) (Maybe b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType (Maybe a) (Maybe b) Source # Methods sub :: Maybe a -> Maybe b -> SubType (Maybe a) (Maybe b) Source #
CanSub a b => CanSub (Complex a) (Complex b) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type SubType (Complex a) (Complex b) Source # Methods sub :: Complex a -> Complex b -> SubType (Complex a) (Complex b) Source #
(CanSub a Integer, CanBeErrors es) => CanSub (CollectErrors es a) Integer Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType (CollectErrors es a) Integer Source # Methods sub :: CollectErrors es a -> Integer -> SubType (CollectErrors es a) Integer Source #
(CanSub a Int, CanBeErrors es) => CanSub (CollectErrors es a) Int Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType (CollectErrors es a) Int Source # Methods sub :: CollectErrors es a -> Int -> SubType (CollectErrors es a) Int Source #
(CanSub a Rational, CanBeErrors es) => CanSub (CollectErrors es a) Rational Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType (CollectErrors es a) Rational Source # Methods sub :: CollectErrors es a -> Rational -> SubType (CollectErrors es a) Rational Source #
(CanSub a Double, CanBeErrors es) => CanSub (CollectErrors es a) Double Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType (CollectErrors es a) Double Source # Methods sub :: CollectErrors es a -> Double -> SubType (CollectErrors es a) Double Source #
(CanSub a b, CanBeErrors es) => CanSub (CollectErrors es a) (CollectErrors es b) Source #
Instance details Defined in Numeric.MixedTypes.AddSub Associated Types type SubType (CollectErrors es a) (CollectErrors es b) Source # Methods sub :: CollectErrors es a -> CollectErrors es b -> SubType (CollectErrors es a) (CollectErrors es b) Source #

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

type CanSubSameType t = CanSubThis t t Source #

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

Tests

specCanSub :: _ => T t1 -> T t2 -> Spec Source #

HSpec properties that each implementation of CanSub should satisfy.

specCanSubNotMixed :: _ => T t -> Spec Source #

HSpec properties that each implementation of CanSub should satisfy.