mixed-types-num-0.6.2: Alternative Prelude with numeric and logic expressions typed bottom-up
Copyright(c) Michal Konecny
LicenseBSD3
Maintainer[email protected]
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell2010

Numeric.MixedTypes.Power

Description

 
Synopsis

Exponentiation

class CanPow b e where Source #

A replacement for Prelude's binary ^ and ^^.

Minimal complete definition

pow

Associated Types

type PowType b e Source #

type PowType b e = b

type PPowType b e Source #

type PPowType b e = PowType b e

Methods

pow :: b -> e -> PowType b e Source #

ppow :: b -> e -> PPowType b e Source #

default ppow :: PPowType b e ~ PowType b e => b -> e -> PPowType b e Source #

Instances

Instances details
CanPow Rational Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Rational Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Rational Integer = Rational
type PPowType Rational Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Rational Integer = PowType Rational Integer

Methods

pow :: Rational -> Integer -> PowType Rational Integer Source #

ppow :: Rational -> Integer -> PPowType Rational Integer Source #

CanPow Rational Double Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Rational Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Rational Double = Double
type PPowType Rational Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Rational Double = PowType Rational Double

Methods

pow :: Rational -> Double -> PowType Rational Double Source #

ppow :: Rational -> Double -> PPowType Rational Double Source #

CanPow Rational Int Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Rational Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Rational Int = Rational
type PPowType Rational Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Rational Int = PowType Rational Int

Methods

pow :: Rational -> Int -> PowType Rational Int Source #

ppow :: Rational -> Int -> PPowType Rational Int Source #

CanPow Integer Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Integer Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Integer Integer = Integer
type PPowType Integer Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Integer Integer = Rational

Methods

pow :: Integer -> Integer -> PowType Integer Integer Source #

ppow :: Integer -> Integer -> PPowType Integer Integer Source #

CanPow Integer Double Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Integer Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Integer Double = Double
type PPowType Integer Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Integer Double = PowType Integer Double

Methods

pow :: Integer -> Double -> PowType Integer Double Source #

ppow :: Integer -> Double -> PPowType Integer Double Source #

CanPow Integer Int Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Integer Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Integer Int = Integer
type PPowType Integer Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Integer Int = Rational

Methods

pow :: Integer -> Int -> PowType Integer Int Source #

ppow :: Integer -> Int -> PPowType Integer Int Source #

CanPow Double Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Double Rational 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Double Rational = Double
type PPowType Double Rational 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Double Rational = PowType Double Rational

Methods

pow :: Double -> Rational -> PowType Double Rational Source #

ppow :: Double -> Rational -> PPowType Double Rational Source #

CanPow Double Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Double Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Double Integer = Double
type PPowType Double Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Double Integer = PowType Double Integer

Methods

pow :: Double -> Integer -> PowType Double Integer Source #

ppow :: Double -> Integer -> PPowType Double Integer Source #

CanPow Double Double Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Double Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Double Double = Double
type PPowType Double Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Double Double = PowType Double Double

Methods

pow :: Double -> Double -> PowType Double Double Source #

ppow :: Double -> Double -> PPowType Double Double Source #

CanPow Double Int Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Double Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Double Int = Double
type PPowType Double Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Double Int = PowType Double Int

Methods

pow :: Double -> Int -> PowType Double Int Source #

ppow :: Double -> Int -> PPowType Double Int Source #

CanPow Int Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Int Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Int Integer = Integer
type PPowType Int Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Int Integer = Rational

Methods

pow :: Int -> Integer -> PowType Int Integer Source #

ppow :: Int -> Integer -> PPowType Int Integer Source #

CanPow Int Double Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Int Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Int Double = Double
type PPowType Int Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Int Double = PowType Int Double

Methods

pow :: Int -> Double -> PowType Int Double Source #

ppow :: Int -> Double -> PPowType Int Double Source #

CanPow Int Int Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Int Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Int Int = Rational
type PPowType Int Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Int Int = PowType Int Int

Methods

pow :: Int -> Int -> PowType Int Int Source #

ppow :: Int -> Int -> PPowType Int Int Source #

(CanPow Rational e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Rational (CN e) Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Rational (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Rational (CN e) = CN (PowType Rational e)
type PPowType Rational (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Rational (CN e) = CN (PPowType Rational e)

Methods

pow :: Rational -> CN e -> PowType Rational (CN e) Source #

ppow :: Rational -> CN e -> PPowType Rational (CN e) Source #

(CanPow Integer e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Integer (CN e) Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Integer (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Integer (CN e) = CN (PowType Integer e)
type PPowType Integer (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Integer (CN e) = CN (PPowType Integer e)

Methods

pow :: Integer -> CN e -> PowType Integer (CN e) Source #

ppow :: Integer -> CN e -> PPowType Integer (CN e) Source #

(CanPow Double e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Double (CN e) Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Double (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Double (CN e) = CN (PowType Double e)
type PPowType Double (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Double (CN e) = CN (PPowType Double e)

Methods

pow :: Double -> CN e -> PowType Double (CN e) Source #

ppow :: Double -> CN e -> PPowType Double (CN e) Source #

(CanPow Int e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Int (CN e) Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType Int (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType Int (CN e) = CN (PowType Int e)
type PPowType Int (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType Int (CN e) = CN (PPowType Int e)

Methods

pow :: Int -> CN e -> PowType Int (CN e) Source #

ppow :: Int -> CN e -> PPowType Int (CN e) Source #

(CanPow b Rational, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CN b) Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType (CN b) Rational 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType (CN b) Rational = CN (PowType b Rational)
type PPowType (CN b) Rational 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType (CN b) Rational = CN (PPowType b Rational)

Methods

pow :: CN b -> Rational -> PowType (CN b) Rational Source #

ppow :: CN b -> Rational -> PPowType (CN b) Rational Source #

(CanPow b Integer, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CN b) Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType (CN b) Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType (CN b) Integer = CN (PowType b Integer)
type PPowType (CN b) Integer 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType (CN b) Integer = CN (PPowType b Integer)

Methods

pow :: CN b -> Integer -> PowType (CN b) Integer Source #

ppow :: CN b -> Integer -> PPowType (CN b) Integer Source #

(CanPow b Double, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CN b) Double Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType (CN b) Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType (CN b) Double = CN (PowType b Double)
type PPowType (CN b) Double 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType (CN b) Double = CN (PPowType b Double)

Methods

pow :: CN b -> Double -> PowType (CN b) Double Source #

ppow :: CN b -> Double -> PPowType (CN b) Double Source #

(CanPow b Int, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CN b) Int Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType (CN b) Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType (CN b) Int = CN (PowType b Int)
type PPowType (CN b) Int 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType (CN b) Int = CN (PPowType b Int)

Methods

pow :: CN b -> Int -> PowType (CN b) Int Source #

ppow :: CN b -> Int -> PPowType (CN b) Int Source #

(CanPow b e, HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, CanTestIsIntegerType b, CanTestIsIntegerType e, CanTestInteger e) => CanPow (CN b) (CN e) Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType (CN b) (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType (CN b) (CN e) = CN (PowType b e)
type PPowType (CN b) (CN e) 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType (CN b) (CN e) = CN (PPowType b e)

Methods

pow :: CN b -> CN e -> PowType (CN b) (CN e) Source #

ppow :: CN b -> CN e -> PPowType (CN b) (CN e) Source #

CanPow a b => CanPow (Maybe a) (Maybe b) Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Associated Types

type PowType (Maybe a) (Maybe b) 
Instance details

Defined in Numeric.MixedTypes.Power

type PowType (Maybe a) (Maybe b) = Maybe (PowType a b)
type PPowType (Maybe a) (Maybe b) 
Instance details

Defined in Numeric.MixedTypes.Power

type PPowType (Maybe a) (Maybe b) = PowType (Maybe a) (Maybe b)

Methods

pow :: Maybe a -> Maybe b -> PowType (Maybe a) (Maybe b) Source #

ppow :: Maybe a -> Maybe b -> PPowType (Maybe a) (Maybe b) Source #

type CanPowBy t1 t2 = (CanPow t1 t2, PowType t1 t2 ~ t1) Source #

(^) :: CanPow t1 t2 => t1 -> t2 -> PowType t1 t2 infixl 8 Source #

(^^) :: CanPow t1 t2 => t1 -> t2 -> PPowType t1 t2 infixl 8 Source #

powUsingMul :: CanBeInteger e => t -> (t -> t -> t) -> t -> e -> t Source #

integerPowCN :: (HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, HasEqCertainly e Integer) => (b -> e -> r) -> CN b -> CN e -> CN r Source #

powUsingMulRecip :: CanBeInteger e => t -> (t -> t -> t) -> (t -> t) -> t -> e -> t Source #

class CanTestIsIntegerType t where Source #

Ability to detect whether a numeric type is restricted to (a subset of) integers.

This is useful eg when checking the arguments of the power operator in the CN instance for power.

Minimal complete definition

Nothing

Methods

isIntegerType :: t -> Bool Source #

Instances

Instances details
CanTestIsIntegerType Rational Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Methods

isIntegerType :: Rational -> Bool Source #

CanTestIsIntegerType Integer Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Methods

isIntegerType :: Integer -> Bool Source #

CanTestIsIntegerType Double Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Methods

isIntegerType :: Double -> Bool Source #

CanTestIsIntegerType Int Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Methods

isIntegerType :: Int -> Bool Source #

CanTestIsIntegerType t => CanTestIsIntegerType (CN t) Source # 
Instance details

Defined in Numeric.MixedTypes.Power

Methods

isIntegerType :: CN t -> Bool Source #

Tests

specCanPow :: (Arbitrary t1, Arbitrary t2, CanTestPosNeg t2, HasEqAsymmetric (PowType t1 t2) t1, HasEqAsymmetric (MulType t1 (PowType t1 t2)) (PowType t1 (AddType t2 Integer)), CanTestCertainly (EqCompareType (PowType t1 t2) t1), CanTestCertainly (EqCompareType (MulType t1 (PowType t1 t2)) (PowType t1 (AddType t2 Integer))), Show t1, Show t2, Show (MulType t1 (PowType t1 t2)), Show (PowType t1 t2), Show (PowType t1 (AddType t2 Integer)), CanMulAsymmetric t1 (PowType t1 t2), CanPow t1 t2, CanPow t1 (AddType t2 Integer), CanAddAsymmetric t2 Integer, ConvertibleExactlyWithSample Integer t1, ConvertibleExactlyWithSample Integer t2) => T t1 -> T t2 -> Spec Source #

HSpec properties that each implementation of CanPow should satisfy.