Numeric.MixedTypes.Ring

Ring

type CanAddSubMulBy t s = (CanAddThis t s, CanSubThis t s, CanSub s t, SubType s t ~ t, CanMulBy t s)

class (RingPre t, CanEnsureCN t, RingPre (EnsureCN t)) => Ring t

Instances

Ring Integer

Ring Rational

Ring (CN Integer)

Ring (CN Rational)

class (Ring t, HasEq t t, HasEq (EnsureCN t) t, HasEq t (EnsureCN t), HasEq t Int, HasEq t Integer, HasEq (EnsureCN t) Int, HasEq (EnsureCN t) Integer, HasOrder t t, HasOrder (EnsureCN t) t, HasOrder t (EnsureCN t), HasOrder t Int, HasOrder t Integer, HasOrder (EnsureCN t) Int, HasOrder (EnsureCN t) Integer) => OrderedRing t

Instances

OrderedRing Integer

OrderedRing Rational

OrderedRing (CN Integer)

OrderedRing (CN Rational)

class (Ring t, HasEqCertainly t t, HasEqCertainly (EnsureCN t) t, HasEqCertainly t (EnsureCN t), HasEqCertainly t Int, HasEq t Integer, HasEqCertainly (EnsureCN t) Int, HasEq (EnsureCN t) Integer, HasOrderCertainly t t, HasOrderCertainly (EnsureCN t) t, HasOrderCertainly t (EnsureCN t), HasOrderCertainly t Int, HasOrderCertainly t Integer, HasOrderCertainly (EnsureCN t) Int, HasOrderCertainly (EnsureCN t) Integer, CanTestPosNeg t) => OrderedCertainlyRing t

Instances

OrderedCertainlyRing Integer

OrderedCertainlyRing Rational

OrderedCertainlyRing (CN Integer)

OrderedCertainlyRing (CN Rational)

Multiplication

type CanMul t1 t2 = (CanMulAsymmetric t1 t2, CanMulAsymmetric t2 t1, MulType t1 t2 ~ MulType t2 t1)

class CanMulAsymmetric 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 MulType t1 t2

Methods

mul :: t1 -> t2 -> MulType t1 t2

mul :: (MulType t1 t2 ~ t1, t1 ~ t2, Num t1) => t1 -> t2 -> MulType t1 t2

Instances

CanMulAsymmetric Double Double

Associated Types

type MulType Double Double :: *

Methods

mul :: Double -> Double -> MulType Double Double

CanMulAsymmetric Double Int

Associated Types

type MulType Double Int :: *

Methods

mul :: Double -> Int -> MulType Double Int

CanMulAsymmetric Double Integer

Associated Types

type MulType Double Integer :: *

Methods

mul :: Double -> Integer -> MulType Double Integer

CanMulAsymmetric Double Rational

Associated Types

type MulType Double Rational :: *

Methods

mul :: Double -> Rational -> MulType Double Rational

CanMulAsymmetric Int Double

Associated Types

type MulType Int Double :: *

Methods

mul :: Int -> Double -> MulType Int Double

CanMulAsymmetric Int Int

Associated Types

type MulType Int Int :: *

Methods

mul :: Int -> Int -> MulType Int Int

CanMulAsymmetric Int Integer

Associated Types

type MulType Int Integer :: *

Methods

mul :: Int -> Integer -> MulType Int Integer

CanMulAsymmetric Int Rational

Associated Types

type MulType Int Rational :: *

Methods

mul :: Int -> Rational -> MulType Int Rational

CanMulAsymmetric Integer Double

Associated Types

type MulType Integer Double :: *

Methods

mul :: Integer -> Double -> MulType Integer Double

CanMulAsymmetric Integer Int

Associated Types

type MulType Integer Int :: *

Methods

mul :: Integer -> Int -> MulType Integer Int

CanMulAsymmetric Integer Integer

Associated Types

type MulType Integer Integer :: *

Methods

mul :: Integer -> Integer -> MulType Integer Integer

CanMulAsymmetric Integer Rational

Associated Types

type MulType Integer Rational :: *

Methods

mul :: Integer -> Rational -> MulType Integer Rational

CanMulAsymmetric Rational Double

Associated Types

type MulType Rational Double :: *

Methods

mul :: Rational -> Double -> MulType Rational Double

CanMulAsymmetric Rational Int

Associated Types

type MulType Rational Int :: *

Methods

mul :: Rational -> Int -> MulType Rational Int

CanMulAsymmetric Rational Integer

Associated Types

type MulType Rational Integer :: *

Methods

mul :: Rational -> Integer -> MulType Rational Integer

CanMulAsymmetric Rational Rational

Associated Types

type MulType Rational Rational :: *

Methods

mul :: Rational -> Rational -> MulType Rational Rational

(CanMulAsymmetric Double b0, CanEnsureCE es0 b0, CanEnsureCE es0 (MulType Double b0), SuitableForCE es0) => CanMulAsymmetric Double (CollectErrors es0 b0)

Associated Types

type MulType Double (CollectErrors es0 b0) :: *

Methods

mul :: Double -> CollectErrors es0 b0 -> MulType Double (CollectErrors es0 b0)

(CanMulAsymmetric Int b0, CanEnsureCE es0 b0, CanEnsureCE es0 (MulType Int b0), SuitableForCE es0) => CanMulAsymmetric Int (CollectErrors es0 b0)

Associated Types

type MulType Int (CollectErrors es0 b0) :: *

Methods

mul :: Int -> CollectErrors es0 b0 -> MulType Int (CollectErrors es0 b0)

(CanMulAsymmetric Integer b0, CanEnsureCE es0 b0, CanEnsureCE es0 (MulType Integer b0), SuitableForCE es0) => CanMulAsymmetric Integer (CollectErrors es0 b0)

Associated Types

type MulType Integer (CollectErrors es0 b0) :: *

Methods

mul :: Integer -> CollectErrors es0 b0 -> MulType Integer (CollectErrors es0 b0)

(CanMulAsymmetric Rational b0, CanEnsureCE es0 b0, CanEnsureCE es0 (MulType Rational b0), SuitableForCE es0) => CanMulAsymmetric Rational (CollectErrors es0 b0)

Associated Types

type MulType Rational (CollectErrors es0 b0) :: *

Methods

mul :: Rational -> CollectErrors es0 b0 -> MulType Rational (CollectErrors es0 b0)

CanMulAsymmetric a b => CanMulAsymmetric [a] [b]

Associated Types

type MulType [a] [b] :: *

Methods

mul :: [a] -> [b] -> MulType [a] [b]

CanMulAsymmetric a b => CanMulAsymmetric (Maybe a) (Maybe b)

Associated Types

type MulType (Maybe a) (Maybe b) :: *

Methods

mul :: Maybe a -> Maybe b -> MulType (Maybe a) (Maybe b)

(CanMulAsymmetric a0 Double, CanEnsureCE es0 a0, CanEnsureCE es0 (MulType a0 Double), SuitableForCE es0) => CanMulAsymmetric (CollectErrors es0 a0) Double

Associated Types

type MulType (CollectErrors es0 a0) Double :: *

Methods

mul :: CollectErrors es0 a0 -> Double -> MulType (CollectErrors es0 a0) Double

(CanMulAsymmetric a0 Rational, CanEnsureCE es0 a0, CanEnsureCE es0 (MulType a0 Rational), SuitableForCE es0) => CanMulAsymmetric (CollectErrors es0 a0) Rational

Associated Types

type MulType (CollectErrors es0 a0) Rational :: *

Methods

mul :: CollectErrors es0 a0 -> Rational -> MulType (CollectErrors es0 a0) Rational

(CanMulAsymmetric a0 Int, CanEnsureCE es0 a0, CanEnsureCE es0 (MulType a0 Int), SuitableForCE es0) => CanMulAsymmetric (CollectErrors es0 a0) Int

Associated Types

type MulType (CollectErrors es0 a0) Int :: *

Methods

mul :: CollectErrors es0 a0 -> Int -> MulType (CollectErrors es0 a0) Int

(CanMulAsymmetric a0 Integer, CanEnsureCE es0 a0, CanEnsureCE es0 (MulType a0 Integer), SuitableForCE es0) => CanMulAsymmetric (CollectErrors es0 a0) Integer

Associated Types

type MulType (CollectErrors es0 a0) Integer :: *

Methods

mul :: CollectErrors es0 a0 -> Integer -> MulType (CollectErrors es0 a0) Integer

(CanMulAsymmetric a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (MulType a b), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) (CollectErrors es b)

Associated Types

type MulType (CollectErrors es a) (CollectErrors es b) :: *

Methods

mul :: CollectErrors es a -> CollectErrors es b -> MulType (CollectErrors es a) (CollectErrors es b)

type CanMulBy t1 t2 = (CanMul t1 t2, MulType t1 t2 ~ t1)

type CanMulSameType t = CanMulBy t t

(*) :: CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2 infixl 7

product :: (CanMulSameType t, ConvertibleExactly Integer t) => [t] -> t

Tests

specCanMul :: (Show t1, Show t2, Show t3, Show (MulType t1 t2), Show (MulType t2 t1), Show (MulType t1 (MulType t2 t3)), Show (MulType (MulType t1 t2) t3), Show (MulType t1 (AddType t2 t3)), Show (AddType (MulType t1 t2) (MulType t1 t3)), Arbitrary t1, Arbitrary t2, Arbitrary t3, ConvertibleExactly Integer t2, CanTestCertainly (EqCompareType (MulType t1 t2) t1), CanTestCertainly (EqCompareType (MulType t1 t2) (MulType t2 t1)), CanTestCertainly (EqCompareType (MulType t1 (MulType t2 t3)) (MulType (MulType t1 t2) t3)), CanTestCertainly (EqCompareType (MulType t1 (AddType t2 t3)) (AddType (MulType t1 t2) (MulType t1 t3))), HasEqAsymmetric (MulType t1 t2) t1, HasEqAsymmetric (MulType t1 t2) (MulType t2 t1), HasEqAsymmetric (MulType t1 (MulType t2 t3)) (MulType (MulType t1 t2) t3), HasEqAsymmetric (MulType t1 (AddType t2 t3)) (AddType (MulType t1 t2) (MulType t1 t3)), CanAddAsymmetric t2 t3, CanAddAsymmetric (MulType t1 t2) (MulType t1 t3), CanMulAsymmetric t1 t2, CanMulAsymmetric t1 t3, CanMulAsymmetric t1 (MulType t2 t3), CanMulAsymmetric t1 (AddType t2 t3), CanMulAsymmetric t2 t1, CanMulAsymmetric t2 t3, CanMulAsymmetric (MulType t1 t2) t3) => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of CanMul should satisfy.

specCanMulNotMixed :: (Show t, Show (MulType t t), Show (MulType t (MulType t t)), Show (MulType (MulType t t) t), Show (MulType t (AddType t t)), Show (AddType (MulType t t) (MulType t t)), Arbitrary t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType (MulType t t) t), CanTestCertainly (EqCompareType (MulType t t) (MulType t t)), CanTestCertainly (EqCompareType (MulType t (MulType t t)) (MulType (MulType t t) t)), CanTestCertainly (EqCompareType (MulType t (AddType t t)) (AddType (MulType t t) (MulType t t))), HasEqAsymmetric (MulType t t) t, HasEqAsymmetric (MulType t t) (MulType t t), HasEqAsymmetric (MulType t (MulType t t)) (MulType (MulType t t) t), HasEqAsymmetric (MulType t (AddType t t)) (AddType (MulType t t) (MulType t t)), CanAddAsymmetric t t, CanAddAsymmetric (MulType t t) (MulType t t), CanMulAsymmetric t t, CanMulAsymmetric t (MulType t t), CanMulAsymmetric t (AddType t t), CanMulAsymmetric (MulType t t) t) => T t -> Spec

HSpec properties that each implementation of CanMul should satisfy.

specCanMulSameType :: (Show t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType t t), HasEqAsymmetric t t, CanMulAsymmetric t t, MulType t t ~ t) => T t -> Spec

HSpec properties that each implementation of CanMulSameType should satisfy.

Exponentiation

class CanPow b e where

A replacement for Prelude's binary ^ and ^^. If Num t1 and Integral t2, then one can use the default implementation to mirror Prelude's ^.

Minimal complete definition

powNoCN

Associated Types

type PowTypeNoCN b e

type PowType b e

Methods

powNoCN :: b -> e -> PowTypeNoCN b e

pow :: b -> e -> PowType b e

pow :: (HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, CanTestInteger e, CanEnsureCN (PowTypeNoCN b e), PowType b e ~ EnsureCN (PowTypeNoCN b e)) => b -> e -> PowType b e

Instances

CanPow Double Int

Associated Types

type PowTypeNoCN Double Int :: *

type PowType Double Int :: *

Methods

powNoCN :: Double -> Int -> PowTypeNoCN Double Int

pow :: Double -> Int -> PowType Double Int

CanPow Double Integer

Associated Types

type PowTypeNoCN Double Integer :: *

type PowType Double Integer :: *

Methods

powNoCN :: Double -> Integer -> PowTypeNoCN Double Integer

pow :: Double -> Integer -> PowType Double Integer

CanPow Int Int

Associated Types

type PowTypeNoCN Int Int :: *

type PowType Int Int :: *

Methods

powNoCN :: Int -> Int -> PowTypeNoCN Int Int

pow :: Int -> Int -> PowType Int Int

CanPow Int Integer

Associated Types

type PowTypeNoCN Int Integer :: *

type PowType Int Integer :: *

Methods

powNoCN :: Int -> Integer -> PowTypeNoCN Int Integer

pow :: Int -> Integer -> PowType Int Integer

CanPow Integer Int

Associated Types

type PowTypeNoCN Integer Int :: *

type PowType Integer Int :: *

Methods

powNoCN :: Integer -> Int -> PowTypeNoCN Integer Int

pow :: Integer -> Int -> PowType Integer Int

CanPow Integer Integer

Associated Types

type PowTypeNoCN Integer Integer :: *

type PowType Integer Integer :: *

Methods

powNoCN :: Integer -> Integer -> PowTypeNoCN Integer Integer

pow :: Integer -> Integer -> PowType Integer Integer

CanPow Rational Int

Associated Types

type PowTypeNoCN Rational Int :: *

type PowType Rational Int :: *

Methods

powNoCN :: Rational -> Int -> PowTypeNoCN Rational Int

pow :: Rational -> Int -> PowType Rational Int

CanPow Rational Integer

Associated Types

type PowTypeNoCN Rational Integer :: *

type PowType Rational Integer :: *

Methods

powNoCN :: Rational -> Integer -> PowTypeNoCN Rational Integer

pow :: Rational -> Integer -> PowType Rational Integer

(CanPow Double b0, CanEnsureCE es0 b0, CanEnsureCE es0 (PowType Double b0), CanEnsureCE es0 (PowTypeNoCN Double b0), SuitableForCE es0) => CanPow Double (CollectErrors es0 b0)

Associated Types

type PowTypeNoCN Double (CollectErrors es0 b0) :: *

type PowType Double (CollectErrors es0 b0) :: *

Methods

powNoCN :: Double -> CollectErrors es0 b0 -> PowTypeNoCN Double (CollectErrors es0 b0)

pow :: Double -> CollectErrors es0 b0 -> PowType Double (CollectErrors es0 b0)

(CanPow Int b0, CanEnsureCE es0 b0, CanEnsureCE es0 (PowType Int b0), CanEnsureCE es0 (PowTypeNoCN Int b0), SuitableForCE es0) => CanPow Int (CollectErrors es0 b0)

Associated Types

type PowTypeNoCN Int (CollectErrors es0 b0) :: *

type PowType Int (CollectErrors es0 b0) :: *

Methods

powNoCN :: Int -> CollectErrors es0 b0 -> PowTypeNoCN Int (CollectErrors es0 b0)

pow :: Int -> CollectErrors es0 b0 -> PowType Int (CollectErrors es0 b0)

(CanPow Integer b0, CanEnsureCE es0 b0, CanEnsureCE es0 (PowType Integer b0), CanEnsureCE es0 (PowTypeNoCN Integer b0), SuitableForCE es0) => CanPow Integer (CollectErrors es0 b0)

Associated Types

type PowTypeNoCN Integer (CollectErrors es0 b0) :: *

type PowType Integer (CollectErrors es0 b0) :: *

Methods

powNoCN :: Integer -> CollectErrors es0 b0 -> PowTypeNoCN Integer (CollectErrors es0 b0)

pow :: Integer -> CollectErrors es0 b0 -> PowType Integer (CollectErrors es0 b0)

(CanPow Rational b0, CanEnsureCE es0 b0, CanEnsureCE es0 (PowType Rational b0), CanEnsureCE es0 (PowTypeNoCN Rational b0), SuitableForCE es0) => CanPow Rational (CollectErrors es0 b0)

Associated Types

type PowTypeNoCN Rational (CollectErrors es0 b0) :: *

type PowType Rational (CollectErrors es0 b0) :: *

Methods

powNoCN :: Rational -> CollectErrors es0 b0 -> PowTypeNoCN Rational (CollectErrors es0 b0)

pow :: Rational -> CollectErrors es0 b0 -> PowType Rational (CollectErrors es0 b0)

CanPow a b => CanPow (Maybe a) (Maybe b)

Associated Types

type PowTypeNoCN (Maybe a) (Maybe b) :: *

type PowType (Maybe a) (Maybe b) :: *

Methods

powNoCN :: Maybe a -> Maybe b -> PowTypeNoCN (Maybe a) (Maybe b)

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

(CanPow a0 Double, CanEnsureCE es0 a0, CanEnsureCE es0 (PowType a0 Double), CanEnsureCE es0 (PowTypeNoCN a0 Double), SuitableForCE es0) => CanPow (CollectErrors es0 a0) Double

Associated Types

type PowTypeNoCN (CollectErrors es0 a0) Double :: *

type PowType (CollectErrors es0 a0) Double :: *

Methods

powNoCN :: CollectErrors es0 a0 -> Double -> PowTypeNoCN (CollectErrors es0 a0) Double

pow :: CollectErrors es0 a0 -> Double -> PowType (CollectErrors es0 a0) Double

(CanPow a0 Rational, CanEnsureCE es0 a0, CanEnsureCE es0 (PowType a0 Rational), CanEnsureCE es0 (PowTypeNoCN a0 Rational), SuitableForCE es0) => CanPow (CollectErrors es0 a0) Rational

Associated Types

type PowTypeNoCN (CollectErrors es0 a0) Rational :: *

type PowType (CollectErrors es0 a0) Rational :: *

Methods

powNoCN :: CollectErrors es0 a0 -> Rational -> PowTypeNoCN (CollectErrors es0 a0) Rational

pow :: CollectErrors es0 a0 -> Rational -> PowType (CollectErrors es0 a0) Rational

(CanPow a0 Int, CanEnsureCE es0 a0, CanEnsureCE es0 (PowType a0 Int), CanEnsureCE es0 (PowTypeNoCN a0 Int), SuitableForCE es0) => CanPow (CollectErrors es0 a0) Int

Associated Types

type PowTypeNoCN (CollectErrors es0 a0) Int :: *

type PowType (CollectErrors es0 a0) Int :: *

Methods

powNoCN :: CollectErrors es0 a0 -> Int -> PowTypeNoCN (CollectErrors es0 a0) Int

pow :: CollectErrors es0 a0 -> Int -> PowType (CollectErrors es0 a0) Int

(CanPow a0 Integer, CanEnsureCE es0 a0, CanEnsureCE es0 (PowType a0 Integer), CanEnsureCE es0 (PowTypeNoCN a0 Integer), SuitableForCE es0) => CanPow (CollectErrors es0 a0) Integer

Associated Types

type PowTypeNoCN (CollectErrors es0 a0) Integer :: *

type PowType (CollectErrors es0 a0) Integer :: *

Methods

powNoCN :: CollectErrors es0 a0 -> Integer -> PowTypeNoCN (CollectErrors es0 a0) Integer

pow :: CollectErrors es0 a0 -> Integer -> PowType (CollectErrors es0 a0) Integer

(CanPow a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (PowTypeNoCN a b), CanEnsureCE es (PowType a b), SuitableForCE es) => CanPow (CollectErrors es a) (CollectErrors es b)

Associated Types

type PowTypeNoCN (CollectErrors es a) (CollectErrors es b) :: *

type PowType (CollectErrors es a) (CollectErrors es b) :: *

Methods

powNoCN :: CollectErrors es a -> CollectErrors es b -> PowTypeNoCN (CollectErrors es a) (CollectErrors es b)

pow :: CollectErrors es a -> CollectErrors es b -> PowType (CollectErrors es a) (CollectErrors es b)

type CanPowBy t1 t2 = (CanPow t1 t2, PowType t1 t2 ~ t1, PowTypeNoCN t1 t2 ~ t1)

type CanPowCNBy t1 t2 = (CanPow t1 t2, PowType t1 t2 ~ EnsureCN t1, PowTypeNoCN t1 t2 ~ t1, CanEnsureCN t1, CanPow (EnsureCN t1) t2, PowType (EnsureCN t1) t2 ~ EnsureCN t1, PowTypeNoCN (EnsureCN t1) t2 ~ EnsureCN t1)

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

(^!) :: CanPow t1 t2 => t1 -> t2 -> PowTypeNoCN t1 t2 infixl 8

Like ^ but throwing an exception if the power is undefined.

powUsingMul :: (CanBeInteger e, CanMulSameType t) => t -> t -> e -> t

integerPowCN :: (HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, HasEqCertainly e Integer, CanEnsureCN r) => (b -> e -> r) -> b -> e -> EnsureCN r

Tests

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

HSpec properties that each implementation of CanPow should satisfy.