Contents Index

Org.Org.Semantic.HBase.Basic.Arithmetic

Description

These classes are nominal.

Synopsis

class HasZero a where isZero :: a -> Bool zero :: a isPositiveStrict :: (HasZero a, MaybeOrdered a) => a -> Bool isNegativeStrict :: (HasZero a, MaybeOrdered a) => a -> Bool isPositiveInclusive :: (HasZero a, MaybeOrdered a) => a -> Bool isNegativeInclusive :: (HasZero a, MaybeOrdered a) => a -> Bool class Additive a b ab | a b -> ab where add :: a -> b -> ab (+) :: Additive a a a => a -> a -> a sum :: (HasZero a, Additive a a a) => [a] -> a class Negatable a where negate :: a -> a class Subtractive a b ab | a b -> ab where subtract :: a -> b -> ab (-) :: Subtractive a a a => a -> a -> a class HasOne a where isOne :: a -> Bool one :: a class Multiplicative a b ab | a b -> ab where multiply :: a -> b -> ab (*) :: Multiplicative a a a => a -> a -> a product :: (HasOne a, Multiplicative a a a) => [a] -> a class HasAbsolute k a | a -> k where absolute :: a -> k class HasSignum a where signum :: a -> a

Documentation

class HasZero a where

Has a value that's 'zero' in some sense. Methods isZero :: a -> Bool zero :: a Typically zero should be identity for add. Instances HasZero Int HasZero Integer HasZero Word8 HasZero Int8 HasZero Word16 HasZero Int16 HasZero Word32 HasZero Int32 HasZero Word64 HasZero Int64 HasZero r => HasZero (Complex r) HasZero Double (HasZero a, HasReturn p, HasReturn q, ExtractableFunctor p, ExtractableFunctor q) => HasZero (FunctorMatrix p q a) (HasZero a, HasReturn t, ExtractableFunctor t) => HasZero (FunctorVector t a) HasZero EIReal HasZero a => HasZero (InfExtended a) HasZero Rational HasZero a => HasZero (VectorWrapper t a) HasZero a => HasZero (UTCDuration a)

isPositiveStrict :: (HasZero a, MaybeOrdered a) => a -> Bool

isNegativeStrict :: (HasZero a, MaybeOrdered a) => a -> Bool

isPositiveInclusive :: (HasZero a, MaybeOrdered a) => a -> Bool

isNegativeInclusive :: (HasZero a, MaybeOrdered a) => a -> Bool

class Additive a b ab | a b -> ab where

Methods add :: a -> b -> ab Add a to b. Instances Additive Int Int Int Additive Integer Integer Integer Additive Word8 Word8 Word8 Additive Int8 Int8 Int8 Additive Word16 Word16 Word16 Additive Int16 Int16 Int16 Additive Word32 Word32 Word32 Additive Int32 Int32 Int32 Additive Word64 Word64 Word64 Additive Int64 Int64 Int64 Additive a a aa => Additive (Complex a) (Complex a) (Complex aa) Additive a a a => Additive a (Complex a) (Complex a) Additive a a a => Additive (Complex a) a (Complex a) Additive Double Double Double (Additive a b c, FunctorApply p, FunctorApply q) => Additive (FunctorMatrix p q a) (FunctorMatrix p q b) (FunctorMatrix p q c) (Additive a b c, FunctorApply t) => Additive (FunctorVector t a) (FunctorVector t b) (FunctorVector t c) Additive EIReal EIReal EIReal Additive a b c => Additive (InfExtended a) (InfExtended b) (NaNExtended (InfExtended c)) () => Additive (NaNExtended Integer) (NaNExtended Integer) (NaNExtended Integer) () => Additive Integer (NaNExtended Integer) (NaNExtended Integer) () => Additive (NaNExtended Integer) Integer (NaNExtended Integer) () => Additive (NaNExtended Int) (NaNExtended Int) (NaNExtended Int) () => Additive Int (NaNExtended Int) (NaNExtended Int) () => Additive (NaNExtended Int) Int (NaNExtended Int) () => Additive (NaNExtended Word8) (NaNExtended Word8) (NaNExtended Word8) () => Additive Word8 (NaNExtended Word8) (NaNExtended Word8) () => Additive (NaNExtended Word8) Word8 (NaNExtended Word8) () => Additive (NaNExtended Int8) (NaNExtended Int8) (NaNExtended Int8) () => Additive Int8 (NaNExtended Int8) (NaNExtended Int8) () => Additive (NaNExtended Int8) Int8 (NaNExtended Int8) () => Additive (NaNExtended Word16) (NaNExtended Word16) (NaNExtended Word16) () => Additive Word16 (NaNExtended Word16) (NaNExtended Word16) () => Additive (NaNExtended Word16) Word16 (NaNExtended Word16) () => Additive (NaNExtended Int16) (NaNExtended Int16) (NaNExtended Int16) () => Additive Int16 (NaNExtended Int16) (NaNExtended Int16) () => Additive (NaNExtended Int16) Int16 (NaNExtended Int16) () => Additive (NaNExtended Word32) (NaNExtended Word32) (NaNExtended Word32) () => Additive Word32 (NaNExtended Word32) (NaNExtended Word32) () => Additive (NaNExtended Word32) Word32 (NaNExtended Word32) () => Additive (NaNExtended Int32) (NaNExtended Int32) (NaNExtended Int32) () => Additive Int32 (NaNExtended Int32) (NaNExtended Int32) () => Additive (NaNExtended Int32) Int32 (NaNExtended Int32) () => Additive (NaNExtended Word64) (NaNExtended Word64) (NaNExtended Word64) () => Additive Word64 (NaNExtended Word64) (NaNExtended Word64) () => Additive (NaNExtended Word64) Word64 (NaNExtended Word64) () => Additive (NaNExtended Int64) (NaNExtended Int64) (NaNExtended Int64) () => Additive Int64 (NaNExtended Int64) (NaNExtended Int64) () => Additive (NaNExtended Int64) Int64 (NaNExtended Int64) () => Additive (NaNExtended Rational) (NaNExtended Rational) (NaNExtended Rational) () => Additive Rational (NaNExtended Rational) (NaNExtended Rational) () => Additive (NaNExtended Rational) Rational (NaNExtended Rational) Additive Rational Rational Rational Additive Integer Rational Rational Additive Rational Integer Rational Additive a b c => Additive (VectorWrapper t a) (VectorWrapper t b) (VectorWrapper t c) Additive a b c => Additive (VectorWrapper t a) (PointWrapper t b) (PointWrapper t c) Additive Integer Char Char (Additive a a a, HasIntegerDivide Integer a, InterpretIntegerLiteral a) => Additive (UTCDuration a) (UTCDuration a) (UTCDuration a) (Additive a a a, HasIntegerDivide Integer a, InterpretIntegerLiteral a) => Additive (UTCDuration a) (UTCTime a) (UTCTime a)

(+) :: Additive a a a => a -> a -> a

This is add with the arguments swapped, as per subtract.

sum :: (HasZero a, Additive a a a) => [a] -> a

class Negatable a where

Methods negate :: a -> a Instances Negatable Int Negatable Integer Negatable Int8 Negatable Int16 Negatable Int32 Negatable Int64 Negatable a => Negatable (Complex a) Negatable Double (Negatable a, Functor p, Functor q) => Negatable (FunctorMatrix p q a) (Negatable a, Functor t) => Negatable (FunctorVector t a) Negatable EIReal Negatable a => Negatable (InfExtended a) Negatable Rational Negatable a => Negatable (VectorWrapper t a)

class Subtractive a b ab | a b -> ab where

Methods subtract :: a -> b -> ab Watch out, "subtract a b" means "subtract a from b" i.e. "b - a". Instances Subtractive Int Int Int Subtractive Integer Integer Integer Subtractive Word8 Word8 Word8 Subtractive Int8 Int8 Int8 Subtractive Word16 Word16 Word16 Subtractive Int16 Int16 Int16 Subtractive Word32 Word32 Word32 Subtractive Int32 Int32 Int32 Subtractive Word64 Word64 Word64 Subtractive Int64 Int64 Int64 Subtractive a a aa => Subtractive (Complex a) (Complex a) (Complex aa) Subtractive a a a => Subtractive a (Complex a) (Complex a) (Subtractive a a a, Negatable a) => Subtractive (Complex a) a (Complex a) Subtractive Double Double Double (Subtractive a b c, FunctorApply p, FunctorApply q) => Subtractive (FunctorMatrix p q a) (FunctorMatrix p q b) (FunctorMatrix p q c) (Subtractive a b c, FunctorApply t) => Subtractive (FunctorVector t a) (FunctorVector t b) (FunctorVector t c) Subtractive EIReal EIReal EIReal Subtractive a b c => Subtractive (InfExtended a) (InfExtended b) (NaNExtended (InfExtended c)) () => Subtractive (NaNExtended Integer) (NaNExtended Integer) (NaNExtended Integer) () => Subtractive Integer (NaNExtended Integer) (NaNExtended Integer) () => Subtractive (NaNExtended Integer) Integer (NaNExtended Integer) () => Subtractive (NaNExtended Int) (NaNExtended Int) (NaNExtended Int) () => Subtractive Int (NaNExtended Int) (NaNExtended Int) () => Subtractive (NaNExtended Int) Int (NaNExtended Int) () => Subtractive (NaNExtended Word8) (NaNExtended Word8) (NaNExtended Word8) () => Subtractive Word8 (NaNExtended Word8) (NaNExtended Word8) () => Subtractive (NaNExtended Word8) Word8 (NaNExtended Word8) () => Subtractive (NaNExtended Int8) (NaNExtended Int8) (NaNExtended Int8) () => Subtractive Int8 (NaNExtended Int8) (NaNExtended Int8) () => Subtractive (NaNExtended Int8) Int8 (NaNExtended Int8) () => Subtractive (NaNExtended Word16) (NaNExtended Word16) (NaNExtended Word16) () => Subtractive Word16 (NaNExtended Word16) (NaNExtended Word16) () => Subtractive (NaNExtended Word16) Word16 (NaNExtended Word16) () => Subtractive (NaNExtended Int16) (NaNExtended Int16) (NaNExtended Int16) () => Subtractive Int16 (NaNExtended Int16) (NaNExtended Int16) () => Subtractive (NaNExtended Int16) Int16 (NaNExtended Int16) () => Subtractive (NaNExtended Word32) (NaNExtended Word32) (NaNExtended Word32) () => Subtractive Word32 (NaNExtended Word32) (NaNExtended Word32) () => Subtractive (NaNExtended Word32) Word32 (NaNExtended Word32) () => Subtractive (NaNExtended Int32) (NaNExtended Int32) (NaNExtended Int32) () => Subtractive Int32 (NaNExtended Int32) (NaNExtended Int32) () => Subtractive (NaNExtended Int32) Int32 (NaNExtended Int32) () => Subtractive (NaNExtended Word64) (NaNExtended Word64) (NaNExtended Word64) () => Subtractive Word64 (NaNExtended Word64) (NaNExtended Word64) () => Subtractive (NaNExtended Word64) Word64 (NaNExtended Word64) () => Subtractive (NaNExtended Int64) (NaNExtended Int64) (NaNExtended Int64) () => Subtractive Int64 (NaNExtended Int64) (NaNExtended Int64) () => Subtractive (NaNExtended Int64) Int64 (NaNExtended Int64) () => Subtractive (NaNExtended Rational) (NaNExtended Rational) (NaNExtended Rational) () => Subtractive Rational (NaNExtended Rational) (NaNExtended Rational) () => Subtractive (NaNExtended Rational) Rational (NaNExtended Rational) Subtractive Rational Rational Rational Subtractive Integer Rational Rational Subtractive Rational Integer Rational Subtractive a b c => Subtractive (VectorWrapper t a) (VectorWrapper t b) (VectorWrapper t c) Subtractive a b c => Subtractive (VectorWrapper t a) (PointWrapper t b) (PointWrapper t c) Subtractive a b c => Subtractive (PointWrapper t a) (PointWrapper t b) (VectorWrapper t c) Subtractive Integer Char Char Subtractive Char Char Integer (Subtractive a a a, HasIntegerDivide Integer a, InterpretIntegerLiteral a) => Subtractive (UTCDuration a) (UTCDuration a) (UTCDuration a) (Subtractive a a a, HasIntegerDivide Integer a, InterpretIntegerLiteral a) => Subtractive (UTCDuration a) (UTCTime a) (UTCTime a) (Subtractive a a a, HasIntegerDivide Integer a, InterpretIntegerLiteral a) => Subtractive (UTCTime a) (UTCTime a) (UTCDuration a)

(-) :: Subtractive a a a => a -> a -> a

This is subtract with the arguments swapped.

class HasOne a where

Has a value that's 'one' in some sense. Methods isOne :: a -> Bool one :: a Typically one should be identity for multiply. Instances HasOne Int HasOne Integer HasOne Word8 HasOne Int8 HasOne Word16 HasOne Int16 HasOne Word32 HasOne Int32 HasOne Word64 HasOne Int64 (HasZero r, HasOne r) => HasOne (Complex r) HasOne Double (HasZero a, HasOne a, ExtractableFunctor p, FunctorApply p, SameIndexSquare p) => HasOne (FunctorMatrix p p a) HasOne EIReal HasOne a => HasOne (InfExtended a) HasOne Rational HasOne a => HasOne (VectorWrapper t a)

class Multiplicative a b ab | a b -> ab where

Methods multiply :: a -> b -> ab multiply b by a. Instances Multiplicative Int Int Int Multiplicative Integer Integer Integer Multiplicative Word8 Word8 Word8 Multiplicative Int8 Int8 Int8 Multiplicative Word16 Word16 Word16 Multiplicative Int16 Int16 Int16 Multiplicative Word32 Word32 Word32 Multiplicative Int32 Int32 Int32 Multiplicative Word64 Word64 Word64 Multiplicative Int64 Int64 Int64 (Multiplicative a a aa, Additive aa aa c, Subtractive aa aa c) => Multiplicative (Complex a) (Complex a) (Complex c) Multiplicative a a c => Multiplicative a (Complex a) (Complex c) Multiplicative Double Double Double Multiplicative Integer Double Double (Multiplicative a a c, Functor p, Functor q) => Multiplicative a (FunctorMatrix p q a) (FunctorMatrix p q c) (Multiplicative a a c, HasZero c, Additive c c c, Functor p, FunctorApply q, ExtractableFunctor q, FunctorApplyReturn r) => Multiplicative (FunctorMatrix p q a) (FunctorMatrix q r a) (FunctorMatrix p r c) (Multiplicative a a c, HasZero c, Additive c c c, Functor p, FunctorApply q, ExtractableFunctor q) => Multiplicative (FunctorMatrix p q a) (FunctorVector q a) (FunctorVector p c) (Multiplicative a a c, Functor t) => Multiplicative a (FunctorVector t a) (FunctorVector t c) Multiplicative EIReal EIReal EIReal (HasZero a, HasZero b, Multiplicative a b c) => Multiplicative (InfExtended a) (InfExtended b) (NaNExtended (InfExtended c)) () => Multiplicative (NaNExtended Integer) (NaNExtended Integer) (NaNExtended Integer) () => Multiplicative Integer (NaNExtended Integer) (NaNExtended Integer) () => Multiplicative (NaNExtended Integer) Integer (NaNExtended Integer) () => Multiplicative (NaNExtended Int) (NaNExtended Int) (NaNExtended Int) () => Multiplicative Int (NaNExtended Int) (NaNExtended Int) () => Multiplicative (NaNExtended Int) Int (NaNExtended Int) () => Multiplicative (NaNExtended Word8) (NaNExtended Word8) (NaNExtended Word8) () => Multiplicative Word8 (NaNExtended Word8) (NaNExtended Word8) () => Multiplicative (NaNExtended Word8) Word8 (NaNExtended Word8) () => Multiplicative (NaNExtended Int8) (NaNExtended Int8) (NaNExtended Int8) () => Multiplicative Int8 (NaNExtended Int8) (NaNExtended Int8) () => Multiplicative (NaNExtended Int8) Int8 (NaNExtended Int8) () => Multiplicative (NaNExtended Word16) (NaNExtended Word16) (NaNExtended Word16) () => Multiplicative Word16 (NaNExtended Word16) (NaNExtended Word16) () => Multiplicative (NaNExtended Word16) Word16 (NaNExtended Word16) () => Multiplicative (NaNExtended Int16) (NaNExtended Int16) (NaNExtended Int16) () => Multiplicative Int16 (NaNExtended Int16) (NaNExtended Int16) () => Multiplicative (NaNExtended Int16) Int16 (NaNExtended Int16) () => Multiplicative (NaNExtended Word32) (NaNExtended Word32) (NaNExtended Word32) () => Multiplicative Word32 (NaNExtended Word32) (NaNExtended Word32) () => Multiplicative (NaNExtended Word32) Word32 (NaNExtended Word32) () => Multiplicative (NaNExtended Int32) (NaNExtended Int32) (NaNExtended Int32) () => Multiplicative Int32 (NaNExtended Int32) (NaNExtended Int32) () => Multiplicative (NaNExtended Int32) Int32 (NaNExtended Int32) () => Multiplicative (NaNExtended Word64) (NaNExtended Word64) (NaNExtended Word64) () => Multiplicative Word64 (NaNExtended Word64) (NaNExtended Word64) () => Multiplicative (NaNExtended Word64) Word64 (NaNExtended Word64) () => Multiplicative (NaNExtended Int64) (NaNExtended Int64) (NaNExtended Int64) () => Multiplicative Int64 (NaNExtended Int64) (NaNExtended Int64) () => Multiplicative (NaNExtended Int64) Int64 (NaNExtended Int64) () => Multiplicative (NaNExtended Rational) (NaNExtended Rational) (NaNExtended Rational) () => Multiplicative Rational (NaNExtended Rational) (NaNExtended Rational) () => Multiplicative (NaNExtended Rational) Rational (NaNExtended Rational) Multiplicative Rational Rational Rational Multiplicative Integer Rational Rational Multiplicative Rational Integer Rational Multiplicative n a b => Multiplicative n (VectorWrapper t a) (VectorWrapper t b)

(*) :: Multiplicative a a a => a -> a -> a

This is multiply with the arguments swapped, as per divide.

product :: (HasOne a, Multiplicative a a a) => [a] -> a

class HasAbsolute k a | a -> k where

Methods absolute :: a -> k Instances HasAbsolute Int Int HasAbsolute Integer Integer HasAbsolute Word8 Word8 HasAbsolute Int8 Int8 HasAbsolute Word16 Word16 HasAbsolute Int16 Int16 HasAbsolute Word32 Word32 HasAbsolute Int32 Int32 HasAbsolute Word64 Word64 HasAbsolute Int64 Int64 (ApproxMath a, HasAbsolute a a) => HasAbsolute a (Complex a) HasAbsolute Double Double HasAbsolute EIReal EIReal HasAbsolute k a => HasAbsolute (InfExtended k) (InfExtended a) HasAbsolute Rational Rational

class HasSignum a where

Methods signum :: a -> a Instances HasSignum Int HasSignum Integer HasSignum Word8 HasSignum Int8 HasSignum Word16 HasSignum Int16 HasSignum Word32 HasSignum Int32 HasSignum Word64 HasSignum Int64 (ApproxMath a, HasAbsolute a a) => HasSignum (Complex a) HasSignum Double HasSignum EIReal HasSignum a => HasSignum (InfExtended a) HasSignum Rational

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