Data.Semigroup.Multiplicative

Documentation

type (-) g f a = f (g a) infixr 1

Hyphenation operator.

newtype Multiplicative a

A (potentially non-commutative) Semigroup under +.

Constructors

Multiplicative

Fields

• unMultiplicative :: a

Instances

Functor Multiplicative

Defined in Data.Semigroup.Multiplicative

Methods

fmap :: (a -> b) -> Multiplicative a -> Multiplicative b

(<$) :: a -> Multiplicative b -> Multiplicative a

Applicative Multiplicative

Defined in Data.Semigroup.Multiplicative

Methods

pure :: a -> Multiplicative a

(<*>) :: Multiplicative (a -> b) -> Multiplicative a -> Multiplicative b

liftA2 :: (a -> b -> c) -> Multiplicative a -> Multiplicative b -> Multiplicative c

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

(<*) :: Multiplicative a -> Multiplicative b -> Multiplicative a

Distributive Multiplicative

Defined in Data.Semigroup.Multiplicative

Methods

distribute :: Functor f => f (Multiplicative a) -> Multiplicative (f a)

collect :: Functor f => (a -> Multiplicative b) -> f a -> Multiplicative (f b)

distributeM :: Monad m => m (Multiplicative a) -> Multiplicative (m a)

collectM :: Monad m => (a -> Multiplicative b) -> m a -> Multiplicative (m b)

Representable Multiplicative

Defined in Data.Semigroup.Multiplicative

Associated Types

type Rep Multiplicative :: Type

Methods

tabulate :: (Rep Multiplicative -> a) -> Multiplicative a

index :: Multiplicative a -> Rep Multiplicative -> a

Eq a => Eq (Multiplicative a)

Defined in Data.Semigroup.Multiplicative

Methods

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

(/=) :: Multiplicative a -> Multiplicative a -> Bool

Ord a => Ord (Multiplicative a)

Defined in Data.Semigroup.Multiplicative

Methods

compare :: Multiplicative a -> Multiplicative a -> Ordering

(<) :: Multiplicative a -> Multiplicative a -> Bool

(<=) :: Multiplicative a -> Multiplicative a -> Bool

(>) :: Multiplicative a -> Multiplicative a -> Bool

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

max :: Multiplicative a -> Multiplicative a -> Multiplicative a

min :: Multiplicative a -> Multiplicative a -> Multiplicative a

Show a => Show (Multiplicative a)

Defined in Data.Semigroup.Multiplicative

Methods

showsPrec :: Int -> Multiplicative a -> ShowS

show :: Multiplicative a -> String

showList :: [Multiplicative a] -> ShowS

Generic (Multiplicative a)

Defined in Data.Semigroup.Multiplicative

Associated Types

type Rep (Multiplicative a) :: Type -> Type

Methods

from :: Multiplicative a -> Rep (Multiplicative a) x

to :: Rep (Multiplicative a) x -> Multiplicative a

Semigroup (Multiplicative Bool)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Bool -> Multiplicative Bool -> Multiplicative Bool

sconcat :: NonEmpty (Multiplicative Bool) -> Multiplicative Bool

stimes :: Integral b => b -> Multiplicative Bool -> Multiplicative Bool

Semigroup (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Double -> Multiplicative Double -> Multiplicative Double

sconcat :: NonEmpty (Multiplicative Double) -> Multiplicative Double

stimes :: Integral b => b -> Multiplicative Double -> Multiplicative Double

Semigroup (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Float -> Multiplicative Float -> Multiplicative Float

sconcat :: NonEmpty (Multiplicative Float) -> Multiplicative Float

stimes :: Integral b => b -> Multiplicative Float -> Multiplicative Float

(Multiplicative - Semigroup) b => Semigroup (Multiplicative (a -> b))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (a -> b) -> Multiplicative (a -> b) -> Multiplicative (a -> b)

sconcat :: NonEmpty (Multiplicative (a -> b)) -> Multiplicative (a -> b)

stimes :: Integral b0 => b0 -> Multiplicative (a -> b) -> Multiplicative (a -> b)

Semigroup (Multiplicative Int)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Int -> Multiplicative Int -> Multiplicative Int

sconcat :: NonEmpty (Multiplicative Int) -> Multiplicative Int

stimes :: Integral b => b -> Multiplicative Int -> Multiplicative Int

Semigroup (Multiplicative Int8)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Int8 -> Multiplicative Int8 -> Multiplicative Int8

sconcat :: NonEmpty (Multiplicative Int8) -> Multiplicative Int8

stimes :: Integral b => b -> Multiplicative Int8 -> Multiplicative Int8

Semigroup (Multiplicative Int16)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Int16 -> Multiplicative Int16 -> Multiplicative Int16

sconcat :: NonEmpty (Multiplicative Int16) -> Multiplicative Int16

stimes :: Integral b => b -> Multiplicative Int16 -> Multiplicative Int16

Semigroup (Multiplicative Int32)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Int32 -> Multiplicative Int32 -> Multiplicative Int32

sconcat :: NonEmpty (Multiplicative Int32) -> Multiplicative Int32

stimes :: Integral b => b -> Multiplicative Int32 -> Multiplicative Int32

Semigroup (Multiplicative Int64)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Int64 -> Multiplicative Int64 -> Multiplicative Int64

sconcat :: NonEmpty (Multiplicative Int64) -> Multiplicative Int64

stimes :: Integral b => b -> Multiplicative Int64 -> Multiplicative Int64

Semigroup (Multiplicative Integer)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Integer -> Multiplicative Integer -> Multiplicative Integer

sconcat :: NonEmpty (Multiplicative Integer) -> Multiplicative Integer

stimes :: Integral b => b -> Multiplicative Integer -> Multiplicative Integer

Semigroup (Multiplicative Natural)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Natural -> Multiplicative Natural -> Multiplicative Natural

sconcat :: NonEmpty (Multiplicative Natural) -> Multiplicative Natural

stimes :: Integral b => b -> Multiplicative Natural -> Multiplicative Natural

(Additive - Semigroup) a => Semigroup (Multiplicative [a])

Defined in Data.Semigroup.Additive

Methods

(<>) :: Multiplicative [a] -> Multiplicative [a] -> Multiplicative [a]

sconcat :: NonEmpty (Multiplicative [a]) -> Multiplicative [a]

stimes :: Integral b => b -> Multiplicative [a] -> Multiplicative [a]

(Multiplicative - Semigroup) a => Semigroup (Multiplicative (Maybe a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Maybe a) -> Multiplicative (Maybe a) -> Multiplicative (Maybe a)

sconcat :: NonEmpty (Multiplicative (Maybe a)) -> Multiplicative (Maybe a)

stimes :: Integral b => b -> Multiplicative (Maybe a) -> Multiplicative (Maybe a)

(Multiplicative - Semigroup) a => Semigroup (Multiplicative (Ratio a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Ratio a) -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

sconcat :: NonEmpty (Multiplicative (Ratio a)) -> Multiplicative (Ratio a)

stimes :: Integral b => b -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

Semigroup (Multiplicative Word)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Word -> Multiplicative Word -> Multiplicative Word

sconcat :: NonEmpty (Multiplicative Word) -> Multiplicative Word

stimes :: Integral b => b -> Multiplicative Word -> Multiplicative Word

Semigroup (Multiplicative Word8)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Word8 -> Multiplicative Word8 -> Multiplicative Word8

sconcat :: NonEmpty (Multiplicative Word8) -> Multiplicative Word8

stimes :: Integral b => b -> Multiplicative Word8 -> Multiplicative Word8

Semigroup (Multiplicative Word16)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Word16 -> Multiplicative Word16 -> Multiplicative Word16

sconcat :: NonEmpty (Multiplicative Word16) -> Multiplicative Word16

stimes :: Integral b => b -> Multiplicative Word16 -> Multiplicative Word16

Semigroup (Multiplicative Word32)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Word32 -> Multiplicative Word32 -> Multiplicative Word32

sconcat :: NonEmpty (Multiplicative Word32) -> Multiplicative Word32

stimes :: Integral b => b -> Multiplicative Word32 -> Multiplicative Word32

Semigroup (Multiplicative Word64)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Word64 -> Multiplicative Word64 -> Multiplicative Word64

sconcat :: NonEmpty (Multiplicative Word64) -> Multiplicative Word64

stimes :: Integral b => b -> Multiplicative Word64 -> Multiplicative Word64

((Multiplicative - Semigroup) a, (Multiplicative - Semigroup) b) => Semigroup (Multiplicative (Either a b))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Either a b) -> Multiplicative (Either a b) -> Multiplicative (Either a b)

sconcat :: NonEmpty (Multiplicative (Either a b)) -> Multiplicative (Either a b)

stimes :: Integral b0 => b0 -> Multiplicative (Either a b) -> Multiplicative (Either a b)

Semigroup (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative () -> Multiplicative () -> Multiplicative ()

sconcat :: NonEmpty (Multiplicative ()) -> Multiplicative ()

stimes :: Integral b => b -> Multiplicative () -> Multiplicative ()

((Multiplicative - Semigroup) a, (Multiplicative - Semigroup) b) => Semigroup (Multiplicative (a, b))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (a, b) -> Multiplicative (a, b) -> Multiplicative (a, b)

sconcat :: NonEmpty (Multiplicative (a, b)) -> Multiplicative (a, b)

stimes :: Integral b0 => b0 -> Multiplicative (a, b) -> Multiplicative (a, b)

((Additive - Group) a, (Multiplicative - Semigroup) a) => Semigroup (Multiplicative (Complex a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

sconcat :: NonEmpty (Multiplicative (Complex a)) -> Multiplicative (Complex a)

stimes :: Integral b => b -> Multiplicative (Complex a) -> Multiplicative (Complex a)

Semigroup (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Uni -> Multiplicative Uni -> Multiplicative Uni

sconcat :: NonEmpty (Multiplicative Uni) -> Multiplicative Uni

stimes :: Integral b => b -> Multiplicative Uni -> Multiplicative Uni

Semigroup (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Deci -> Multiplicative Deci -> Multiplicative Deci

sconcat :: NonEmpty (Multiplicative Deci) -> Multiplicative Deci

stimes :: Integral b => b -> Multiplicative Deci -> Multiplicative Deci

Semigroup (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Centi -> Multiplicative Centi -> Multiplicative Centi

sconcat :: NonEmpty (Multiplicative Centi) -> Multiplicative Centi

stimes :: Integral b => b -> Multiplicative Centi -> Multiplicative Centi

Semigroup (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Milli -> Multiplicative Milli -> Multiplicative Milli

sconcat :: NonEmpty (Multiplicative Milli) -> Multiplicative Milli

stimes :: Integral b => b -> Multiplicative Milli -> Multiplicative Milli

Semigroup (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Micro -> Multiplicative Micro -> Multiplicative Micro

sconcat :: NonEmpty (Multiplicative Micro) -> Multiplicative Micro

stimes :: Integral b => b -> Multiplicative Micro -> Multiplicative Micro

Semigroup (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Nano -> Multiplicative Nano -> Multiplicative Nano

sconcat :: NonEmpty (Multiplicative Nano) -> Multiplicative Nano

stimes :: Integral b => b -> Multiplicative Nano -> Multiplicative Nano

Semigroup (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative Pico -> Multiplicative Pico -> Multiplicative Pico

sconcat :: NonEmpty (Multiplicative Pico) -> Multiplicative Pico

stimes :: Integral b => b -> Multiplicative Pico -> Multiplicative Pico

(Additive - Semigroup) a => Semigroup (Multiplicative (Min a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Multiplicative (Min a) -> Multiplicative (Min a) -> Multiplicative (Min a)

sconcat :: NonEmpty (Multiplicative (Min a)) -> Multiplicative (Min a)

stimes :: Integral b => b -> Multiplicative (Min a) -> Multiplicative (Min a)

(Multiplicative - Semigroup) a => Semigroup (Multiplicative (Max a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Max a) -> Multiplicative (Max a) -> Multiplicative (Max a)

sconcat :: NonEmpty (Multiplicative (Max a)) -> Multiplicative (Max a)

stimes :: Integral b => b -> Multiplicative (Max a) -> Multiplicative (Max a)

(Multiplicative - Semigroup) a => Semigroup (Multiplicative (Dual a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Dual a) -> Multiplicative (Dual a) -> Multiplicative (Dual a)

sconcat :: NonEmpty (Multiplicative (Dual a)) -> Multiplicative (Dual a)

stimes :: Integral b => b -> Multiplicative (Dual a) -> Multiplicative (Dual a)

(Multiplicative - Semigroup) a => Semigroup (Multiplicative (Down a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Down a) -> Multiplicative (Down a) -> Multiplicative (Down a)

sconcat :: NonEmpty (Multiplicative (Down a)) -> Multiplicative (Down a)

stimes :: Integral b => b -> Multiplicative (Down a) -> Multiplicative (Down a)

Semigroup (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative CFloat -> Multiplicative CFloat -> Multiplicative CFloat

sconcat :: NonEmpty (Multiplicative CFloat) -> Multiplicative CFloat

stimes :: Integral b => b -> Multiplicative CFloat -> Multiplicative CFloat

Semigroup (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative CDouble -> Multiplicative CDouble -> Multiplicative CDouble

sconcat :: NonEmpty (Multiplicative CDouble) -> Multiplicative CDouble

stimes :: Integral b => b -> Multiplicative CDouble -> Multiplicative CDouble

(Additive - Semigroup) a => Semigroup (Multiplicative (NonEmpty a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Multiplicative (NonEmpty a) -> Multiplicative (NonEmpty a) -> Multiplicative (NonEmpty a)

sconcat :: NonEmpty (Multiplicative (NonEmpty a)) -> Multiplicative (NonEmpty a)

stimes :: Integral b => b -> Multiplicative (NonEmpty a) -> Multiplicative (NonEmpty a)

(Multiplicative - Semigroup) a => Semigroup (Multiplicative (IntMap a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (IntMap a) -> Multiplicative (IntMap a) -> Multiplicative (IntMap a)

sconcat :: NonEmpty (Multiplicative (IntMap a)) -> Multiplicative (IntMap a)

stimes :: Integral b => b -> Multiplicative (IntMap a) -> Multiplicative (IntMap a)

Semigroup (Multiplicative IntSet)

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative IntSet -> Multiplicative IntSet -> Multiplicative IntSet

sconcat :: NonEmpty (Multiplicative IntSet) -> Multiplicative IntSet

stimes :: Integral b => b -> Multiplicative IntSet -> Multiplicative IntSet

(Ord k, (Multiplicative - Semigroup) a) => Semigroup (Multiplicative (Map k a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Map k a) -> Multiplicative (Map k a) -> Multiplicative (Map k a)

sconcat :: NonEmpty (Multiplicative (Map k a)) -> Multiplicative (Map k a)

stimes :: Integral b => b -> Multiplicative (Map k a) -> Multiplicative (Map k a)

Ord a => Semigroup (Multiplicative (Set a))

Defined in Data.Semigroup.Multiplicative

Methods

(<>) :: Multiplicative (Set a) -> Multiplicative (Set a) -> Multiplicative (Set a)

sconcat :: NonEmpty (Multiplicative (Set a)) -> Multiplicative (Set a)

stimes :: Integral b => b -> Multiplicative (Set a) -> Multiplicative (Set a)

Semiring a => Semigroup (Multiplicative (M44 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M44 a) -> Multiplicative (M44 a) -> Multiplicative (M44 a)

sconcat :: NonEmpty (Multiplicative (M44 a)) -> Multiplicative (M44 a)

stimes :: Integral b => b -> Multiplicative (M44 a) -> Multiplicative (M44 a)

Semiring a => Semigroup (Multiplicative (M33 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M33 a) -> Multiplicative (M33 a) -> Multiplicative (M33 a)

sconcat :: NonEmpty (Multiplicative (M33 a)) -> Multiplicative (M33 a)

stimes :: Integral b => b -> Multiplicative (M33 a) -> Multiplicative (M33 a)

Semiring a => Semigroup (Multiplicative (M22 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M22 a) -> Multiplicative (M22 a) -> Multiplicative (M22 a)

sconcat :: NonEmpty (Multiplicative (M22 a)) -> Multiplicative (M22 a)

stimes :: Integral b => b -> Multiplicative (M22 a) -> Multiplicative (M22 a)

Semiring a => Semigroup (Multiplicative (M11 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M11 a) -> Multiplicative (M11 a) -> Multiplicative (M11 a)

sconcat :: NonEmpty (Multiplicative (M11 a)) -> Multiplicative (M11 a)

stimes :: Integral b => b -> Multiplicative (M11 a) -> Multiplicative (M11 a)

Monoid (Multiplicative Bool)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Bool

mappend :: Multiplicative Bool -> Multiplicative Bool -> Multiplicative Bool

mconcat :: [Multiplicative Bool] -> Multiplicative Bool

Monoid (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Double

mappend :: Multiplicative Double -> Multiplicative Double -> Multiplicative Double

mconcat :: [Multiplicative Double] -> Multiplicative Double

Monoid (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Float

mappend :: Multiplicative Float -> Multiplicative Float -> Multiplicative Float

mconcat :: [Multiplicative Float] -> Multiplicative Float

(Multiplicative - Monoid) b => Monoid (Multiplicative (a -> b))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (a -> b)

mappend :: Multiplicative (a -> b) -> Multiplicative (a -> b) -> Multiplicative (a -> b)

mconcat :: [Multiplicative (a -> b)] -> Multiplicative (a -> b)

Monoid (Multiplicative Int)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Int

mappend :: Multiplicative Int -> Multiplicative Int -> Multiplicative Int

mconcat :: [Multiplicative Int] -> Multiplicative Int

Monoid (Multiplicative Int8)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Int8

mappend :: Multiplicative Int8 -> Multiplicative Int8 -> Multiplicative Int8

mconcat :: [Multiplicative Int8] -> Multiplicative Int8

Monoid (Multiplicative Int16)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Int16

mappend :: Multiplicative Int16 -> Multiplicative Int16 -> Multiplicative Int16

mconcat :: [Multiplicative Int16] -> Multiplicative Int16

Monoid (Multiplicative Int32)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Int32

mappend :: Multiplicative Int32 -> Multiplicative Int32 -> Multiplicative Int32

mconcat :: [Multiplicative Int32] -> Multiplicative Int32

Monoid (Multiplicative Int64)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Int64

mappend :: Multiplicative Int64 -> Multiplicative Int64 -> Multiplicative Int64

mconcat :: [Multiplicative Int64] -> Multiplicative Int64

Monoid (Multiplicative Integer)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Integer

mappend :: Multiplicative Integer -> Multiplicative Integer -> Multiplicative Integer

mconcat :: [Multiplicative Integer] -> Multiplicative Integer

Monoid (Multiplicative Natural)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Natural

mappend :: Multiplicative Natural -> Multiplicative Natural -> Multiplicative Natural

mconcat :: [Multiplicative Natural] -> Multiplicative Natural

(Additive - Monoid) a => Monoid (Multiplicative [a])

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative [a]

mappend :: Multiplicative [a] -> Multiplicative [a] -> Multiplicative [a]

mconcat :: [Multiplicative [a]] -> Multiplicative [a]

(Multiplicative - Monoid) a => Monoid (Multiplicative (Maybe a))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (Maybe a)

mappend :: Multiplicative (Maybe a) -> Multiplicative (Maybe a) -> Multiplicative (Maybe a)

mconcat :: [Multiplicative (Maybe a)] -> Multiplicative (Maybe a)

(Multiplicative - Monoid) a => Monoid (Multiplicative (Ratio a))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (Ratio a)

mappend :: Multiplicative (Ratio a) -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

mconcat :: [Multiplicative (Ratio a)] -> Multiplicative (Ratio a)

Monoid (Multiplicative Word)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Word

mappend :: Multiplicative Word -> Multiplicative Word -> Multiplicative Word

mconcat :: [Multiplicative Word] -> Multiplicative Word

Monoid (Multiplicative Word8)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Word8

mappend :: Multiplicative Word8 -> Multiplicative Word8 -> Multiplicative Word8

mconcat :: [Multiplicative Word8] -> Multiplicative Word8

Monoid (Multiplicative Word16)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Word16

mappend :: Multiplicative Word16 -> Multiplicative Word16 -> Multiplicative Word16

mconcat :: [Multiplicative Word16] -> Multiplicative Word16

Monoid (Multiplicative Word32)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Word32

mappend :: Multiplicative Word32 -> Multiplicative Word32 -> Multiplicative Word32

mconcat :: [Multiplicative Word32] -> Multiplicative Word32

Monoid (Multiplicative Word64)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Word64

mappend :: Multiplicative Word64 -> Multiplicative Word64 -> Multiplicative Word64

mconcat :: [Multiplicative Word64] -> Multiplicative Word64

Monoid (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative ()

mappend :: Multiplicative () -> Multiplicative () -> Multiplicative ()

mconcat :: [Multiplicative ()] -> Multiplicative ()

((Additive - Group) a, (Multiplicative - Monoid) a) => Monoid (Multiplicative (Complex a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative (Complex a)

mappend :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

mconcat :: [Multiplicative (Complex a)] -> Multiplicative (Complex a)

Monoid (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Uni

mappend :: Multiplicative Uni -> Multiplicative Uni -> Multiplicative Uni

mconcat :: [Multiplicative Uni] -> Multiplicative Uni

Monoid (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Deci

mappend :: Multiplicative Deci -> Multiplicative Deci -> Multiplicative Deci

mconcat :: [Multiplicative Deci] -> Multiplicative Deci

Monoid (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Centi

mappend :: Multiplicative Centi -> Multiplicative Centi -> Multiplicative Centi

mconcat :: [Multiplicative Centi] -> Multiplicative Centi

Monoid (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Milli

mappend :: Multiplicative Milli -> Multiplicative Milli -> Multiplicative Milli

mconcat :: [Multiplicative Milli] -> Multiplicative Milli

Monoid (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Micro

mappend :: Multiplicative Micro -> Multiplicative Micro -> Multiplicative Micro

mconcat :: [Multiplicative Micro] -> Multiplicative Micro

Monoid (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Nano

mappend :: Multiplicative Nano -> Multiplicative Nano -> Multiplicative Nano

mconcat :: [Multiplicative Nano] -> Multiplicative Nano

Monoid (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative Pico

mappend :: Multiplicative Pico -> Multiplicative Pico -> Multiplicative Pico

mconcat :: [Multiplicative Pico] -> Multiplicative Pico

(Additive - Monoid) a => Monoid (Multiplicative (Min a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative (Min a)

mappend :: Multiplicative (Min a) -> Multiplicative (Min a) -> Multiplicative (Min a)

mconcat :: [Multiplicative (Min a)] -> Multiplicative (Min a)

(Multiplicative - Monoid) a => Monoid (Multiplicative (Max a))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (Max a)

mappend :: Multiplicative (Max a) -> Multiplicative (Max a) -> Multiplicative (Max a)

mconcat :: [Multiplicative (Max a)] -> Multiplicative (Max a)

(Multiplicative - Monoid) a => Monoid (Multiplicative (Dual a))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (Dual a)

mappend :: Multiplicative (Dual a) -> Multiplicative (Dual a) -> Multiplicative (Dual a)

mconcat :: [Multiplicative (Dual a)] -> Multiplicative (Dual a)

(Multiplicative - Monoid) a => Monoid (Multiplicative (Down a))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (Down a)

mappend :: Multiplicative (Down a) -> Multiplicative (Down a) -> Multiplicative (Down a)

mconcat :: [Multiplicative (Down a)] -> Multiplicative (Down a)

Monoid (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative CFloat

mappend :: Multiplicative CFloat -> Multiplicative CFloat -> Multiplicative CFloat

mconcat :: [Multiplicative CFloat] -> Multiplicative CFloat

Monoid (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative CDouble

mappend :: Multiplicative CDouble -> Multiplicative CDouble -> Multiplicative CDouble

mconcat :: [Multiplicative CDouble] -> Multiplicative CDouble

(Multiplicative - Monoid) a => Monoid (Multiplicative (IntMap a))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (IntMap a)

mappend :: Multiplicative (IntMap a) -> Multiplicative (IntMap a) -> Multiplicative (IntMap a)

mconcat :: [Multiplicative (IntMap a)] -> Multiplicative (IntMap a)

(Ord k, (Multiplicative - Monoid) k, (Multiplicative - Monoid) a) => Monoid (Multiplicative (Map k a))

Defined in Data.Semigroup.Multiplicative

Methods

mempty :: Multiplicative (Map k a)

mappend :: Multiplicative (Map k a) -> Multiplicative (Map k a) -> Multiplicative (Map k a)

mconcat :: [Multiplicative (Map k a)] -> Multiplicative (Map k a)

Semiring a => Monoid (Multiplicative (M44 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M44 a)

mappend :: Multiplicative (M44 a) -> Multiplicative (M44 a) -> Multiplicative (M44 a)

mconcat :: [Multiplicative (M44 a)] -> Multiplicative (M44 a)

Semiring a => Monoid (Multiplicative (M33 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M33 a)

mappend :: Multiplicative (M33 a) -> Multiplicative (M33 a) -> Multiplicative (M33 a)

mconcat :: [Multiplicative (M33 a)] -> Multiplicative (M33 a)

Semiring a => Monoid (Multiplicative (M22 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M22 a)

mappend :: Multiplicative (M22 a) -> Multiplicative (M22 a) -> Multiplicative (M22 a)

mconcat :: [Multiplicative (M22 a)] -> Multiplicative (M22 a)

Semiring a => Monoid (Multiplicative (M11 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M11 a)

mappend :: Multiplicative (M11 a) -> Multiplicative (M11 a) -> Multiplicative (M11 a)

mconcat :: [Multiplicative (M11 a)] -> Multiplicative (M11 a)

Group (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Double -> Multiplicative Double

greplicate :: Integer -> Multiplicative Double -> Multiplicative Double

Group (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Float -> Multiplicative Float

greplicate :: Integer -> Multiplicative Float -> Multiplicative Float

(Multiplicative - Monoid) a => Group (Multiplicative (Ratio a))

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative (Ratio a) -> Multiplicative (Ratio a)

greplicate :: Integer -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

Group (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative () -> Multiplicative ()

greplicate :: Integer -> Multiplicative () -> Multiplicative ()

((Additive - Group) a, (Multiplicative - Group) a) => Group (Multiplicative (Complex a))

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative (Complex a) -> Multiplicative (Complex a)

greplicate :: Integer -> Multiplicative (Complex a) -> Multiplicative (Complex a)

Group (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Uni -> Multiplicative Uni

greplicate :: Integer -> Multiplicative Uni -> Multiplicative Uni

Group (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Deci -> Multiplicative Deci

greplicate :: Integer -> Multiplicative Deci -> Multiplicative Deci

Group (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Centi -> Multiplicative Centi

greplicate :: Integer -> Multiplicative Centi -> Multiplicative Centi

Group (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Milli -> Multiplicative Milli

greplicate :: Integer -> Multiplicative Milli -> Multiplicative Milli

Group (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Micro -> Multiplicative Micro

greplicate :: Integer -> Multiplicative Micro -> Multiplicative Micro

Group (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Nano -> Multiplicative Nano

greplicate :: Integer -> Multiplicative Nano -> Multiplicative Nano

Group (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Pico -> Multiplicative Pico

greplicate :: Integer -> Multiplicative Pico -> Multiplicative Pico

Group (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative CFloat -> Multiplicative CFloat

greplicate :: Integer -> Multiplicative CFloat -> Multiplicative CFloat

Group (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative CDouble -> Multiplicative CDouble

greplicate :: Integer -> Multiplicative CDouble -> Multiplicative CDouble

Loop (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Double

lreplicate :: Natural -> Multiplicative Double -> Multiplicative Double

Loop (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Float

lreplicate :: Natural -> Multiplicative Float -> Multiplicative Float

(Multiplicative - Monoid) a => Loop (Multiplicative (Ratio a))

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative (Ratio a)

lreplicate :: Natural -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

Loop (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative ()

lreplicate :: Natural -> Multiplicative () -> Multiplicative ()

((Additive - Group) a, (Multiplicative - Group) a) => Loop (Multiplicative (Complex a))

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative (Complex a)

lreplicate :: Natural -> Multiplicative (Complex a) -> Multiplicative (Complex a)

Loop (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Uni

lreplicate :: Natural -> Multiplicative Uni -> Multiplicative Uni

Loop (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Deci

lreplicate :: Natural -> Multiplicative Deci -> Multiplicative Deci

Loop (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Centi

lreplicate :: Natural -> Multiplicative Centi -> Multiplicative Centi

Loop (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Milli

lreplicate :: Natural -> Multiplicative Milli -> Multiplicative Milli

Loop (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Micro

lreplicate :: Natural -> Multiplicative Micro -> Multiplicative Micro

Loop (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Nano

lreplicate :: Natural -> Multiplicative Nano -> Multiplicative Nano

Loop (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Pico

lreplicate :: Natural -> Multiplicative Pico -> Multiplicative Pico

Loop (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative CFloat

lreplicate :: Natural -> Multiplicative CFloat -> Multiplicative CFloat

Loop (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative CDouble

lreplicate :: Natural -> Multiplicative CDouble -> Multiplicative CDouble

Quasigroup (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Double -> Multiplicative Double -> Multiplicative Double

(\\) :: Multiplicative Double -> Multiplicative Double -> Multiplicative Double

Quasigroup (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Float -> Multiplicative Float -> Multiplicative Float

(\\) :: Multiplicative Float -> Multiplicative Float -> Multiplicative Float

(Multiplicative - Monoid) a => Quasigroup (Multiplicative (Ratio a))

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative (Ratio a) -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

(\\) :: Multiplicative (Ratio a) -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

Quasigroup (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative () -> Multiplicative () -> Multiplicative ()

(\\) :: Multiplicative () -> Multiplicative () -> Multiplicative ()

((Additive - Group) a, (Multiplicative - Group) a) => Quasigroup (Multiplicative (Complex a))

Defined in Data.Semigroup.Additive

Methods

(//) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

(\\) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

Quasigroup (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Uni -> Multiplicative Uni -> Multiplicative Uni

(\\) :: Multiplicative Uni -> Multiplicative Uni -> Multiplicative Uni

Quasigroup (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Deci -> Multiplicative Deci -> Multiplicative Deci

(\\) :: Multiplicative Deci -> Multiplicative Deci -> Multiplicative Deci

Quasigroup (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Centi -> Multiplicative Centi -> Multiplicative Centi

(\\) :: Multiplicative Centi -> Multiplicative Centi -> Multiplicative Centi

Quasigroup (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Milli -> Multiplicative Milli -> Multiplicative Milli

(\\) :: Multiplicative Milli -> Multiplicative Milli -> Multiplicative Milli

Quasigroup (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Micro -> Multiplicative Micro -> Multiplicative Micro

(\\) :: Multiplicative Micro -> Multiplicative Micro -> Multiplicative Micro

Quasigroup (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Nano -> Multiplicative Nano -> Multiplicative Nano

(\\) :: Multiplicative Nano -> Multiplicative Nano -> Multiplicative Nano

Quasigroup (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative Pico -> Multiplicative Pico -> Multiplicative Pico

(\\) :: Multiplicative Pico -> Multiplicative Pico -> Multiplicative Pico

Quasigroup (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative CFloat -> Multiplicative CFloat -> Multiplicative CFloat

(\\) :: Multiplicative CFloat -> Multiplicative CFloat -> Multiplicative CFloat

Quasigroup (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

(//) :: Multiplicative CDouble -> Multiplicative CDouble -> Multiplicative CDouble

(\\) :: Multiplicative CDouble -> Multiplicative CDouble -> Multiplicative CDouble

Magma (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Double -> Multiplicative Double -> Multiplicative Double

Magma (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Float -> Multiplicative Float -> Multiplicative Float

(Multiplicative - Monoid) a => Magma (Multiplicative (Ratio a))

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative (Ratio a) -> Multiplicative (Ratio a) -> Multiplicative (Ratio a)

Magma (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative () -> Multiplicative () -> Multiplicative ()

((Additive - Group) a, (Multiplicative - Group) a) => Magma (Multiplicative (Complex a))

Defined in Data.Semigroup.Additive

Methods

(<<) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

Magma (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Uni -> Multiplicative Uni -> Multiplicative Uni

Magma (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Deci -> Multiplicative Deci -> Multiplicative Deci

Magma (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Centi -> Multiplicative Centi -> Multiplicative Centi

Magma (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Milli -> Multiplicative Milli -> Multiplicative Milli

Magma (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Micro -> Multiplicative Micro -> Multiplicative Micro

Magma (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Nano -> Multiplicative Nano -> Multiplicative Nano

Magma (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative Pico -> Multiplicative Pico -> Multiplicative Pico

Magma (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative CFloat -> Multiplicative CFloat -> Multiplicative CFloat

Magma (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

(<<) :: Multiplicative CDouble -> Multiplicative CDouble -> Multiplicative CDouble

type Rep Multiplicative

Defined in Data.Semigroup.Multiplicative

type Rep Multiplicative = ()

type Rep (Multiplicative a)

Defined in Data.Semigroup.Multiplicative

type Rep (Multiplicative a) = D1 (MetaData "Multiplicative" "Data.Semigroup.Multiplicative" "rings-0.0.3.1-DwLnaNEC0zm7jV53dvw3Pn" True) (C1 (MetaCons "Multiplicative" PrefixI True) (S1 (MetaSel (Just "unMultiplicative") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

one :: (Multiplicative - Monoid) a => a

(*) :: (Multiplicative - Semigroup) a => a -> a -> a infixl 7

(/) :: (Multiplicative - Group) a => a -> a -> a infixl 7

(\\) :: (Multiplicative - Group) a => a -> a -> a infixl 7

Left division by a multiplicative group element.

When * is commutative we must have:

 x \\ y = y / x

(^^) :: (Multiplicative - Group) a => a -> Integer -> a infixr 8

Integral power of a multiplicative group element.

 one == a ^^ 0

>>> 8 ^^ 0 :: Double
1.0
>>> 8 ^^ 0 :: Pico
1.000000000000

recip :: (Multiplicative - Group) a => a -> a

Reciprocal of a multiplicative group element.

x / y = x * recip y
x \\ y = recip x * y

>>> recip (3 :+ 4) :: Complex Rational
3 % 25 :+ (-4) % 25
>>> recip (3 :+ 4) :: Complex Double
0.12 :+ (-0.16)
>>> recip (3 :+ 4) :: Complex Pico
0.120000000000 :+ -0.160000000000