Data.Semigroup.Additive

Documentation

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

Hyphenation operator.

newtype Additive a

A commutative Semigroup under +.

Constructors

Additive

Fields

• unAdditive :: a

Instances

Functor Additive

Defined in Data.Semigroup.Additive

Methods

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

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

Applicative Additive

Defined in Data.Semigroup.Additive

Methods

pure :: a -> Additive a

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

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

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

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

Distributive Additive

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Representable Additive

Defined in Data.Semigroup.Additive

Associated Types

type Rep Additive :: Type

Methods

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

index :: Additive a -> Rep Additive -> a

Eq a => Eq (Additive a)

Defined in Data.Semigroup.Additive

Methods

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

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

Ord a => Ord (Additive a)

Defined in Data.Semigroup.Additive

Methods

compare :: Additive a -> Additive a -> Ordering

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

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

(>) :: Additive a -> Additive a -> Bool

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

max :: Additive a -> Additive a -> Additive a

min :: Additive a -> Additive a -> Additive a

Show a => Show (Additive a)

Defined in Data.Semigroup.Additive

Methods

showsPrec :: Int -> Additive a -> ShowS

show :: Additive a -> String

showList :: [Additive a] -> ShowS

Generic (Additive a)

Defined in Data.Semigroup.Additive

Associated Types

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

Methods

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

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

Semigroup (Additive Bool)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Bool -> Additive Bool -> Additive Bool

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

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

Semigroup (Additive Double)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Double -> Additive Double -> Additive Double

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

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

Semigroup (Additive Float)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Float -> Additive Float -> Additive Float

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Int)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int -> Additive Int -> Additive Int

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

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

Semigroup (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int8 -> Additive Int8 -> Additive Int8

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

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

Semigroup (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int16 -> Additive Int16 -> Additive Int16

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

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

Semigroup (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int32 -> Additive Int32 -> Additive Int32

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

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

Semigroup (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int64 -> Additive Int64 -> Additive Int64

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

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

Semigroup (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Integer -> Additive Integer -> Additive Integer

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

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

Semigroup (Additive Natural)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Natural -> Additive Natural -> Additive Natural

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

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

Semigroup (Additive [a])

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Word)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word -> Additive Word -> Additive Word

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

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

Semigroup (Additive Word8)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word8 -> Additive Word8 -> Additive Word8

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

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

Semigroup (Additive Word16)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word16 -> Additive Word16 -> Additive Word16

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

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

Semigroup (Additive Word32)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word32 -> Additive Word32 -> Additive Word32

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

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

Semigroup (Additive Word64)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word64 -> Additive Word64 -> Additive Word64

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive ())

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive () -> Additive () -> Additive ()

sconcat :: NonEmpty (Additive ()) -> Additive ()

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

((Additive - Semigroup) a, (Additive - Semigroup) b, (Additive - Semigroup) c) => Semigroup (Additive (a, b, c))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (a, b, c) -> Additive (a, b, c) -> Additive (a, b, c)

sconcat :: NonEmpty (Additive (a, b, c)) -> Additive (a, b, c)

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

(Additive - Semigroup) a => Semigroup (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Uni -> Additive Uni -> Additive Uni

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

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

Semigroup (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Deci -> Additive Deci -> Additive Deci

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

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

Semigroup (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Centi -> Additive Centi -> Additive Centi

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

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

Semigroup (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Milli -> Additive Milli -> Additive Milli

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

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

Semigroup (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Micro -> Additive Micro -> Additive Micro

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

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

Semigroup (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Nano -> Additive Nano -> Additive Nano

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

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

Semigroup (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Pico -> Additive Pico -> Additive Pico

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive CFloat -> Additive CFloat -> Additive CFloat

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

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

Semigroup (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive CDouble -> Additive CDouble -> Additive CDouble

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

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

Semigroup (Additive (NonEmpty a))

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive IntSet)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive IntSet -> Additive IntSet -> Additive IntSet

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

(Additive - Semigroup) a => Semigroup (Additive (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

(<>) :: Additive (Tran a b c) -> Additive (Tran a b c) -> Additive (Tran a b c)

sconcat :: NonEmpty (Additive (Tran a b c)) -> Additive (Tran a b c)

stimes :: Integral b0 => b0 -> Additive (Tran a b c) -> Additive (Tran a b c)

(Additive - Semigroup) a => Semigroup (Additive (Dual a b))

Defined in Data.Semimodule.Dual

Methods

(<>) :: Additive (Dual a b) -> Additive (Dual a b) -> Additive (Dual a b)

sconcat :: NonEmpty (Additive (Dual a b)) -> Additive (Dual a b)

stimes :: Integral b0 => b0 -> Additive (Dual a b) -> Additive (Dual a b)

(Additive - Semigroup) a => Semigroup (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

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

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

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

(Additive - Semigroup) a => Semigroup (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

sconcat :: NonEmpty (Additive (M43 a)) -> Additive (M43 a)

stimes :: Integral b => b -> Additive (M43 a) -> Additive (M43 a)

(Additive - Semigroup) a => Semigroup (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

sconcat :: NonEmpty (Additive (M42 a)) -> Additive (M42 a)

stimes :: Integral b => b -> Additive (M42 a) -> Additive (M42 a)

(Additive - Semigroup) a => Semigroup (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

sconcat :: NonEmpty (Additive (M34 a)) -> Additive (M34 a)

stimes :: Integral b => b -> Additive (M34 a) -> Additive (M34 a)

(Additive - Semigroup) a => Semigroup (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

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

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

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

(Additive - Semigroup) a => Semigroup (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

sconcat :: NonEmpty (Additive (M32 a)) -> Additive (M32 a)

stimes :: Integral b => b -> Additive (M32 a) -> Additive (M32 a)

(Additive - Semigroup) a => Semigroup (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

sconcat :: NonEmpty (Additive (M24 a)) -> Additive (M24 a)

stimes :: Integral b => b -> Additive (M24 a) -> Additive (M24 a)

(Additive - Semigroup) a => Semigroup (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

sconcat :: NonEmpty (Additive (M23 a)) -> Additive (M23 a)

stimes :: Integral b => b -> Additive (M23 a) -> Additive (M23 a)

(Additive - Semigroup) a => Semigroup (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

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

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

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

(Additive - Semigroup) a => Semigroup (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

sconcat :: NonEmpty (Additive (M41 a)) -> Additive (M41 a)

stimes :: Integral b => b -> Additive (M41 a) -> Additive (M41 a)

(Additive - Semigroup) a => Semigroup (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

sconcat :: NonEmpty (Additive (M31 a)) -> Additive (M31 a)

stimes :: Integral b => b -> Additive (M31 a) -> Additive (M31 a)

(Additive - Semigroup) a => Semigroup (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

sconcat :: NonEmpty (Additive (M21 a)) -> Additive (M21 a)

stimes :: Integral b => b -> Additive (M21 a) -> Additive (M21 a)

(Additive - Semigroup) a => Semigroup (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

sconcat :: NonEmpty (Additive (M14 a)) -> Additive (M14 a)

stimes :: Integral b => b -> Additive (M14 a) -> Additive (M14 a)

(Additive - Semigroup) a => Semigroup (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

sconcat :: NonEmpty (Additive (M13 a)) -> Additive (M13 a)

stimes :: Integral b => b -> Additive (M13 a) -> Additive (M13 a)

(Additive - Semigroup) a => Semigroup (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

sconcat :: NonEmpty (Additive (M12 a)) -> Additive (M12 a)

stimes :: Integral b => b -> Additive (M12 a) -> Additive (M12 a)

(Additive - Semigroup) a => Semigroup (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

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

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

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

(Additive - Semigroup) a => Semigroup (Additive (V4 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

sconcat :: NonEmpty (Additive (V4 a)) -> Additive (V4 a)

stimes :: Integral b => b -> Additive (V4 a) -> Additive (V4 a)

(Additive - Semigroup) a => Semigroup (Additive (V3 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

sconcat :: NonEmpty (Additive (V3 a)) -> Additive (V3 a)

stimes :: Integral b => b -> Additive (V3 a) -> Additive (V3 a)

(Additive - Semigroup) a => Semigroup (Additive (V2 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

sconcat :: NonEmpty (Additive (V2 a)) -> Additive (V2 a)

stimes :: Integral b => b -> Additive (V2 a) -> Additive (V2 a)

(Additive - Semigroup) a => Semigroup (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

sconcat :: NonEmpty (Additive (V1 a)) -> Additive (V1 a)

stimes :: Integral b => b -> Additive (V1 a) -> Additive (V1 a)

Monoid (Additive Bool)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Bool

mappend :: Additive Bool -> Additive Bool -> Additive Bool

mconcat :: [Additive Bool] -> Additive Bool

Monoid (Additive Double)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Double

mappend :: Additive Double -> Additive Double -> Additive Double

mconcat :: [Additive Double] -> Additive Double

Monoid (Additive Float)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Float

mappend :: Additive Float -> Additive Float -> Additive Float

mconcat :: [Additive Float] -> Additive Float

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

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (a -> b)

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

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

Monoid (Additive Int)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int

mappend :: Additive Int -> Additive Int -> Additive Int

mconcat :: [Additive Int] -> Additive Int

Monoid (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int8

mappend :: Additive Int8 -> Additive Int8 -> Additive Int8

mconcat :: [Additive Int8] -> Additive Int8

Monoid (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int16

mappend :: Additive Int16 -> Additive Int16 -> Additive Int16

mconcat :: [Additive Int16] -> Additive Int16

Monoid (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int32

mappend :: Additive Int32 -> Additive Int32 -> Additive Int32

mconcat :: [Additive Int32] -> Additive Int32

Monoid (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int64

mappend :: Additive Int64 -> Additive Int64 -> Additive Int64

mconcat :: [Additive Int64] -> Additive Int64

Monoid (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Integer

mappend :: Additive Integer -> Additive Integer -> Additive Integer

mconcat :: [Additive Integer] -> Additive Integer

Monoid (Additive Natural)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Natural

mappend :: Additive Natural -> Additive Natural -> Additive Natural

mconcat :: [Additive Natural] -> Additive Natural

Monoid (Additive [a])

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive [a]

mappend :: Additive [a] -> Additive [a] -> Additive [a]

mconcat :: [Additive [a]] -> Additive [a]

(Additive - Semigroup) a => Monoid (Additive (Maybe a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Maybe a)

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

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

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

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Ratio a)

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

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

Monoid (Additive Word)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word

mappend :: Additive Word -> Additive Word -> Additive Word

mconcat :: [Additive Word] -> Additive Word

Monoid (Additive Word8)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word8

mappend :: Additive Word8 -> Additive Word8 -> Additive Word8

mconcat :: [Additive Word8] -> Additive Word8

Monoid (Additive Word16)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word16

mappend :: Additive Word16 -> Additive Word16 -> Additive Word16

mconcat :: [Additive Word16] -> Additive Word16

Monoid (Additive Word32)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word32

mappend :: Additive Word32 -> Additive Word32 -> Additive Word32

mconcat :: [Additive Word32] -> Additive Word32

Monoid (Additive Word64)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word64

mappend :: Additive Word64 -> Additive Word64 -> Additive Word64

mconcat :: [Additive Word64] -> Additive Word64

Monoid (Additive ())

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive ()

mappend :: Additive () -> Additive () -> Additive ()

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

((Additive - Monoid) a, (Additive - Monoid) b) => Monoid (Additive (a, b))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (a, b)

mappend :: Additive (a, b) -> Additive (a, b) -> Additive (a, b)

mconcat :: [Additive (a, b)] -> Additive (a, b)

((Additive - Monoid) a, (Additive - Monoid) b, (Additive - Monoid) c) => Monoid (Additive (a, b, c))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (a, b, c)

mappend :: Additive (a, b, c) -> Additive (a, b, c) -> Additive (a, b, c)

mconcat :: [Additive (a, b, c)] -> Additive (a, b, c)

(Additive - Monoid) a => Monoid (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Complex a)

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

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

Monoid (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Uni

mappend :: Additive Uni -> Additive Uni -> Additive Uni

mconcat :: [Additive Uni] -> Additive Uni

Monoid (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Deci

mappend :: Additive Deci -> Additive Deci -> Additive Deci

mconcat :: [Additive Deci] -> Additive Deci

Monoid (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Centi

mappend :: Additive Centi -> Additive Centi -> Additive Centi

mconcat :: [Additive Centi] -> Additive Centi

Monoid (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Milli

mappend :: Additive Milli -> Additive Milli -> Additive Milli

mconcat :: [Additive Milli] -> Additive Milli

Monoid (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Micro

mappend :: Additive Micro -> Additive Micro -> Additive Micro

mconcat :: [Additive Micro] -> Additive Micro

Monoid (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Nano

mappend :: Additive Nano -> Additive Nano -> Additive Nano

mconcat :: [Additive Nano] -> Additive Nano

Monoid (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Pico

mappend :: Additive Pico -> Additive Pico -> Additive Pico

mconcat :: [Additive Pico] -> Additive Pico

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

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Down a)

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

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

Monoid (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive CFloat

mappend :: Additive CFloat -> Additive CFloat -> Additive CFloat

mconcat :: [Additive CFloat] -> Additive CFloat

Monoid (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive CDouble

mappend :: Additive CDouble -> Additive CDouble -> Additive CDouble

mconcat :: [Additive CDouble] -> Additive CDouble

(Additive - Semigroup) a => Monoid (Additive (IntMap a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (IntMap a)

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

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

Monoid (Additive IntSet)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive IntSet

mappend :: Additive IntSet -> Additive IntSet -> Additive IntSet

mconcat :: [Additive IntSet] -> Additive IntSet

(Ord k, (Additive - Semigroup) a) => Monoid (Additive (Map k a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Map k a)

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

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

Ord a => Monoid (Additive (Set a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Set a)

mappend :: Additive (Set a) -> Additive (Set a) -> Additive (Set a)

mconcat :: [Additive (Set a)] -> Additive (Set a)

(Additive - Monoid) a => Monoid (Additive (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

mempty :: Additive (Tran a b c)

mappend :: Additive (Tran a b c) -> Additive (Tran a b c) -> Additive (Tran a b c)

mconcat :: [Additive (Tran a b c)] -> Additive (Tran a b c)

(Additive - Monoid) a => Monoid (Additive (Dual a b))

Defined in Data.Semimodule.Dual

Methods

mempty :: Additive (Dual a b)

mappend :: Additive (Dual a b) -> Additive (Dual a b) -> Additive (Dual a b)

mconcat :: [Additive (Dual a b)] -> Additive (Dual a b)

(Additive - Monoid) a => Monoid (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M44 a)

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

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

(Additive - Monoid) a => Monoid (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M43 a)

mappend :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

mconcat :: [Additive (M43 a)] -> Additive (M43 a)

(Additive - Monoid) a => Monoid (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M42 a)

mappend :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

mconcat :: [Additive (M42 a)] -> Additive (M42 a)

(Additive - Monoid) a => Monoid (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M34 a)

mappend :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

mconcat :: [Additive (M34 a)] -> Additive (M34 a)

(Additive - Monoid) a => Monoid (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M33 a)

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

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

(Additive - Monoid) a => Monoid (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M32 a)

mappend :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

mconcat :: [Additive (M32 a)] -> Additive (M32 a)

(Additive - Monoid) a => Monoid (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M24 a)

mappend :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

mconcat :: [Additive (M24 a)] -> Additive (M24 a)

(Additive - Monoid) a => Monoid (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M23 a)

mappend :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

mconcat :: [Additive (M23 a)] -> Additive (M23 a)

(Additive - Monoid) a => Monoid (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M22 a)

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

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

(Additive - Monoid) a => Monoid (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M41 a)

mappend :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

mconcat :: [Additive (M41 a)] -> Additive (M41 a)

(Additive - Monoid) a => Monoid (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M31 a)

mappend :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

mconcat :: [Additive (M31 a)] -> Additive (M31 a)

(Additive - Monoid) a => Monoid (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M21 a)

mappend :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

mconcat :: [Additive (M21 a)] -> Additive (M21 a)

(Additive - Monoid) a => Monoid (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M14 a)

mappend :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

mconcat :: [Additive (M14 a)] -> Additive (M14 a)

(Additive - Monoid) a => Monoid (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M13 a)

mappend :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

mconcat :: [Additive (M13 a)] -> Additive (M13 a)

(Additive - Monoid) a => Monoid (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M12 a)

mappend :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

mconcat :: [Additive (M12 a)] -> Additive (M12 a)

(Additive - Monoid) a => Monoid (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M11 a)

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

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

(Additive - Monoid) a => Monoid (Additive (V4 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (V4 a)

mappend :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

mconcat :: [Additive (V4 a)] -> Additive (V4 a)

(Additive - Monoid) a => Monoid (Additive (V3 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (V3 a)

mappend :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

mconcat :: [Additive (V3 a)] -> Additive (V3 a)

(Additive - Monoid) a => Monoid (Additive (V2 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (V2 a)

mappend :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

mconcat :: [Additive (V2 a)] -> Additive (V2 a)

(Additive - Monoid) a => Monoid (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (V1 a)

mappend :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

mconcat :: [Additive (V1 a)] -> Additive (V1 a)

Group (Additive Double)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Double -> Additive Double

greplicate :: Integer -> Additive Double -> Additive Double

Group (Additive Float)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Float -> Additive Float

greplicate :: Integer -> Additive Float -> Additive Float

(Additive - Group) b => Group (Additive (a -> b))

Defined in Data.Semigroup.Additive

Methods

inv :: Additive (a -> b) -> Additive (a -> b)

greplicate :: Integer -> Additive (a -> b) -> Additive (a -> b)

Group (Additive Int)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int -> Additive Int

greplicate :: Integer -> Additive Int -> Additive Int

Group (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int8 -> Additive Int8

greplicate :: Integer -> Additive Int8 -> Additive Int8

Group (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int16 -> Additive Int16

greplicate :: Integer -> Additive Int16 -> Additive Int16

Group (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int32 -> Additive Int32

greplicate :: Integer -> Additive Int32 -> Additive Int32

Group (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int64 -> Additive Int64

greplicate :: Integer -> Additive Int64 -> Additive Int64

Group (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Integer -> Additive Integer

greplicate :: Integer -> Additive Integer -> Additive Integer

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

Defined in Data.Semigroup.Additive

Methods

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

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

Group (Additive ())

Defined in Data.Semigroup.Additive

Methods

inv :: Additive () -> Additive ()

greplicate :: Integer -> Additive () -> Additive ()

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

Defined in Data.Semigroup.Additive

Methods

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

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

Group (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Uni -> Additive Uni

greplicate :: Integer -> Additive Uni -> Additive Uni

Group (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Deci -> Additive Deci

greplicate :: Integer -> Additive Deci -> Additive Deci

Group (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Centi -> Additive Centi

greplicate :: Integer -> Additive Centi -> Additive Centi

Group (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Milli -> Additive Milli

greplicate :: Integer -> Additive Milli -> Additive Milli

Group (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Micro -> Additive Micro

greplicate :: Integer -> Additive Micro -> Additive Micro

Group (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Nano -> Additive Nano

greplicate :: Integer -> Additive Nano -> Additive Nano

Group (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Pico -> Additive Pico

greplicate :: Integer -> Additive Pico -> Additive Pico

Group (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive CFloat -> Additive CFloat

greplicate :: Integer -> Additive CFloat -> Additive CFloat

Group (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive CDouble -> Additive CDouble

greplicate :: Integer -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Group (Additive (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

inv :: Additive (Tran a b c) -> Additive (Tran a b c)

greplicate :: Integer -> Additive (Tran a b c) -> Additive (Tran a b c)

(Additive - Group) a => Group (Additive (Dual a b))

Defined in Data.Semimodule.Dual

Methods

inv :: Additive (Dual a b) -> Additive (Dual a b)

greplicate :: Integer -> Additive (Dual a b) -> Additive (Dual a b)

(Additive - Group) a => Group (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M44 a) -> Additive (M44 a)

greplicate :: Integer -> Additive (M44 a) -> Additive (M44 a)

(Additive - Group) a => Group (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M43 a) -> Additive (M43 a)

greplicate :: Integer -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Group (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M42 a) -> Additive (M42 a)

greplicate :: Integer -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Group (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M34 a) -> Additive (M34 a)

greplicate :: Integer -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Group (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M33 a) -> Additive (M33 a)

greplicate :: Integer -> Additive (M33 a) -> Additive (M33 a)

(Additive - Group) a => Group (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M32 a) -> Additive (M32 a)

greplicate :: Integer -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Group (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M24 a) -> Additive (M24 a)

greplicate :: Integer -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Group (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M23 a) -> Additive (M23 a)

greplicate :: Integer -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Group (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M22 a) -> Additive (M22 a)

greplicate :: Integer -> Additive (M22 a) -> Additive (M22 a)

(Additive - Group) a => Group (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M41 a) -> Additive (M41 a)

greplicate :: Integer -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Group (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M31 a) -> Additive (M31 a)

greplicate :: Integer -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Group (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M21 a) -> Additive (M21 a)

greplicate :: Integer -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Group (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M14 a) -> Additive (M14 a)

greplicate :: Integer -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Group (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M13 a) -> Additive (M13 a)

greplicate :: Integer -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Group (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M12 a) -> Additive (M12 a)

greplicate :: Integer -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Group (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M11 a) -> Additive (M11 a)

greplicate :: Integer -> Additive (M11 a) -> Additive (M11 a)

(Additive - Group) a => Group (Additive (V4 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (V4 a) -> Additive (V4 a)

greplicate :: Integer -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Group (Additive (V3 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (V3 a) -> Additive (V3 a)

greplicate :: Integer -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Group (Additive (V2 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (V2 a) -> Additive (V2 a)

greplicate :: Integer -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Group (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (V1 a) -> Additive (V1 a)

greplicate :: Integer -> Additive (V1 a) -> Additive (V1 a)

Loop (Additive Double)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Double

lreplicate :: Natural -> Additive Double -> Additive Double

Loop (Additive Float)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Float

lreplicate :: Natural -> Additive Float -> Additive Float

(Additive - Group) b => Loop (Additive (a -> b))

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive (a -> b)

lreplicate :: Natural -> Additive (a -> b) -> Additive (a -> b)

Loop (Additive Int)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int

lreplicate :: Natural -> Additive Int -> Additive Int

Loop (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int8

lreplicate :: Natural -> Additive Int8 -> Additive Int8

Loop (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int16

lreplicate :: Natural -> Additive Int16 -> Additive Int16

Loop (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int32

lreplicate :: Natural -> Additive Int32 -> Additive Int32

Loop (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int64

lreplicate :: Natural -> Additive Int64 -> Additive Int64

Loop (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Integer

lreplicate :: Natural -> Additive Integer -> Additive Integer

((Additive - Group) a, (Multiplicative - Monoid) a) => Loop (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive (Ratio a)

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

Loop (Additive ())

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive ()

lreplicate :: Natural -> Additive () -> Additive ()

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

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive (Complex a)

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

Loop (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Uni

lreplicate :: Natural -> Additive Uni -> Additive Uni

Loop (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Deci

lreplicate :: Natural -> Additive Deci -> Additive Deci

Loop (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Centi

lreplicate :: Natural -> Additive Centi -> Additive Centi

Loop (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Milli

lreplicate :: Natural -> Additive Milli -> Additive Milli

Loop (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Micro

lreplicate :: Natural -> Additive Micro -> Additive Micro

Loop (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Nano

lreplicate :: Natural -> Additive Nano -> Additive Nano

Loop (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Pico

lreplicate :: Natural -> Additive Pico -> Additive Pico

Loop (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive CFloat

lreplicate :: Natural -> Additive CFloat -> Additive CFloat

Loop (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive CDouble

lreplicate :: Natural -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Loop (Additive (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

lempty :: Additive (Tran a b c)

lreplicate :: Natural -> Additive (Tran a b c) -> Additive (Tran a b c)

(Additive - Group) a => Loop (Additive (Dual a b))

Defined in Data.Semimodule.Dual

Methods

lempty :: Additive (Dual a b)

lreplicate :: Natural -> Additive (Dual a b) -> Additive (Dual a b)

(Additive - Group) a => Loop (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M44 a)

lreplicate :: Natural -> Additive (M44 a) -> Additive (M44 a)

(Additive - Group) a => Loop (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M43 a)

lreplicate :: Natural -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Loop (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M42 a)

lreplicate :: Natural -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Loop (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M34 a)

lreplicate :: Natural -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Loop (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M33 a)

lreplicate :: Natural -> Additive (M33 a) -> Additive (M33 a)

(Additive - Group) a => Loop (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M32 a)

lreplicate :: Natural -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Loop (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M24 a)

lreplicate :: Natural -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Loop (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M23 a)

lreplicate :: Natural -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Loop (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M22 a)

lreplicate :: Natural -> Additive (M22 a) -> Additive (M22 a)

(Additive - Group) a => Loop (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M41 a)

lreplicate :: Natural -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Loop (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M31 a)

lreplicate :: Natural -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Loop (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M21 a)

lreplicate :: Natural -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Loop (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M14 a)

lreplicate :: Natural -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Loop (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M13 a)

lreplicate :: Natural -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Loop (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M12 a)

lreplicate :: Natural -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Loop (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M11 a)

lreplicate :: Natural -> Additive (M11 a) -> Additive (M11 a)

(Additive - Group) a => Loop (Additive (V4 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V4 a)

lreplicate :: Natural -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Loop (Additive (V3 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V3 a)

lreplicate :: Natural -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Loop (Additive (V2 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V2 a)

lreplicate :: Natural -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Loop (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V1 a)

lreplicate :: Natural -> Additive (V1 a) -> Additive (V1 a)

Quasigroup (Additive Double)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Double -> Additive Double -> Additive Double

(\\) :: Additive Double -> Additive Double -> Additive Double

Quasigroup (Additive Float)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Float -> Additive Float -> Additive Float

(\\) :: Additive Float -> Additive Float -> Additive Float

(Additive - Group) b => Quasigroup (Additive (a -> b))

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive (a -> b) -> Additive (a -> b) -> Additive (a -> b)

(\\) :: Additive (a -> b) -> Additive (a -> b) -> Additive (a -> b)

Quasigroup (Additive Int)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int -> Additive Int -> Additive Int

(\\) :: Additive Int -> Additive Int -> Additive Int

Quasigroup (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int8 -> Additive Int8 -> Additive Int8

(\\) :: Additive Int8 -> Additive Int8 -> Additive Int8

Quasigroup (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int16 -> Additive Int16 -> Additive Int16

(\\) :: Additive Int16 -> Additive Int16 -> Additive Int16

Quasigroup (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int32 -> Additive Int32 -> Additive Int32

(\\) :: Additive Int32 -> Additive Int32 -> Additive Int32

Quasigroup (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int64 -> Additive Int64 -> Additive Int64

(\\) :: Additive Int64 -> Additive Int64 -> Additive Int64

Quasigroup (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Integer -> Additive Integer -> Additive Integer

(\\) :: Additive Integer -> Additive Integer -> Additive Integer

((Additive - Group) a, (Multiplicative - Monoid) a) => Quasigroup (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive ())

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive () -> Additive () -> Additive ()

(\\) :: Additive () -> Additive () -> Additive ()

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

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Uni -> Additive Uni -> Additive Uni

(\\) :: Additive Uni -> Additive Uni -> Additive Uni

Quasigroup (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Deci -> Additive Deci -> Additive Deci

(\\) :: Additive Deci -> Additive Deci -> Additive Deci

Quasigroup (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Centi -> Additive Centi -> Additive Centi

(\\) :: Additive Centi -> Additive Centi -> Additive Centi

Quasigroup (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Milli -> Additive Milli -> Additive Milli

(\\) :: Additive Milli -> Additive Milli -> Additive Milli

Quasigroup (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Micro -> Additive Micro -> Additive Micro

(\\) :: Additive Micro -> Additive Micro -> Additive Micro

Quasigroup (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Nano -> Additive Nano -> Additive Nano

(\\) :: Additive Nano -> Additive Nano -> Additive Nano

Quasigroup (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Pico -> Additive Pico -> Additive Pico

(\\) :: Additive Pico -> Additive Pico -> Additive Pico

Quasigroup (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive CFloat -> Additive CFloat -> Additive CFloat

(\\) :: Additive CFloat -> Additive CFloat -> Additive CFloat

Quasigroup (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive CDouble -> Additive CDouble -> Additive CDouble

(\\) :: Additive CDouble -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Quasigroup (Additive (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

(//) :: Additive (Tran a b c) -> Additive (Tran a b c) -> Additive (Tran a b c)

(\\) :: Additive (Tran a b c) -> Additive (Tran a b c) -> Additive (Tran a b c)

(Additive - Group) a => Quasigroup (Additive (Dual a b))

Defined in Data.Semimodule.Dual

Methods

(//) :: Additive (Dual a b) -> Additive (Dual a b) -> Additive (Dual a b)

(\\) :: Additive (Dual a b) -> Additive (Dual a b) -> Additive (Dual a b)

(Additive - Group) a => Quasigroup (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M44 a) -> Additive (M44 a) -> Additive (M44 a)

(\\) :: Additive (M44 a) -> Additive (M44 a) -> Additive (M44 a)

(Additive - Group) a => Quasigroup (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(\\) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Quasigroup (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(\\) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Quasigroup (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(\\) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Quasigroup (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M33 a) -> Additive (M33 a) -> Additive (M33 a)

(\\) :: Additive (M33 a) -> Additive (M33 a) -> Additive (M33 a)

(Additive - Group) a => Quasigroup (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(\\) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Quasigroup (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(\\) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Quasigroup (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(\\) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Quasigroup (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M22 a) -> Additive (M22 a) -> Additive (M22 a)

(\\) :: Additive (M22 a) -> Additive (M22 a) -> Additive (M22 a)

(Additive - Group) a => Quasigroup (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(\\) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Quasigroup (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(\\) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Quasigroup (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(\\) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Quasigroup (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

(\\) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Quasigroup (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

(\\) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Quasigroup (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

(\\) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Quasigroup (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M11 a) -> Additive (M11 a) -> Additive (M11 a)

(\\) :: Additive (M11 a) -> Additive (M11 a) -> Additive (M11 a)

(Additive - Group) a => Quasigroup (Additive (V4 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(\\) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Quasigroup (Additive (V3 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

(\\) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Quasigroup (Additive (V2 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(\\) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Quasigroup (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

(\\) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

Magma (Additive Double)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Double -> Additive Double -> Additive Double

Magma (Additive Float)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Float -> Additive Float -> Additive Float

(Additive - Group) b => Magma (Additive (a -> b))

Defined in Data.Semigroup.Additive

Methods

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

Magma (Additive Int)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int -> Additive Int -> Additive Int

Magma (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int8 -> Additive Int8 -> Additive Int8

Magma (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int16 -> Additive Int16 -> Additive Int16

Magma (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int32 -> Additive Int32 -> Additive Int32

Magma (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int64 -> Additive Int64 -> Additive Int64

Magma (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Integer -> Additive Integer -> Additive Integer

((Additive - Group) a, (Multiplicative - Monoid) a) => Magma (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

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

Magma (Additive ())

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive () -> Additive () -> Additive ()

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

Defined in Data.Semigroup.Additive

Methods

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

Magma (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Uni -> Additive Uni -> Additive Uni

Magma (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Deci -> Additive Deci -> Additive Deci

Magma (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Centi -> Additive Centi -> Additive Centi

Magma (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Milli -> Additive Milli -> Additive Milli

Magma (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Micro -> Additive Micro -> Additive Micro

Magma (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Nano -> Additive Nano -> Additive Nano

Magma (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Pico -> Additive Pico -> Additive Pico

Magma (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive CFloat -> Additive CFloat -> Additive CFloat

Magma (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive CDouble -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Magma (Additive (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

(<<) :: Additive (Tran a b c) -> Additive (Tran a b c) -> Additive (Tran a b c)

(Additive - Group) a => Magma (Additive (Dual a b))

Defined in Data.Semimodule.Dual

Methods

(<<) :: Additive (Dual a b) -> Additive (Dual a b) -> Additive (Dual a b)

(Additive - Group) a => Magma (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

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

(Additive - Group) a => Magma (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Magma (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Magma (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Magma (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

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

(Additive - Group) a => Magma (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Magma (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Magma (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Magma (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

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

(Additive - Group) a => Magma (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Magma (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Magma (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Magma (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Magma (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Magma (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Magma (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

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

(Additive - Group) a => Magma (Additive (V4 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Magma (Additive (V3 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Magma (Additive (V2 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Magma (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

type Rep Additive

Defined in Data.Semigroup.Additive

type Rep Additive = ()

type Rep (Additive a)

Defined in Data.Semigroup.Additive

type Rep (Additive a) = D1 (MetaData "Additive" "Data.Semigroup.Additive" "rings-0.1.2-5cupeQ1NQKcKNC2Ls8OsAI" True) (C1 (MetaCons "Additive" PrefixI True) (S1 (MetaSel (Just "unAdditive") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

zero :: (Additive - Monoid) a => a

Additive unit of a semiring.

(+) :: (Additive - Semigroup) a => a -> a -> a infixl 6

Additive semigroup operation on a semiring.

>>> Dual [2] + Dual [3] :: Dual [Int]
Dual {getDual = [3,2]}

subtract :: (Additive - Group) a => a -> a -> a

Subtract two elements.

newtype Multiplicative a

A (potentially non-commutative) Semigroup under *.

Constructors

Multiplicative

Fields

• unMultiplicative :: a

Instances

Functor Multiplicative

Defined in Data.Semigroup.Additive

Methods

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

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

Applicative Multiplicative

Defined in Data.Semigroup.Additive

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.Additive

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.Additive

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.Additive

Methods

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

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

Ord a => Ord (Multiplicative a)

Defined in Data.Semigroup.Additive

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.Additive

Methods

showsPrec :: Int -> Multiplicative a -> ShowS

show :: Multiplicative a -> String

showList :: [Multiplicative a] -> ShowS

Generic (Multiplicative a)

Defined in Data.Semigroup.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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.Additive

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)

Coalgebra a c => Semigroup (Multiplicative (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

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

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

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

Coalgebra a b => Semigroup (Multiplicative (Dual a b))

Defined in Data.Semimodule.Dual

Methods

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

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

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

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.Additive

Methods

mempty :: Multiplicative Bool

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

mconcat :: [Multiplicative Bool] -> Multiplicative Bool

Monoid (Multiplicative Double)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Double

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

mconcat :: [Multiplicative Double] -> Multiplicative Double

Monoid (Multiplicative Float)

Defined in Data.Semigroup.Additive

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.Additive

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.Additive

Methods

mempty :: Multiplicative Int

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

mconcat :: [Multiplicative Int] -> Multiplicative Int

Monoid (Multiplicative Int8)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Int8

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

mconcat :: [Multiplicative Int8] -> Multiplicative Int8

Monoid (Multiplicative Int16)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Int16

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

mconcat :: [Multiplicative Int16] -> Multiplicative Int16

Monoid (Multiplicative Int32)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Int32

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

mconcat :: [Multiplicative Int32] -> Multiplicative Int32

Monoid (Multiplicative Int64)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Int64

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

mconcat :: [Multiplicative Int64] -> Multiplicative Int64

Monoid (Multiplicative Integer)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Integer

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

mconcat :: [Multiplicative Integer] -> Multiplicative Integer

Monoid (Multiplicative Natural)

Defined in Data.Semigroup.Additive

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.Additive

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.Additive

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.Additive

Methods

mempty :: Multiplicative Word

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

mconcat :: [Multiplicative Word] -> Multiplicative Word

Monoid (Multiplicative Word8)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Word8

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

mconcat :: [Multiplicative Word8] -> Multiplicative Word8

Monoid (Multiplicative Word16)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Word16

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

mconcat :: [Multiplicative Word16] -> Multiplicative Word16

Monoid (Multiplicative Word32)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Word32

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

mconcat :: [Multiplicative Word32] -> Multiplicative Word32

Monoid (Multiplicative Word64)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Word64

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

mconcat :: [Multiplicative Word64] -> Multiplicative Word64

Monoid (Multiplicative ())

Defined in Data.Semigroup.Additive

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.Additive

Methods

mempty :: Multiplicative Uni

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

mconcat :: [Multiplicative Uni] -> Multiplicative Uni

Monoid (Multiplicative Deci)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Deci

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

mconcat :: [Multiplicative Deci] -> Multiplicative Deci

Monoid (Multiplicative Centi)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Centi

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

mconcat :: [Multiplicative Centi] -> Multiplicative Centi

Monoid (Multiplicative Milli)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Milli

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

mconcat :: [Multiplicative Milli] -> Multiplicative Milli

Monoid (Multiplicative Micro)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Micro

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

mconcat :: [Multiplicative Micro] -> Multiplicative Micro

Monoid (Multiplicative Nano)

Defined in Data.Semigroup.Additive

Methods

mempty :: Multiplicative Nano

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

mconcat :: [Multiplicative Nano] -> Multiplicative Nano

Monoid (Multiplicative Pico)

Defined in Data.Semigroup.Additive

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.Additive

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.Additive

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.Additive

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.Additive

Methods

mempty :: Multiplicative CFloat

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

mconcat :: [Multiplicative CFloat] -> Multiplicative CFloat

Monoid (Multiplicative CDouble)

Defined in Data.Semigroup.Additive

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.Additive

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.Additive

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)

Counital a c => Monoid (Multiplicative (Tran a b c))

Defined in Data.Semimodule.Algebra

Methods

mempty :: Multiplicative (Tran a b c)

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

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

Counital a b => Monoid (Multiplicative (Dual a b))

Defined in Data.Semimodule.Dual

Methods

mempty :: Multiplicative (Dual a b)

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

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

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.Additive

Methods

inv :: Multiplicative Double -> Multiplicative Double

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

Group (Multiplicative Float)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative Float -> Multiplicative Float

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

Group (Multiplicative ())

Defined in Data.Semigroup.Additive

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.Additive

Methods

inv :: Multiplicative Uni -> Multiplicative Uni

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

Group (Multiplicative Deci)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative Deci -> Multiplicative Deci

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

Group (Multiplicative Centi)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative Centi -> Multiplicative Centi

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

Group (Multiplicative Milli)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative Milli -> Multiplicative Milli

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

Group (Multiplicative Micro)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative Micro -> Multiplicative Micro

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

Group (Multiplicative Nano)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative Nano -> Multiplicative Nano

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

Group (Multiplicative Pico)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative Pico -> Multiplicative Pico

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

Group (Multiplicative CFloat)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative CFloat -> Multiplicative CFloat

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

Group (Multiplicative CDouble)

Defined in Data.Semigroup.Additive

Methods

inv :: Multiplicative CDouble -> Multiplicative CDouble

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

Loop (Multiplicative Double)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Double

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

Loop (Multiplicative Float)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Float

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

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

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative (Ratio a)

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

Loop (Multiplicative ())

Defined in Data.Semigroup.Additive

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.Additive

Methods

lempty :: Multiplicative Uni

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

Loop (Multiplicative Deci)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Deci

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

Loop (Multiplicative Centi)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Centi

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

Loop (Multiplicative Milli)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Milli

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

Loop (Multiplicative Micro)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Micro

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

Loop (Multiplicative Nano)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Nano

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

Loop (Multiplicative Pico)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative Pico

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

Loop (Multiplicative CFloat)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative CFloat

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

Loop (Multiplicative CDouble)

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative CDouble

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

Quasigroup (Multiplicative Double)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative Float)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Defined in Data.Semigroup.Additive

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.Additive

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.Additive

Methods

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

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

Quasigroup (Multiplicative Deci)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative Centi)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative Milli)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative Micro)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative Nano)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative Pico)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative CFloat)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative CDouble)

Defined in Data.Semigroup.Additive

Methods

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

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

Magma (Multiplicative Double)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative Float)

Defined in Data.Semigroup.Additive

Methods

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

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

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative ())

Defined in Data.Semigroup.Additive

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.Additive

Methods

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

Magma (Multiplicative Deci)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative Centi)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative Milli)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative Micro)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative Nano)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative Pico)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative CFloat)

Defined in Data.Semigroup.Additive

Methods

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

Magma (Multiplicative CDouble)

Defined in Data.Semigroup.Additive

Methods

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

type Rep Multiplicative

Defined in Data.Semigroup.Additive

type Rep Multiplicative = ()

type Rep (Multiplicative a)

Defined in Data.Semigroup.Additive

type Rep (Multiplicative a) = D1 (MetaData "Multiplicative" "Data.Semigroup.Additive" "rings-0.1.2-5cupeQ1NQKcKNC2Ls8OsAI" True) (C1 (MetaCons "Multiplicative" PrefixI True) (S1 (MetaSel (Just "unMultiplicative") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

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

Multiplicative unit of a semiring.

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

Multiplicative semigroup operation on a semiring.

>>> Dual [2] * Dual [3] :: Dual [Int]
Dual {getDual = [5]}

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

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

Right division by a multiplicative group element.

(\\) :: (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