Data.Semiring

Types

type (-) g f a = f (g a) infixl 6

Hyphenation operator.

type (**) f g = Compose f g infixr 2

Tensor product.

type (++) f g = Product f g infixr 1

Direct sum.

type Free = Representable

Presemirings

type PresemiringLaw a = ((Additive - Semigroup) a, (Multiplicative - Semigroup) a)

class PresemiringLaw a => Presemiring a

Right pre-semirings. and (non-unital and unital) right semirings.

A right pre-semiring (sometimes referred to as a bisemigroup) is a type R endowed with two associative binary (i.e. semigroup) operations: + and *, along with a right-distributivity property connecting them:

Distributivity

(a + b) * c = (a * c) + (b * c)

Note that addition and multiplication needn't be commutative.

See the properties module for a detailed specification of the laws.

Instances

Presemiring Bool

Defined in Data.Semiring

Presemiring Double

Defined in Data.Semiring

Presemiring Float

Defined in Data.Semiring

Presemiring Int

Defined in Data.Semiring

Presemiring Int8

Defined in Data.Semiring

Presemiring Int16

Defined in Data.Semiring

Presemiring Int32

Defined in Data.Semiring

Presemiring Int64

Defined in Data.Semiring

Presemiring Integer

Defined in Data.Semiring

Presemiring Natural

Defined in Data.Semiring

Presemiring Word

Defined in Data.Semiring

Presemiring Word8

Defined in Data.Semiring

Presemiring Word16

Defined in Data.Semiring

Presemiring Word32

Defined in Data.Semiring

Presemiring Word64

Defined in Data.Semiring

Presemiring ()

Defined in Data.Semiring

Presemiring Uni

Defined in Data.Semiring

Presemiring Deci

Defined in Data.Semiring

Presemiring Centi

Defined in Data.Semiring

Presemiring Milli

Defined in Data.Semiring

Presemiring Micro

Defined in Data.Semiring

Presemiring Nano

Defined in Data.Semiring

Presemiring Pico

Defined in Data.Semiring

Presemiring CFloat

Defined in Data.Semiring

Presemiring CDouble

Defined in Data.Semiring

Presemiring IntSet

Defined in Data.Semiring

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

Defined in Data.Semiring

Presemiring a => Presemiring (Maybe a)

Defined in Data.Semiring

Presemiring (Ratio Integer)

Defined in Data.Semiring

Presemiring (Ratio Natural)

Defined in Data.Semiring

Ring a => Presemiring (Complex a)

Defined in Data.Semiring

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

Defined in Data.Semiring

Presemiring a => Presemiring (IntMap a)

Defined in Data.Semiring

Ord a => Presemiring (Set a)

Defined in Data.Semiring

Semiring a => Presemiring (M44 a)

Defined in Data.Semimodule.Finite

Semiring a => Presemiring (M33 a)

Defined in Data.Semimodule.Finite

Semiring a => Presemiring (M22 a)

Defined in Data.Semimodule.Finite

Semiring a => Presemiring (M11 a)

Defined in Data.Semimodule.Finite

Presemiring a => Presemiring (e -> a)

Defined in Data.Semiring

(Presemiring a, Presemiring b) => Presemiring (Either a b)

Defined in Data.Semiring

(Ord k, Presemiring a) => Presemiring (Map k a)

Defined in Data.Semiring

Presemiring a => Presemiring (End a b)

Defined in Data.Semimodule.Free

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

Additive semigroup operation on a semiring.

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

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

Multiplicative semigroup operation on a semiring.

>>> Dual [2] * Dual [3] :: Dual [Int]
Dual {getDual = [5]}

Presemiring folds

sum1 :: (Additive - Semigroup) a => Foldable1 f => f a -> a

Evaluate a non-empty presemiring sum.

sumWith1 :: (Additive - Semigroup) a => Foldable1 t => (b -> a) -> t b -> a

Evaluate a non-empty presemiring sum using a given presemiring.

>>> evalWith1 Max $ (1 :| [2..5 :: Int]) :| [1 :| [2..5 :: Int]]
| Fold over a non-empty collection using the additive operation of an arbitrary semiring.

>>> sumWith1 First $ (1 :| [2..5 :: Int]) * (1 :| [2..5 :: Int])
First {getFirst = 1}
>>> sumWith1 First $ Nothing :| [Just (5 :: Int), Just 6,  Nothing]
First {getFirst = Nothing}
>>> sumWith1 Just $ 1 :| [2..5 :: Int]
Just 15

product1 :: (Multiplicative - Semigroup) a => Foldable1 f => f a -> a

Evaluate a non-empty presemiring product.

productWith1 :: (Multiplicative - Semigroup) a => Foldable1 t => (b -> a) -> t b -> a

Evaluate a non-empty presemiring product using a given presemiring.

As the collection is non-empty this does not require a distinct multiplicative unit:

>>> productWith1 Just $ 1 :| [2..5 :: Int]
Just 120
>>> productWith1 First $ 1 :| [2..(5 :: Int)]
First {getFirst = 15}
>>> productWith1 First $ Nothing :| [Just (5 :: Int), Just 6,  Nothing]
First {getFirst = Just 11}

xmult1 :: Presemiring a => Foldable1 f => Apply f => f a -> f a -> a

Cross-multiply two non-empty collections.

>>> xmult1 (Right 2 :| [Left "oops"]) (Right 2 :| [Right 3]) :: Either [Char] Int
Right 4

eval1 :: Presemiring a => Functor f => Foldable1 f => Foldable1 g => f (g a) -> a

Evaluate a presemiring expression.

evalWith1 :: Presemiring r => Functor f => Functor g => Foldable1 f => Foldable1 g => (a -> r) -> f (g a) -> r

Evaluate a presemiring expression using a given presemiring.

>>> evalWith1 (Max . Down) $ (1 :| [2..5 :: Int]) :| [-5 :| [2..5 :: Int]]
Max {getMax = Down 9}
>>> evalWith1 Max $ (1 :| [2..5 :: Int]) :| [-5 :| [2..5 :: Int]]
Max {getMax = 15}

Semirings

type SemiringLaw a = ((Additive - Monoid) a, (Multiplicative - Monoid) a)

class (Presemiring a, SemiringLaw a) => Semiring a

Right semirings.

A right semiring is a pre-semiring with two distinct neutral elements, zero and one, such that zero is right-neutral wrt addition, one is right-neutral wrt multiplication, and zero is right-annihilative wrt multiplication.

Neutrality

zero + r = r
one * r = r

Absorbtion

zero * a = zero

Instances

Semiring Bool

Defined in Data.Semiring

Semiring Double

Defined in Data.Semiring

Semiring Float

Defined in Data.Semiring

Semiring Int

Defined in Data.Semiring

Semiring Int8

Defined in Data.Semiring

Semiring Int16

Defined in Data.Semiring

Semiring Int32

Defined in Data.Semiring

Semiring Int64

Defined in Data.Semiring

Semiring Integer

Defined in Data.Semiring

Semiring Natural

Defined in Data.Semiring

Semiring Word

Defined in Data.Semiring

Semiring Word8

Defined in Data.Semiring

Semiring Word16

Defined in Data.Semiring

Semiring Word32

Defined in Data.Semiring

Semiring Word64

Defined in Data.Semiring

Semiring ()

Defined in Data.Semiring

Semiring Uni

Defined in Data.Semiring

Semiring Deci

Defined in Data.Semiring

Semiring Centi

Defined in Data.Semiring

Semiring Milli

Defined in Data.Semiring

Semiring Micro

Defined in Data.Semiring

Semiring Nano

Defined in Data.Semiring

Semiring Pico

Defined in Data.Semiring

Semiring CFloat

Defined in Data.Semiring

Semiring CDouble

Defined in Data.Semiring

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

Defined in Data.Semiring

Semiring a => Semiring (Maybe a)

Defined in Data.Semiring

Semiring (Ratio Integer)

Defined in Data.Semiring

Semiring (Ratio Natural)

Defined in Data.Semiring

Semiring a => Semiring (IntMap a)

Defined in Data.Semiring

Semiring a => Semiring (M44 a)

Defined in Data.Semimodule.Finite

Semiring a => Semiring (M33 a)

Defined in Data.Semimodule.Finite

Semiring a => Semiring (M22 a)

Defined in Data.Semimodule.Finite

Semiring a => Semiring (M11 a)

Defined in Data.Semimodule.Finite

Semiring a => Semiring (e -> a)

Defined in Data.Semiring

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

Defined in Data.Semiring

Semiring a => Semiring (End a b)

Defined in Data.Semimodule.Free

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

Additive unit of a semiring.

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

Multiplicative unit of a semiring.

two :: Semiring a => a

two = one + one

(^) :: Semiring a => a -> Natural -> a infixr 8

Evaluate a natural-numbered power of a semiring element.

 one = a ^ 0

>>> 8 ^ 0 :: Int
1

Semiring folds

sum :: (Additive - Monoid) a => Foldable f => f a -> a

Evaluate a semiring sum.

>>> sum [1..5 :: Int]
15

sumWith :: (Additive - Monoid) a => Foldable f => (b -> a) -> f b -> a

Evaluate a semiring sum using a given semiring.

product :: (Multiplicative - Monoid) a => Foldable f => f a -> a

Evaluate a semiring product.

>>> product [1..5 :: Int]
120

productWith :: (Multiplicative - Monoid) a => Foldable f => (b -> a) -> f b -> a

Evaluate a semiring product using a given semiring.

product f = foldr' ((*) . f) one

>>> productWith Just [1..5 :: Int]
Just 120

xmult :: Semiring a => Foldable f => Applicative f => f a -> f a -> a

Cross-multiply two collections.

>>> xmult (V3 1 2 3) (V3 1 2 3)
14
>>> xmult [1,2,3 :: Int] [1,2,3]
36
>>> xmult [1,2,3 :: Int] []
0

eval :: Semiring a => Functor f => Foldable f => Foldable g => f (g a) -> a

Evaluate a semiring expression.

 (a11 * .. * a1m) + (a21 * .. * a2n) + ...

>>> eval [[1, 2], [3, 4 :: Int]] -- 1 * 2 + 3 * 4
14
>>> eval $ sequence [[1, 2], [3, 4 :: Int]] -- 1 + 2 * 3 + 4
21

evalWith :: Semiring r => Functor f => Functor g => Foldable f => Foldable g => (a -> r) -> f (g a) -> r

Evaluate a semiring expression using a given semiring.

>>> evalWith Max [[1..4 :: Int], [0..2 :: Int]]
Max {getMax = 24}

Rings

type RingLaw a = ((Additive - Group) a, (Multiplicative - Monoid) a)

class (Semiring a, RingLaw a) => Ring a

Rings.

A ring R is a commutative group with a second monoidal operation * that distributes over +.

The basic properties of a ring follow immediately from the axioms:

 r * zero = zero = zero * r

 negate one * r = negate r

Furthermore, the binomial formula holds for any commuting pair of elements (that is, any a and b such that a * b = b * a).

If zero = one in a ring R, then R has only one element, and is called the zero ring. Otherwise the additive identity, the additive inverse of each element, and the multiplicative identity are unique.

See https://en.wikipedia.org/wiki/Ring_(mathematics).

If the ring is ordered (i.e. has an Ord instance), then the following additional properties must hold:

 a <= b ⇒ a + c <= b + c

 zero <= a && zero <= b ⇒ zero <= a * b

See the properties module for a detailed specification of the laws.

Instances

Ring Double

Defined in Data.Semiring

Ring Float

Defined in Data.Semiring

Ring Int

Defined in Data.Semiring

Ring Int8

Defined in Data.Semiring

Ring Int16

Defined in Data.Semiring

Ring Int32

Defined in Data.Semiring

Ring Int64

Defined in Data.Semiring

Ring Integer

Defined in Data.Semiring

Ring ()

Defined in Data.Semiring

Ring Uni

Defined in Data.Semiring

Ring Deci

Defined in Data.Semiring

Ring Centi

Defined in Data.Semiring

Ring Milli

Defined in Data.Semiring

Ring Micro

Defined in Data.Semiring

Ring Nano

Defined in Data.Semiring

Ring Pico

Defined in Data.Semiring

Ring CFloat

Defined in Data.Semiring

Ring CDouble

Defined in Data.Semiring

Ring (Ratio Integer)

Defined in Data.Semiring

Ring a => Ring (M44 a)

Defined in Data.Semimodule.Finite

Ring a => Ring (M33 a)

Defined in Data.Semimodule.Finite

Ring a => Ring (M22 a)

Defined in Data.Semimodule.Finite

Ring a => Ring (M11 a)

Defined in Data.Semimodule.Finite

Ring a => Ring (e -> a)

Defined in Data.Semiring

Ring a => Ring (End a b)

Defined in Data.Semimodule.Free

(-) :: (Additive - Group) a => a -> a -> a infixl 6

Subtract two elements.

a - b = subtract b a

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

Subtract two elements.

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

Reverse the sign of an element.

abs :: (Additive - Group) a => Ord a => a -> a

Absolute value of an element.

 abs r = r * (signum r)

signum :: Ring a => Ord a => a -> a

Extract the sign of an element.

signum satisfies a trichotomy law:

 signum r = negate r || zero || r

This follows from the fact that ordered rings are abelian, linearly ordered groups with respect to addition.

See https://en.wikipedia.org/wiki/Linearly_ordered_group.

Additive

newtype Additive a

A commutative Semigroup under +.

Constructors

Additive

Fields

• unAdditive :: a

Instances

Functor Additive

Defined in Data.Semiring

Methods

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

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

Applicative Additive

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

Methods

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

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

Ord a => Ord (Additive a)

Defined in Data.Semiring

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.Semiring

Methods

showsPrec :: Int -> Additive a -> ShowS

show :: Additive a -> String

showList :: [Additive a] -> ShowS

Generic (Additive a)

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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 (Op a b))

Defined in Data.Semiring

Methods

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

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

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

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

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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, Free f, Free g) => Semigroup (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

(<>) :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

sconcat :: NonEmpty (Additive ((f ++ g) a)) -> Additive ((f ++ g) a)

stimes :: Integral b => b -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Semigroup) a, Free f, Free g) => Semigroup (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

(<>) :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

sconcat :: NonEmpty (Additive ((f ** g) a)) -> Additive ((f ** g) a)

stimes :: Integral b => b -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

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

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

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.Semiring

Methods

mempty :: Additive Bool

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

mconcat :: [Additive Bool] -> Additive Bool

Monoid (Additive Double)

Defined in Data.Semiring

Methods

mempty :: Additive Double

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

mconcat :: [Additive Double] -> Additive Double

Monoid (Additive Float)

Defined in Data.Semiring

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.Semiring

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.Semiring

Methods

mempty :: Additive Int

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

mconcat :: [Additive Int] -> Additive Int

Monoid (Additive Int8)

Defined in Data.Semiring

Methods

mempty :: Additive Int8

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

mconcat :: [Additive Int8] -> Additive Int8

Monoid (Additive Int16)

Defined in Data.Semiring

Methods

mempty :: Additive Int16

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

mconcat :: [Additive Int16] -> Additive Int16

Monoid (Additive Int32)

Defined in Data.Semiring

Methods

mempty :: Additive Int32

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

mconcat :: [Additive Int32] -> Additive Int32

Monoid (Additive Int64)

Defined in Data.Semiring

Methods

mempty :: Additive Int64

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

mconcat :: [Additive Int64] -> Additive Int64

Monoid (Additive Integer)

Defined in Data.Semiring

Methods

mempty :: Additive Integer

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

mconcat :: [Additive Integer] -> Additive Integer

Monoid (Additive Natural)

Defined in Data.Semiring

Methods

mempty :: Additive Natural

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

mconcat :: [Additive Natural] -> Additive Natural

Monoid (Additive [a])

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

Methods

mempty :: Additive Word

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

mconcat :: [Additive Word] -> Additive Word

Monoid (Additive Word8)

Defined in Data.Semiring

Methods

mempty :: Additive Word8

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

mconcat :: [Additive Word8] -> Additive Word8

Monoid (Additive Word16)

Defined in Data.Semiring

Methods

mempty :: Additive Word16

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

mconcat :: [Additive Word16] -> Additive Word16

Monoid (Additive Word32)

Defined in Data.Semiring

Methods

mempty :: Additive Word32

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

mconcat :: [Additive Word32] -> Additive Word32

Monoid (Additive Word64)

Defined in Data.Semiring

Methods

mempty :: Additive Word64

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

mconcat :: [Additive Word64] -> Additive Word64

Monoid (Additive ())

Defined in Data.Semiring

Methods

mempty :: Additive ()

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

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

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

Defined in Data.Semiring

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.Semiring

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 (Op a b))

Defined in Data.Semiring

Methods

mempty :: Additive (Op a b)

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

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

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

Defined in Data.Semiring

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.Semiring

Methods

mempty :: Additive Uni

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

mconcat :: [Additive Uni] -> Additive Uni

Monoid (Additive Deci)

Defined in Data.Semiring

Methods

mempty :: Additive Deci

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

mconcat :: [Additive Deci] -> Additive Deci

Monoid (Additive Centi)

Defined in Data.Semiring

Methods

mempty :: Additive Centi

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

mconcat :: [Additive Centi] -> Additive Centi

Monoid (Additive Milli)

Defined in Data.Semiring

Methods

mempty :: Additive Milli

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

mconcat :: [Additive Milli] -> Additive Milli

Monoid (Additive Micro)

Defined in Data.Semiring

Methods

mempty :: Additive Micro

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

mconcat :: [Additive Micro] -> Additive Micro

Monoid (Additive Nano)

Defined in Data.Semiring

Methods

mempty :: Additive Nano

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

mconcat :: [Additive Nano] -> Additive Nano

Monoid (Additive Pico)

Defined in Data.Semiring

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.Semiring

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.Semiring

Methods

mempty :: Additive CFloat

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

mconcat :: [Additive CFloat] -> Additive CFloat

Monoid (Additive CDouble)

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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, Free f, Free g) => Monoid (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

mempty :: Additive ((f ++ g) a)

mappend :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

mconcat :: [Additive ((f ++ g) a)] -> Additive ((f ++ g) a)

((Additive - Monoid) a, Free f, Free g) => Monoid (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

mempty :: Additive ((f ** g) a)

mappend :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

mconcat :: [Additive ((f ** g) a)] -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (Lin a b c)

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

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

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

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (Cov a b)

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

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

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

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (Vec a b)

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

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.Semiring

Methods

inv :: Additive Double -> Additive Double

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

Group (Additive Float)

Defined in Data.Semiring

Methods

inv :: Additive Float -> Additive Float

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

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

Defined in Data.Semiring

Methods

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

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

Group (Additive Int)

Defined in Data.Semiring

Methods

inv :: Additive Int -> Additive Int

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

Group (Additive Int8)

Defined in Data.Semiring

Methods

inv :: Additive Int8 -> Additive Int8

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

Group (Additive Int16)

Defined in Data.Semiring

Methods

inv :: Additive Int16 -> Additive Int16

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

Group (Additive Int32)

Defined in Data.Semiring

Methods

inv :: Additive Int32 -> Additive Int32

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

Group (Additive Int64)

Defined in Data.Semiring

Methods

inv :: Additive Int64 -> Additive Int64

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

Group (Additive Integer)

Defined in Data.Semiring

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.Semiring

Methods

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

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

Group (Additive ())

Defined in Data.Semiring

Methods

inv :: Additive () -> Additive ()

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

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

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

Methods

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

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

Group (Additive Uni)

Defined in Data.Semiring

Methods

inv :: Additive Uni -> Additive Uni

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

Group (Additive Deci)

Defined in Data.Semiring

Methods

inv :: Additive Deci -> Additive Deci

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

Group (Additive Centi)

Defined in Data.Semiring

Methods

inv :: Additive Centi -> Additive Centi

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

Group (Additive Milli)

Defined in Data.Semiring

Methods

inv :: Additive Milli -> Additive Milli

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

Group (Additive Micro)

Defined in Data.Semiring

Methods

inv :: Additive Micro -> Additive Micro

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

Group (Additive Nano)

Defined in Data.Semiring

Methods

inv :: Additive Nano -> Additive Nano

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

Group (Additive Pico)

Defined in Data.Semiring

Methods

inv :: Additive Pico -> Additive Pico

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

Group (Additive CFloat)

Defined in Data.Semiring

Methods

inv :: Additive CFloat -> Additive CFloat

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

Group (Additive CDouble)

Defined in Data.Semiring

Methods

inv :: Additive CDouble -> Additive CDouble

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

((Additive - Group) a, Free f, Free g) => Group (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

inv :: Additive ((f ++ g) a) -> Additive ((f ++ g) a)

greplicate :: Integer -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Group (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

inv :: Additive ((f ** g) a) -> Additive ((f ** g) a)

greplicate :: Integer -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

Methods

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

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

Loop (Additive Double)

Defined in Data.Semiring

Methods

lempty :: Additive Double

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

Loop (Additive Float)

Defined in Data.Semiring

Methods

lempty :: Additive Float

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (a -> b)

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

Loop (Additive Int)

Defined in Data.Semiring

Methods

lempty :: Additive Int

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

Loop (Additive Int8)

Defined in Data.Semiring

Methods

lempty :: Additive Int8

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

Loop (Additive Int16)

Defined in Data.Semiring

Methods

lempty :: Additive Int16

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

Loop (Additive Int32)

Defined in Data.Semiring

Methods

lempty :: Additive Int32

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

Loop (Additive Int64)

Defined in Data.Semiring

Methods

lempty :: Additive Int64

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

Loop (Additive Integer)

Defined in Data.Semiring

Methods

lempty :: Additive Integer

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (Ratio a)

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

Loop (Additive ())

Defined in Data.Semiring

Methods

lempty :: Additive ()

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (Op a b)

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (Complex a)

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

Loop (Additive Uni)

Defined in Data.Semiring

Methods

lempty :: Additive Uni

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

Loop (Additive Deci)

Defined in Data.Semiring

Methods

lempty :: Additive Deci

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

Loop (Additive Centi)

Defined in Data.Semiring

Methods

lempty :: Additive Centi

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

Loop (Additive Milli)

Defined in Data.Semiring

Methods

lempty :: Additive Milli

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

Loop (Additive Micro)

Defined in Data.Semiring

Methods

lempty :: Additive Micro

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

Loop (Additive Nano)

Defined in Data.Semiring

Methods

lempty :: Additive Nano

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

Loop (Additive Pico)

Defined in Data.Semiring

Methods

lempty :: Additive Pico

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

Loop (Additive CFloat)

Defined in Data.Semiring

Methods

lempty :: Additive CFloat

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

Loop (Additive CDouble)

Defined in Data.Semiring

Methods

lempty :: Additive CDouble

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

((Additive - Group) a, Free f, Free g) => Loop (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

lempty :: Additive ((f ++ g) a)

lreplicate :: Natural -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Loop (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

lempty :: Additive ((f ** g) a)

lreplicate :: Natural -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (Lin a b c)

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

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (Cov a b)

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

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (Vec a b)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V4 a)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V3 a)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V2 a)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V1 a)

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

Quasigroup (Additive Double)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Float)

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

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.Semiring

Methods

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

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

Quasigroup (Additive Int8)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Int16)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Int32)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Int64)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Integer)

Defined in Data.Semiring

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.Semiring

Methods

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

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

Quasigroup (Additive ())

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

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.Semiring

Methods

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

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

Quasigroup (Additive Deci)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Centi)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Milli)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Micro)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Nano)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Pico)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive CFloat)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive CDouble)

Defined in Data.Semiring

Methods

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

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

((Additive - Group) a, Free f, Free g) => Quasigroup (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

(//) :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

(\\) :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Quasigroup (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

(//) :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

(\\) :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

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.Semiring

Methods

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

Magma (Additive Float)

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Additive Int)

Defined in Data.Semiring

Methods

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

Magma (Additive Int8)

Defined in Data.Semiring

Methods

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

Magma (Additive Int16)

Defined in Data.Semiring

Methods

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

Magma (Additive Int32)

Defined in Data.Semiring

Methods

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

Magma (Additive Int64)

Defined in Data.Semiring

Methods

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

Magma (Additive Integer)

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Additive ())

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Additive Uni)

Defined in Data.Semiring

Methods

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

Magma (Additive Deci)

Defined in Data.Semiring

Methods

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

Magma (Additive Centi)

Defined in Data.Semiring

Methods

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

Magma (Additive Milli)

Defined in Data.Semiring

Methods

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

Magma (Additive Micro)

Defined in Data.Semiring

Methods

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

Magma (Additive Nano)

Defined in Data.Semiring

Methods

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

Magma (Additive Pico)

Defined in Data.Semiring

Methods

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

Magma (Additive CFloat)

Defined in Data.Semiring

Methods

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

Magma (Additive CDouble)

Defined in Data.Semiring

Methods

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

((Additive - Group) a, Free f, Free g) => Magma (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

(<<) :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Magma (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

(<<) :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

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

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

Defined in Data.Semimodule.Free

Methods

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

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

Defined in Data.Semimodule.Free

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

type Rep Additive

Defined in Data.Semiring

type Rep Additive = ()

type Rep (Additive a)

Defined in Data.Semiring

type Rep (Additive a) = D1 (MetaData "Additive" "Data.Semiring" "rings-0.1.3-BFdOLcheYTn8vzZgCGb7ir" True) (C1 (MetaCons "Additive" PrefixI True) (S1 (MetaSel (Just "unAdditive") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

Multiplicative

newtype Multiplicative a

A (potentially non-commutative) Semigroup under *.

Constructors

Multiplicative

Fields

• unMultiplicative :: a

Instances

Functor Multiplicative

Defined in Data.Semiring

Methods

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

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

Applicative Multiplicative

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

Methods

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

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

Ord a => Ord (Multiplicative a)

Defined in Data.Semiring

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.Semiring

Methods

showsPrec :: Int -> Multiplicative a -> ShowS

show :: Multiplicative a -> String

showList :: [Multiplicative a] -> ShowS

Generic (Multiplicative a)

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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)

Presemiring a => Semigroup (Multiplicative (End a b))

Defined in Data.Semimodule.Free

Methods

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

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

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.Semiring

Methods

mempty :: Multiplicative Bool

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

mconcat :: [Multiplicative Bool] -> Multiplicative Bool

Monoid (Multiplicative Double)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Double

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

mconcat :: [Multiplicative Double] -> Multiplicative Double

Monoid (Multiplicative Float)

Defined in Data.Semiring

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.Semiring

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.Semiring

Methods

mempty :: Multiplicative Int

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

mconcat :: [Multiplicative Int] -> Multiplicative Int

Monoid (Multiplicative Int8)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Int8

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

mconcat :: [Multiplicative Int8] -> Multiplicative Int8

Monoid (Multiplicative Int16)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Int16

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

mconcat :: [Multiplicative Int16] -> Multiplicative Int16

Monoid (Multiplicative Int32)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Int32

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

mconcat :: [Multiplicative Int32] -> Multiplicative Int32

Monoid (Multiplicative Int64)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Int64

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

mconcat :: [Multiplicative Int64] -> Multiplicative Int64

Monoid (Multiplicative Integer)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Integer

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

mconcat :: [Multiplicative Integer] -> Multiplicative Integer

Monoid (Multiplicative Natural)

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

Methods

mempty :: Multiplicative Word

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

mconcat :: [Multiplicative Word] -> Multiplicative Word

Monoid (Multiplicative Word8)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Word8

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

mconcat :: [Multiplicative Word8] -> Multiplicative Word8

Monoid (Multiplicative Word16)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Word16

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

mconcat :: [Multiplicative Word16] -> Multiplicative Word16

Monoid (Multiplicative Word32)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Word32

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

mconcat :: [Multiplicative Word32] -> Multiplicative Word32

Monoid (Multiplicative Word64)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Word64

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

mconcat :: [Multiplicative Word64] -> Multiplicative Word64

Monoid (Multiplicative ())

Defined in Data.Semiring

Methods

mempty :: Multiplicative ()

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

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

Monoid (Multiplicative Uni)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Uni

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

mconcat :: [Multiplicative Uni] -> Multiplicative Uni

Monoid (Multiplicative Deci)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Deci

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

mconcat :: [Multiplicative Deci] -> Multiplicative Deci

Monoid (Multiplicative Centi)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Centi

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

mconcat :: [Multiplicative Centi] -> Multiplicative Centi

Monoid (Multiplicative Milli)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Milli

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

mconcat :: [Multiplicative Milli] -> Multiplicative Milli

Monoid (Multiplicative Micro)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Micro

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

mconcat :: [Multiplicative Micro] -> Multiplicative Micro

Monoid (Multiplicative Nano)

Defined in Data.Semiring

Methods

mempty :: Multiplicative Nano

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

mconcat :: [Multiplicative Nano] -> Multiplicative Nano

Monoid (Multiplicative Pico)

Defined in Data.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

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.Semiring

Methods

mempty :: Multiplicative CFloat

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

mconcat :: [Multiplicative CFloat] -> Multiplicative CFloat

Monoid (Multiplicative CDouble)

Defined in Data.Semiring

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.Semiring

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.Semiring

Methods

mempty :: Multiplicative (Map k a)

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

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

Semiring a => Monoid (Multiplicative (End a b))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (End a b)

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

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.Semiring

Methods

inv :: Multiplicative Double -> Multiplicative Double

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

Group (Multiplicative Float)

Defined in Data.Semiring

Methods

inv :: Multiplicative Float -> Multiplicative Float

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

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

Defined in Data.Semiring

Methods

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

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

Group (Multiplicative ())

Defined in Data.Semiring

Methods

inv :: Multiplicative () -> Multiplicative ()

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

Group (Multiplicative Uni)

Defined in Data.Semiring

Methods

inv :: Multiplicative Uni -> Multiplicative Uni

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

Group (Multiplicative Deci)

Defined in Data.Semiring

Methods

inv :: Multiplicative Deci -> Multiplicative Deci

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

Group (Multiplicative Centi)

Defined in Data.Semiring

Methods

inv :: Multiplicative Centi -> Multiplicative Centi

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

Group (Multiplicative Milli)

Defined in Data.Semiring

Methods

inv :: Multiplicative Milli -> Multiplicative Milli

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

Group (Multiplicative Micro)

Defined in Data.Semiring

Methods

inv :: Multiplicative Micro -> Multiplicative Micro

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

Group (Multiplicative Nano)

Defined in Data.Semiring

Methods

inv :: Multiplicative Nano -> Multiplicative Nano

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

Group (Multiplicative Pico)

Defined in Data.Semiring

Methods

inv :: Multiplicative Pico -> Multiplicative Pico

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

Group (Multiplicative CFloat)

Defined in Data.Semiring

Methods

inv :: Multiplicative CFloat -> Multiplicative CFloat

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

Group (Multiplicative CDouble)

Defined in Data.Semiring

Methods

inv :: Multiplicative CDouble -> Multiplicative CDouble

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

Loop (Multiplicative Double)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Double

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

Loop (Multiplicative Float)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Float

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

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

Defined in Data.Semiring

Methods

lempty :: Multiplicative (Ratio a)

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

Loop (Multiplicative ())

Defined in Data.Semiring

Methods

lempty :: Multiplicative ()

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

Loop (Multiplicative Uni)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Uni

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

Loop (Multiplicative Deci)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Deci

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

Loop (Multiplicative Centi)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Centi

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

Loop (Multiplicative Milli)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Milli

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

Loop (Multiplicative Micro)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Micro

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

Loop (Multiplicative Nano)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Nano

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

Loop (Multiplicative Pico)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Pico

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

Loop (Multiplicative CFloat)

Defined in Data.Semiring

Methods

lempty :: Multiplicative CFloat

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

Loop (Multiplicative CDouble)

Defined in Data.Semiring

Methods

lempty :: Multiplicative CDouble

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

Quasigroup (Multiplicative Double)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Float)

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative ())

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Uni)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Deci)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Centi)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Milli)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Micro)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Nano)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Pico)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative CFloat)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative CDouble)

Defined in Data.Semiring

Methods

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

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

Magma (Multiplicative Double)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Float)

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Multiplicative ())

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Uni)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Deci)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Centi)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Milli)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Micro)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Nano)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Pico)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative CFloat)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative CDouble)

Defined in Data.Semiring

Methods

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

type Rep Multiplicative

Defined in Data.Semiring

type Rep Multiplicative = ()

type Rep (Multiplicative a)

Defined in Data.Semiring

type Rep (Multiplicative a) = D1 (MetaData "Multiplicative" "Data.Semiring" "rings-0.1.3-BFdOLcheYTn8vzZgCGb7ir" True) (C1 (MetaCons "Multiplicative" PrefixI True) (S1 (MetaSel (Just "unMultiplicative") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

Re-exports

mreplicate :: Monoid a => Natural -> a -> a

A generalization of replicate to an arbitrary Monoid.

Adapted from http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html.

class Magma a where

Methods

(<<) :: a -> a -> a infixl 6

Instances

Magma (Multiplicative Double)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Float)

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Multiplicative ())

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Uni)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Deci)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Centi)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Milli)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Micro)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Nano)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative Pico)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative CFloat)

Defined in Data.Semiring

Methods

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

Magma (Multiplicative CDouble)

Defined in Data.Semiring

Methods

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

Magma (Additive Double)

Defined in Data.Semiring

Methods

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

Magma (Additive Float)

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Additive Int)

Defined in Data.Semiring

Methods

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

Magma (Additive Int8)

Defined in Data.Semiring

Methods

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

Magma (Additive Int16)

Defined in Data.Semiring

Methods

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

Magma (Additive Int32)

Defined in Data.Semiring

Methods

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

Magma (Additive Int64)

Defined in Data.Semiring

Methods

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

Magma (Additive Integer)

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Additive ())

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

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

Defined in Data.Semiring

Methods

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

Magma (Additive Uni)

Defined in Data.Semiring

Methods

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

Magma (Additive Deci)

Defined in Data.Semiring

Methods

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

Magma (Additive Centi)

Defined in Data.Semiring

Methods

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

Magma (Additive Milli)

Defined in Data.Semiring

Methods

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

Magma (Additive Micro)

Defined in Data.Semiring

Methods

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

Magma (Additive Nano)

Defined in Data.Semiring

Methods

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

Magma (Additive Pico)

Defined in Data.Semiring

Methods

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

Magma (Additive CFloat)

Defined in Data.Semiring

Methods

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

Magma (Additive CDouble)

Defined in Data.Semiring

Methods

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

((Additive - Group) a, Free f, Free g) => Magma (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

(<<) :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Magma (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

(<<) :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

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

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

Defined in Data.Semimodule.Free

Methods

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

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

Defined in Data.Semimodule.Free

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

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

Defined in Data.Semimodule.Finite

Methods

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

class Magma a => Quasigroup a

Instances

Quasigroup (Multiplicative Double)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Float)

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative ())

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Uni)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Deci)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Centi)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Milli)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Micro)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Nano)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative Pico)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative CFloat)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Multiplicative CDouble)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Double)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Float)

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

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.Semiring

Methods

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

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

Quasigroup (Additive Int8)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Int16)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Int32)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Int64)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Integer)

Defined in Data.Semiring

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.Semiring

Methods

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

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

Quasigroup (Additive ())

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

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.Semiring

Methods

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

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

Quasigroup (Additive Deci)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Centi)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Milli)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Micro)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Nano)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive Pico)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive CFloat)

Defined in Data.Semiring

Methods

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

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

Quasigroup (Additive CDouble)

Defined in Data.Semiring

Methods

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

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

((Additive - Group) a, Free f, Free g) => Quasigroup (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

(//) :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

(\\) :: Additive ((f ++ g) a) -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Quasigroup (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

(//) :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

(\\) :: Additive ((f ** g) a) -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

Methods

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

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

class Quasigroup a => Loop a

Instances

(Semigroup a, Quasigroup (Maybe a)) => Loop (Maybe a)

Defined in Data.Group

Methods

lempty :: Maybe a

lreplicate :: Natural -> Maybe a -> Maybe a

Loop (Multiplicative Double)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Double

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

Loop (Multiplicative Float)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Float

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

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

Defined in Data.Semiring

Methods

lempty :: Multiplicative (Ratio a)

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

Loop (Multiplicative ())

Defined in Data.Semiring

Methods

lempty :: Multiplicative ()

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

Loop (Multiplicative Uni)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Uni

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

Loop (Multiplicative Deci)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Deci

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

Loop (Multiplicative Centi)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Centi

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

Loop (Multiplicative Milli)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Milli

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

Loop (Multiplicative Micro)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Micro

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

Loop (Multiplicative Nano)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Nano

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

Loop (Multiplicative Pico)

Defined in Data.Semiring

Methods

lempty :: Multiplicative Pico

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

Loop (Multiplicative CFloat)

Defined in Data.Semiring

Methods

lempty :: Multiplicative CFloat

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

Loop (Multiplicative CDouble)

Defined in Data.Semiring

Methods

lempty :: Multiplicative CDouble

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

Loop (Additive Double)

Defined in Data.Semiring

Methods

lempty :: Additive Double

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

Loop (Additive Float)

Defined in Data.Semiring

Methods

lempty :: Additive Float

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (a -> b)

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

Loop (Additive Int)

Defined in Data.Semiring

Methods

lempty :: Additive Int

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

Loop (Additive Int8)

Defined in Data.Semiring

Methods

lempty :: Additive Int8

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

Loop (Additive Int16)

Defined in Data.Semiring

Methods

lempty :: Additive Int16

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

Loop (Additive Int32)

Defined in Data.Semiring

Methods

lempty :: Additive Int32

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

Loop (Additive Int64)

Defined in Data.Semiring

Methods

lempty :: Additive Int64

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

Loop (Additive Integer)

Defined in Data.Semiring

Methods

lempty :: Additive Integer

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (Ratio a)

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

Loop (Additive ())

Defined in Data.Semiring

Methods

lempty :: Additive ()

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (Op a b)

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

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

Defined in Data.Semiring

Methods

lempty :: Additive (Complex a)

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

Loop (Additive Uni)

Defined in Data.Semiring

Methods

lempty :: Additive Uni

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

Loop (Additive Deci)

Defined in Data.Semiring

Methods

lempty :: Additive Deci

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

Loop (Additive Centi)

Defined in Data.Semiring

Methods

lempty :: Additive Centi

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

Loop (Additive Milli)

Defined in Data.Semiring

Methods

lempty :: Additive Milli

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

Loop (Additive Micro)

Defined in Data.Semiring

Methods

lempty :: Additive Micro

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

Loop (Additive Nano)

Defined in Data.Semiring

Methods

lempty :: Additive Nano

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

Loop (Additive Pico)

Defined in Data.Semiring

Methods

lempty :: Additive Pico

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

Loop (Additive CFloat)

Defined in Data.Semiring

Methods

lempty :: Additive CFloat

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

Loop (Additive CDouble)

Defined in Data.Semiring

Methods

lempty :: Additive CDouble

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

((Additive - Group) a, Free f, Free g) => Loop (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

lempty :: Additive ((f ++ g) a)

lreplicate :: Natural -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Loop (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

lempty :: Additive ((f ** g) a)

lreplicate :: Natural -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (Lin a b c)

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

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (Cov a b)

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

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (Vec a b)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V4 a)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V3 a)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V2 a)

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

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

Defined in Data.Semimodule.Finite

Methods

lempty :: Additive (V1 a)

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

class (Loop a, Monoid a) => Group a where

Minimal complete definition

Nothing

Methods

inv :: a -> a

greplicate :: Integer -> a -> a

Instances

(Semigroup a, Quasigroup (Maybe a)) => Group (Maybe a)

Defined in Data.Group

Methods

inv :: Maybe a -> Maybe a

greplicate :: Integer -> Maybe a -> Maybe a

Group (Multiplicative Double)

Defined in Data.Semiring

Methods

inv :: Multiplicative Double -> Multiplicative Double

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

Group (Multiplicative Float)

Defined in Data.Semiring

Methods

inv :: Multiplicative Float -> Multiplicative Float

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

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

Defined in Data.Semiring

Methods

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

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

Group (Multiplicative ())

Defined in Data.Semiring

Methods

inv :: Multiplicative () -> Multiplicative ()

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

Group (Multiplicative Uni)

Defined in Data.Semiring

Methods

inv :: Multiplicative Uni -> Multiplicative Uni

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

Group (Multiplicative Deci)

Defined in Data.Semiring

Methods

inv :: Multiplicative Deci -> Multiplicative Deci

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

Group (Multiplicative Centi)

Defined in Data.Semiring

Methods

inv :: Multiplicative Centi -> Multiplicative Centi

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

Group (Multiplicative Milli)

Defined in Data.Semiring

Methods

inv :: Multiplicative Milli -> Multiplicative Milli

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

Group (Multiplicative Micro)

Defined in Data.Semiring

Methods

inv :: Multiplicative Micro -> Multiplicative Micro

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

Group (Multiplicative Nano)

Defined in Data.Semiring

Methods

inv :: Multiplicative Nano -> Multiplicative Nano

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

Group (Multiplicative Pico)

Defined in Data.Semiring

Methods

inv :: Multiplicative Pico -> Multiplicative Pico

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

Group (Multiplicative CFloat)

Defined in Data.Semiring

Methods

inv :: Multiplicative CFloat -> Multiplicative CFloat

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

Group (Multiplicative CDouble)

Defined in Data.Semiring

Methods

inv :: Multiplicative CDouble -> Multiplicative CDouble

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

Group (Additive Double)

Defined in Data.Semiring

Methods

inv :: Additive Double -> Additive Double

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

Group (Additive Float)

Defined in Data.Semiring

Methods

inv :: Additive Float -> Additive Float

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

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

Defined in Data.Semiring

Methods

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

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

Group (Additive Int)

Defined in Data.Semiring

Methods

inv :: Additive Int -> Additive Int

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

Group (Additive Int8)

Defined in Data.Semiring

Methods

inv :: Additive Int8 -> Additive Int8

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

Group (Additive Int16)

Defined in Data.Semiring

Methods

inv :: Additive Int16 -> Additive Int16

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

Group (Additive Int32)

Defined in Data.Semiring

Methods

inv :: Additive Int32 -> Additive Int32

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

Group (Additive Int64)

Defined in Data.Semiring

Methods

inv :: Additive Int64 -> Additive Int64

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

Group (Additive Integer)

Defined in Data.Semiring

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.Semiring

Methods

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

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

Group (Additive ())

Defined in Data.Semiring

Methods

inv :: Additive () -> Additive ()

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

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

Defined in Data.Semiring

Methods

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

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

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

Defined in Data.Semiring

Methods

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

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

Group (Additive Uni)

Defined in Data.Semiring

Methods

inv :: Additive Uni -> Additive Uni

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

Group (Additive Deci)

Defined in Data.Semiring

Methods

inv :: Additive Deci -> Additive Deci

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

Group (Additive Centi)

Defined in Data.Semiring

Methods

inv :: Additive Centi -> Additive Centi

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

Group (Additive Milli)

Defined in Data.Semiring

Methods

inv :: Additive Milli -> Additive Milli

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

Group (Additive Micro)

Defined in Data.Semiring

Methods

inv :: Additive Micro -> Additive Micro

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

Group (Additive Nano)

Defined in Data.Semiring

Methods

inv :: Additive Nano -> Additive Nano

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

Group (Additive Pico)

Defined in Data.Semiring

Methods

inv :: Additive Pico -> Additive Pico

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

Group (Additive CFloat)

Defined in Data.Semiring

Methods

inv :: Additive CFloat -> Additive CFloat

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

Group (Additive CDouble)

Defined in Data.Semiring

Methods

inv :: Additive CDouble -> Additive CDouble

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

((Additive - Group) a, Free f, Free g) => Group (Additive ((f ++ g) a))

Defined in Data.Semiring

Methods

inv :: Additive ((f ++ g) a) -> Additive ((f ++ g) a)

greplicate :: Integer -> Additive ((f ++ g) a) -> Additive ((f ++ g) a)

((Additive - Group) a, Free f, Free g) => Group (Additive ((f ** g) a))

Defined in Data.Semiring

Methods

inv :: Additive ((f ** g) a) -> Additive ((f ** g) a)

greplicate :: Integer -> Additive ((f ** g) a) -> Additive ((f ** g) a)

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Free

Methods

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

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

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

Defined in Data.Semimodule.Finite

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.Finite

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.Finite

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.Finite

Methods

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

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