Data.Group

Documentation

class Semigroup a where

The class of semigroups (types with an associative binary operation).

Instances should satisfy the associativity law:

• x <> (y <> z) = (x <> y) <> z

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

stimes :: Integral b => b -> a -> a

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in O(1) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

Instances

Semigroup Ordering

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup ()

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty () -> ()

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

Semigroup Void

Since: base-4.9.0.0

Defined in Data.Void

Methods

(<>) :: Void -> Void -> Void

sconcat :: NonEmpty Void -> Void

stimes :: Integral b => b -> Void -> Void

Semigroup All

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Semigroup Any

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Semigroup IntSet

Since: containers-0.5.7

Defined in Data.IntSet.Internal

Methods

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

sconcat :: NonEmpty IntSet -> IntSet

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

Semigroup Doc

Defined in Text.PrettyPrint.HughesPJ

Methods

(<>) :: Doc -> Doc -> Doc

sconcat :: NonEmpty Doc -> Doc

stimes :: Integral b => b -> Doc -> Doc

Semigroup [a]

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty [a] -> [a]

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

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

stimes :: Integral b => b -> Maybe a -> Maybe a

Semigroup a => Semigroup (IO a)

Since: base-4.10.0.0

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a

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

stimes :: Integral b => b -> IO a -> IO a

Semigroup p => Semigroup (Par1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p

sconcat :: NonEmpty (Par1 p) -> Par1 p

stimes :: Integral b => b -> Par1 p -> Par1 p

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

stimes :: Integral b => b -> Min a -> Min a

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

stimes :: Integral b => b -> Max a -> Max a

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a

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

stimes :: Integral b => b -> First a -> First a

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a

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

stimes :: Integral b => b -> Last a -> Last a

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup a => Semigroup (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Option a -> Option a -> Option a

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

stimes :: Integral b => b -> Option a -> Option a

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(<>) :: Identity a -> Identity a -> Identity a

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

stimes :: Integral b => b -> Identity a -> Identity a

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Monoid

Methods

(<>) :: First a -> First a -> First a

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

stimes :: Integral b => b -> First a -> First a

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a

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

stimes :: Integral b => b -> Last a -> Last a

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

stimes :: Integral b => b -> Dual a -> Dual a

Semigroup (Endo a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a

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

stimes :: Integral b => b -> Endo a -> Endo a

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a

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

stimes :: Integral b => b -> Sum a -> Sum a

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a

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

stimes :: Integral b => b -> Product a -> Product a

Semigroup a => Semigroup (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

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

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

stimes :: Integral b => b -> Down a -> Down a

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Semigroup (IntMap a)

Since: containers-0.5.7

Defined in Data.IntMap.Internal

Methods

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

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

stimes :: Integral b => b -> IntMap a -> IntMap a

Semigroup (Seq a)

Since: containers-0.5.7

Defined in Data.Sequence.Internal

Methods

(<>) :: Seq a -> Seq a -> Seq a

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

stimes :: Integral b => b -> Seq a -> Seq a

Ord a => Semigroup (Set a)

Since: containers-0.5.7

Defined in Data.Set.Internal

Methods

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

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

stimes :: Integral b => b -> Set a -> Set a

Semigroup (Doc a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

(<>) :: Doc a -> Doc a -> Doc a

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

stimes :: Integral b => b -> Doc a -> Doc a

(Hashable a, Eq a) => Semigroup (HashSet a)

Defined in Data.HashSet.Base

Methods

(<>) :: HashSet a -> HashSet a -> HashSet a

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

stimes :: Integral b => b -> HashSet a -> HashSet a

Semigroup a => Semigroup (JoinWith a)

Defined in Data.Semigroup.Foldable

Methods

(<>) :: JoinWith a -> JoinWith a -> JoinWith a

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

stimes :: Integral b => b -> JoinWith a -> JoinWith a

Semigroup (Multiplicative Bool)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Int)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Int8)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Int16)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Int32)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Int64)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Integer)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Natural)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Word)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Word8)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Word16)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Word32)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Word64)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Semigroup (Multiplicative IntSet)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Ring a => Semigroup (Multiplicative (Quaternion a))

Defined in Data.Algebra.Quaternion

Methods

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

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

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

Semigroup (MergeSet a)

Defined in Data.Set.Internal

Methods

(<>) :: MergeSet a -> MergeSet a -> MergeSet a

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

stimes :: Integral b => b -> MergeSet a -> MergeSet a

Semigroup (Additive Bool)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Double)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Float)

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Int)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Natural)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive [a])

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Word)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Word8)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Word16)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Word32)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Word64)

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive ())

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive (NonEmpty a))

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

Semigroup (Additive IntSet)

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

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

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

Matrix addition.

>>> m24 1 2 3 4 5 6 7 8 <> m24 1 2 3 4 5 6 7 8 :: M24 Int
V2 (VFour 2 4 6 8) (VFour 10 12 14 16)

Defined in Data.Semimodule.Basis

Methods

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

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

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

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

Matrix addition.

>>> m24 1 2 3 4 5 6 7 8 <> m24 1 2 3 4 5 6 7 8 :: M24 Int
V2 (V4 2 4 6 8) (V4 10 12 14 16)

Defined in Data.Semimodule.Basis

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)

Semigroup (Additive E3)

Defined in Data.Semimodule.Basis

Methods

(<>) :: Additive E3 -> Additive E3 -> Additive E3

sconcat :: NonEmpty (Additive E3) -> Additive E3

stimes :: Integral b => b -> Additive E3 -> Additive E3

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

Matrix addition.

>>> V2 (V3 1 2 3) (V3 4 5 6) <> V2 (V3 7 8 9) (V3 1 2 3)
V2 (V3 8 10 12) (V3 5 7 9)

Defined in Data.Semimodule.Basis

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)

Semigroup (Additive E2)

Defined in Data.Semimodule.Basis

Methods

(<>) :: Additive E2 -> Additive E2 -> Additive E2

sconcat :: NonEmpty (Additive E2) -> Additive E2

stimes :: Integral b => b -> Additive E2 -> Additive E2

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

Matrix addition.

>>> m23 1 2 3 4 5 6 <> m23 7 8 9 1 2 3 :: M23 Int
V2 (V3 8 10 12) (V3 5 7 9)

Defined in Data.Semimodule.Basis

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 (Cad a))

Matrix addition.

Defined in Data.Semimodule.Transform

Methods

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

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

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

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

Matrix addition.

Defined in Data.Semimodule.Transform

Methods

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

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

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

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

Defined in Data.Algebra.Quaternion

Methods

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

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

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

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

Vector addition.

>>> VFour 1 2 3 4 <> VFour 5 6 7 8
VFour 6 8 10 12 

Defined in Data.Semimodule.Basis

Methods

(<>) :: VFour a -> VFour a -> VFour a

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

stimes :: Integral b => b -> VFour a -> VFour a

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

Vector addition.

>>> V4 1 2 3 4 <> V4 5 6 7 8
V4 6 8 10 12 

Defined in Data.Semimodule.Basis

Methods

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

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

stimes :: Integral b => b -> V4 a -> V4 a

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

Vector addition.

>>> V3 1 2 3 <> V3 4 5 6
V3 5 7 9

Defined in Data.Semimodule.Basis

Methods

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

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

stimes :: Integral b => b -> V3 a -> V3 a

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

Vector addition.

>>> V2 1 2 <> V2 3 4
V2 4 6

Defined in Data.Semimodule.Basis

Methods

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

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

stimes :: Integral b => b -> V2 a -> V2 a

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

Vector addition.

>>> Cad 1 2 3 <> Cad 4 5 6
Cad 5 7 9

Defined in Data.Semimodule.Transform

Methods

(<>) :: Cad a -> Cad a -> Cad a

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

stimes :: Integral b => b -> Cad a -> Cad a

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

Vector addition.

>>> Ned 1 2 3 <> Ned 4 5 6
Ned 5 7 9

Defined in Data.Semimodule.Transform

Methods

(<>) :: Ned a -> Ned a -> Ned a

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

stimes :: Integral b => b -> Ned a -> Ned a

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

Defined in Data.Algebra.Quaternion

Methods

(<>) :: Quaternion a -> Quaternion a -> Quaternion a

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

stimes :: Integral b => b -> Quaternion a -> Quaternion a

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

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

Semigroup (Either a b)

Since: base-4.9.0.0

Defined in Data.Either

Methods

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

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

stimes :: Integral b0 => b0 -> Either a b -> Either a b

Semigroup (V1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p

sconcat :: NonEmpty (V1 p) -> V1 p

stimes :: Integral b => b -> V1 p -> V1 p

Semigroup (U1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: U1 p -> U1 p -> U1 p

sconcat :: NonEmpty (U1 p) -> U1 p

stimes :: Integral b => b -> U1 p -> U1 p

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

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

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

Semigroup (Proxy s)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s

sconcat :: NonEmpty (Proxy s) -> Proxy s

stimes :: Integral b => b -> Proxy s -> Proxy s

Ord k => Semigroup (Map k v)

Defined in Data.Map.Internal

Methods

(<>) :: Map k v -> Map k v -> Map k v

sconcat :: NonEmpty (Map k v) -> Map k v

stimes :: Integral b => b -> Map k v -> Map k v

(Eq k, Hashable k) => Semigroup (HashMap k v)

Defined in Data.HashMap.Base

Methods

(<>) :: HashMap k v -> HashMap k v -> HashMap k v

sconcat :: NonEmpty (HashMap k v) -> HashMap k v

stimes :: Integral b => b -> HashMap k v -> HashMap k v

Apply f => Semigroup (Act f a)

Defined in Data.Semigroup.Foldable

Methods

(<>) :: Act f a -> Act f a -> Act f a

sconcat :: NonEmpty (Act f a) -> Act f a

stimes :: Integral b => b -> Act f a -> Act f a

Alt f => Semigroup (Alt_ f a)

Defined in Data.Semigroup.Foldable

Methods

(<>) :: Alt_ f a -> Alt_ f a -> Alt_ f a

sconcat :: NonEmpty (Alt_ f a) -> Alt_ f a

stimes :: Integral b => b -> Alt_ f a -> Alt_ f a

Semigroup (f p) => Semigroup (Rec1 f p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p

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

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

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

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

stimes :: Integral b0 => b0 -> Const a b -> Const a b

(Applicative f, Semigroup a) => Semigroup (Ap f a)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a

sconcat :: NonEmpty (Ap f a) -> Ap f a

stimes :: Integral b => b -> Ap f a -> Ap f a

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a

sconcat :: NonEmpty (Alt f a) -> Alt f a

stimes :: Integral b => b -> Alt f a -> Alt f a

(Profunctor p, Arrow p, Semigroup b) => Semigroup (Closure p a b)

Defined in Data.Profunctor.Closed

Methods

(<>) :: Closure p a b -> Closure p a b -> Closure p a b

sconcat :: NonEmpty (Closure p a b) -> Closure p a b

stimes :: Integral b0 => b0 -> Closure p a b -> Closure p a b

ArrowPlus p => Semigroup (Tambara p a b)

Defined in Data.Profunctor.Strong

Methods

(<>) :: Tambara p a b -> Tambara p a b -> Tambara p a b

sconcat :: NonEmpty (Tambara p a b) -> Tambara p a b

stimes :: Integral b0 => b0 -> Tambara p a b -> Tambara p a b

Semigroup a => Semigroup (Tagged s a)

Defined in Data.Tagged

Methods

(<>) :: Tagged s a -> Tagged s a -> Tagged s a

sconcat :: NonEmpty (Tagged s a) -> Tagged s a

stimes :: Integral b => b -> Tagged s a -> Tagged s a

Semigroup a => Semigroup (Constant a b)

Defined in Data.Functor.Constant

Methods

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

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

stimes :: Integral b0 => b0 -> Constant a b -> Constant a b

Semigroup c => Semigroup (K1 i c p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p

sconcat :: NonEmpty (K1 i c p) -> K1 i c p

stimes :: Integral b => b -> K1 i c p -> K1 i c p

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p

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

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

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

Semigroup (f p) => Semigroup (M1 i c f p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p

Semigroup (f (g p)) => Semigroup ((f :.: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e)

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

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 => Quasigroup a where

Minimal complete definition

Nothing

Methods

(//) :: a -> a -> a

(//) :: Semigroup a => a -> a -> a

(\\) :: a -> a -> a

(\\) :: Semigroup a => a -> a -> a

Instances

Quasigroup (Multiplicative Double)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Quasigroup (Additive Double)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Float)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Int)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive ())

Defined in Data.Semigroup.Additive

Methods

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

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

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

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

Quasigroup (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

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

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

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

Defined in Data.Semimodule.Basis

Methods

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

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

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

Defined in Data.Semimodule.Basis

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.Basis

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.Basis

Methods

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

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

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

Defined in Data.Semimodule.Transform

Methods

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

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

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

Defined in Data.Semimodule.Transform

Methods

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

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

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

Defined in Data.Algebra.Quaternion

Methods

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

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

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

Defined in Data.Semimodule.Basis

Methods

(//) :: VFour a -> VFour a -> VFour a

(\\) :: VFour a -> VFour a -> VFour a

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

Defined in Data.Semimodule.Basis

Methods

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

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

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

Defined in Data.Semimodule.Basis

Methods

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

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

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

Defined in Data.Semimodule.Basis

Methods

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

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

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

Defined in Data.Semimodule.Transform

Methods

(//) :: Cad a -> Cad a -> Cad a

(\\) :: Cad a -> Cad a -> Cad a

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

Defined in Data.Semimodule.Transform

Methods

(//) :: Ned a -> Ned a -> Ned a

(\\) :: Ned a -> Ned a -> Ned a

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

Defined in Data.Algebra.Quaternion

Methods

(//) :: Quaternion a -> Quaternion a -> Quaternion a

(\\) :: Quaternion a -> Quaternion a -> Quaternion a

class Quasigroup a => Loop a where

Minimal complete definition

Nothing

Methods

lempty :: a

lempty :: Monoid a => a

lreplicate :: Natural -> a -> a

lreplicate :: Group a => Natural -> a -> 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.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Double

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

Loop (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Float

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

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

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative (Ratio a)

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

Loop (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative ()

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

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

Defined in Data.Semigroup.Additive

Methods

lempty :: Multiplicative (Complex a)

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

Loop (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Uni

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

Loop (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Deci

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

Loop (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Centi

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

Loop (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Milli

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

Loop (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Micro

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

Loop (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Nano

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

Loop (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative Pico

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

Loop (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative CFloat

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

Loop (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

lempty :: Multiplicative CDouble

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

Loop (Additive Double)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Double

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

Loop (Additive Float)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Float

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

Loop (Additive Int)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int

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

Loop (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int8

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

Loop (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int16

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

Loop (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int32

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

Loop (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int64

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

Loop (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Integer

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

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

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive (Ratio a)

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

Loop (Additive ())

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive ()

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

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

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive (Complex a)

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

Loop (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Uni

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

Loop (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Deci

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

Loop (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Centi

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

Loop (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Milli

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

Loop (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Micro

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

Loop (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Nano

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

Loop (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Pico

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

Loop (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive CFloat

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

Loop (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive CDouble

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

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

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (VFour a)

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

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

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (V4 a)

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

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

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (V3 a)

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

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

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (V2 a)

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

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

Defined in Data.Semimodule.Transform

Methods

lempty :: Additive (Cad a)

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

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

Defined in Data.Semimodule.Transform

Methods

lempty :: Additive (Ned a)

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

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

Defined in Data.Algebra.Quaternion

Methods

lempty :: Additive (Quaternion a)

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

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

Defined in Data.Semimodule.Basis

Methods

lempty :: VFour a

lreplicate :: Natural -> VFour a -> VFour a

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

Defined in Data.Semimodule.Basis

Methods

lempty :: V4 a

lreplicate :: Natural -> V4 a -> V4 a

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

Defined in Data.Semimodule.Basis

Methods

lempty :: V3 a

lreplicate :: Natural -> V3 a -> V3 a

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

Defined in Data.Semimodule.Basis

Methods

lempty :: V2 a

lreplicate :: Natural -> V2 a -> V2 a

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

Defined in Data.Semimodule.Transform

Methods

lempty :: Cad a

lreplicate :: Natural -> Cad a -> Cad a

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

Defined in Data.Semimodule.Transform

Methods

lempty :: Ned a

lreplicate :: Natural -> Ned a -> Ned a

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

Defined in Data.Algebra.Quaternion

Methods

lempty :: Quaternion a

lreplicate :: Natural -> Quaternion a -> Quaternion 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.Semigroup.Multiplicative

Methods

inv :: Multiplicative Double -> Multiplicative Double

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

Group (Multiplicative Float)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Float -> Multiplicative Float

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

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

Defined in Data.Semigroup.Multiplicative

Methods

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

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

Group (Multiplicative ())

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative () -> Multiplicative ()

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

Group (Multiplicative Uni)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Uni -> Multiplicative Uni

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

Group (Multiplicative Deci)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Deci -> Multiplicative Deci

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

Group (Multiplicative Centi)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Centi -> Multiplicative Centi

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

Group (Multiplicative Milli)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Milli -> Multiplicative Milli

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

Group (Multiplicative Micro)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Micro -> Multiplicative Micro

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

Group (Multiplicative Nano)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Nano -> Multiplicative Nano

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

Group (Multiplicative Pico)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative Pico -> Multiplicative Pico

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

Group (Multiplicative CFloat)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative CFloat -> Multiplicative CFloat

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

Group (Multiplicative CDouble)

Defined in Data.Semigroup.Multiplicative

Methods

inv :: Multiplicative CDouble -> Multiplicative CDouble

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

Group (Additive Double)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Double -> Additive Double

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

Group (Additive Float)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Float -> Additive Float

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

Group (Additive Int)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int -> Additive Int

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

Group (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int8 -> Additive Int8

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

Group (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int16 -> Additive Int16

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

Group (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int32 -> Additive Int32

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

Group (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int64 -> Additive Int64

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

Group (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Integer -> Additive Integer

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

Group (Additive ())

Defined in Data.Semigroup.Additive

Methods

inv :: Additive () -> Additive ()

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

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

Defined in Data.Semigroup.Additive

Methods

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

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

Group (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Uni -> Additive Uni

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

Group (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Deci -> Additive Deci

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

Group (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Centi -> Additive Centi

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

Group (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Milli -> Additive Milli

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

Group (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Micro -> Additive Micro

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

Group (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Nano -> Additive Nano

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

Group (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Pico -> Additive Pico

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

Group (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive CFloat -> Additive CFloat

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

Group (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive CDouble -> Additive CDouble

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

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

Defined in Data.Semimodule.Basis

Methods

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

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

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

Defined in Data.Semimodule.Basis

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.Basis

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.Basis

Methods

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

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

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

Defined in Data.Semimodule.Transform

Methods

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

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

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

Defined in Data.Semimodule.Transform

Methods

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

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

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

Defined in Data.Algebra.Quaternion

Methods

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

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

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

Defined in Data.Semimodule.Basis

Methods

inv :: VFour a -> VFour a

greplicate :: Integer -> VFour a -> VFour a

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

Defined in Data.Semimodule.Basis

Methods

inv :: V4 a -> V4 a

greplicate :: Integer -> V4 a -> V4 a

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

Defined in Data.Semimodule.Basis

Methods

inv :: V3 a -> V3 a

greplicate :: Integer -> V3 a -> V3 a

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

Defined in Data.Semimodule.Basis

Methods

inv :: V2 a -> V2 a

greplicate :: Integer -> V2 a -> V2 a

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

Defined in Data.Semimodule.Transform

Methods

inv :: Cad a -> Cad a

greplicate :: Integer -> Cad a -> Cad a

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

Defined in Data.Semimodule.Transform

Methods

inv :: Ned a -> Ned a

greplicate :: Integer -> Ned a -> Ned a

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

Defined in Data.Algebra.Quaternion

Methods

inv :: Quaternion a -> Quaternion a

greplicate :: Integer -> Quaternion a -> Quaternion a