Safe Haskell	None
Language	Haskell2010

Data.Semigroup.SSet

Description

Actions of semigroup (SSet).

Synopsis

class Semigroup s => SSet s a where
- act :: s -> a -> a
rep :: SSet s a => s -> Endo a
fact :: (Functor f, SSet s a) => s -> f a -> f a
newtype S s = S {
- runS :: s
}

Documentation

class Semigroup s => SSet s a where Source #

A lawful instance should satisfy:

g `act` h `act` a = g <> h `act` a

This is the same as to say that act is a semigroup homomorphism from s to the monoid of endomorphisms of a (i.e. maps from a to a).

Note that if g is a Group then MAct g is simply a GSet, this is because monoids and groups share the same morphisms (a monoid homomorphis between groups necessarily preserves inverses).

Methods

act :: s -> a -> a Source #

Instances

Semigroup s => SSet s s Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> s -> s Source #
SSet s a => SSet s (IO a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> IO a -> IO a Source #
SSet s a => SSet s (Down a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Down a -> Down a Source #
SSet s a => SSet s (Maybe a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Maybe a -> Maybe a Source #
SSet s a => SSet s (Identity a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Identity a -> Identity a Source #
(SSet s a, Ord a) => SSet s (Set a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Set a -> Set a Source #
SSet s a => SSet s (NonEmpty a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> NonEmpty a -> NonEmpty a Source #
SSet s a => SSet s [a] Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> [a] -> [a] Source #
SSet s b => SSet s (a -> b) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a -> b) -> a -> b Source #
SSet s b => SSet s (Either a b) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Either a b -> Either a b Source #
(SSet s a, SSet s b) => SSet s (a, b) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a, b) -> (a, b) Source #
Semigroup m => SSet m (FreeMSet m a) Source #
Instance details Defined in Data.Monoid.MSet Methods act :: m -> FreeMSet m a -> FreeMSet m a Source #
SSet s a => SSet s (Const a b) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Const a b -> Const a b Source #
(SSet s a, SSet s b, SSet s c) => SSet s (a, b, c) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a, b, c) -> (a, b, c) Source #
(Functor f, Functor h, SSet s a) => SSet s (Sum f h a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Sum f h a -> Sum f h a Source #
(Functor f, Functor h, SSet s a) => SSet s (Product f h a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> Product f h a -> Product f h a Source #
(SSet s a, SSet s b, SSet s c, SSet s d) => SSet s (a, b, c, d) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a, b, c, d) -> (a, b, c, d) Source #
(SSet s a, SSet s b, SSet s c, SSet s d, SSet s e) => SSet s (a, b, c, d, e) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a, b, c, d, e) -> (a, b, c, d, e) Source #
(SSet s a, SSet s b, SSet s c, SSet s d, SSet s e, SSet s f) => SSet s (a, b, c, d, e, f) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source #
(SSet s a, SSet s b, SSet s c, SSet s d, SSet s e, SSet s f, SSet s h) => SSet s (a, b, c, d, e, f, h) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a, b, c, d, e, f, h) -> (a, b, c, d, e, f, h) Source #
(SSet s a, SSet s b, SSet s c, SSet s d, SSet s e, SSet s f, SSet s h, SSet s i) => SSet s (a, b, c, d, e, f, h, i) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: s -> (a, b, c, d, e, f, h, i) -> (a, b, c, d, e, f, h, i) Source #
SSet s a => SSet (Identity s) a Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: Identity s -> a -> a Source #
SSet (Endo a) a Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: Endo a -> a -> a Source #
Group g => SSet (Sum Integer) g Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: Sum Integer -> g -> g Source #
Num s => SSet (Sum s) s Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: Sum s -> s -> s Source #
Monoid s => SSet (Sum Natural) s Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: Sum Natural -> s -> s Source #
Num s => SSet (Product s) s Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: Product s -> s -> s Source #
SSet s a => SSet (S s) (Endo a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: S s -> Endo a -> Endo a Source #

rep :: SSet s a => s -> Endo a Source #

fact :: (Functor f, SSet s a) => s -> f a -> f a Source #

Any SSet wrapped in a functor is a valid SSet.

newtype S s Source #

A newtype wrapper to avoid overlapping instances.

Constructors

S
Fields runS :: s

Instances

Eq s => Eq (S s) Source #
Instance details Defined in Data.Semigroup.SSet Methods (==) :: S s -> S s -> Bool # (/=) :: S s -> S s -> Bool #
Ord s => Ord (S s) Source #
Instance details Defined in Data.Semigroup.SSet Methods compare :: S s -> S s -> Ordering # (<) :: S s -> S s -> Bool # (<=) :: S s -> S s -> Bool # (>) :: S s -> S s -> Bool # (>=) :: S s -> S s -> Bool # max :: S s -> S s -> S s # min :: S s -> S s -> S s #
Show s => Show (S s) Source #
Instance details Defined in Data.Semigroup.SSet Methods showsPrec :: Int -> S s -> ShowS # show :: S s -> String # showList :: [S s] -> ShowS #
Semigroup m => Semigroup (S m) Source #
Instance details Defined in Data.Semigroup.SSet Methods (<>) :: S m -> S m -> S m # sconcat :: NonEmpty (S m) -> S m # stimes :: Integral b => b -> S m -> S m #
Monoid m => Monoid (S m) Source #
Instance details Defined in Data.Semigroup.SSet Methods mempty :: S m # mappend :: S m -> S m -> S m # mconcat :: [S m] -> S m #
SSet s a => SSet (S s) (Endo a) Source #
Instance details Defined in Data.Semigroup.SSet Methods act :: S s -> Endo a -> Endo a Source #
MSet m b => MSet (S m) (Endo b) Source #
Instance details Defined in Data.Monoid.MSet Methods mact :: S m -> Endo b -> Endo b Source #