Data.Semigroup.SSet

Actions of semigroup (SSet).

Documentation

class Semigroup s => SSet s a where

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).

Minimal complete definition

act

Methods

act :: s -> a -> a

Instances

Semigroup s => SSet s s

Defined in Data.Semigroup.SSet

Methods

act :: s -> s -> s

SSet s a => SSet s (IO a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> IO a -> IO a

SSet s a => SSet s (Down a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Down a -> Down a

SSet s a => SSet s (Maybe a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Maybe a -> Maybe a

SSet s a => SSet s (Identity a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Identity a -> Identity a

(SSet s a, Ord a) => SSet s (Set a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Set a -> Set a

SSet s a => SSet s (NonEmpty a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> NonEmpty a -> NonEmpty a

SSet s a => SSet s [a]

Defined in Data.Semigroup.SSet

Methods

act :: s -> [a] -> [a]

SSet s b => SSet s (a -> b)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a -> b) -> a -> b

SSet s b => SSet s (Either a b)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Either a b -> Either a b

(SSet s a, SSet s b) => SSet s (a, b)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a, b) -> (a, b)

Semigroup m => SSet m (FreeMSet m a)

Defined in Data.Monoid.MSet

Methods

act :: m -> FreeMSet m a -> FreeMSet m a

SSet s a => SSet s (Const a b)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Const a b -> Const a b

(SSet s a, SSet s b, SSet s c) => SSet s (a, b, c)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a, b, c) -> (a, b, c)

(Functor f, Functor h, SSet s a) => SSet s (Sum f h a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Sum f h a -> Sum f h a

(Functor f, Functor h, SSet s a) => SSet s (Product f h a)

Defined in Data.Semigroup.SSet

Methods

act :: s -> Product f h a -> Product f h a

(SSet s a, SSet s b, SSet s c, SSet s d) => SSet s (a, b, c, d)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a, b, c, d) -> (a, b, c, d)

(SSet s a, SSet s b, SSet s c, SSet s d, SSet s e) => SSet s (a, b, c, d, e)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a, b, c, d, e) -> (a, b, c, d, e)

(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)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)

(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)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a, b, c, d, e, f, h) -> (a, b, c, d, e, f, h)

(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)

Defined in Data.Semigroup.SSet

Methods

act :: s -> (a, b, c, d, e, f, h, i) -> (a, b, c, d, e, f, h, i)

SSet s a => SSet (Identity s) a

Defined in Data.Semigroup.SSet

Methods

act :: Identity s -> a -> a

SSet (Endo a) a

Defined in Data.Semigroup.SSet

Methods

act :: Endo a -> a -> a

Group g => SSet (Sum Integer) g

Defined in Data.Semigroup.SSet

Methods

act :: Sum Integer -> g -> g

Monoid s => SSet (Sum Natural) s

Defined in Data.Semigroup.SSet

Methods

act :: Sum Natural -> s -> s

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

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

Any SSet wrapped in a functor is a valid SSet.