free-algebras-0.0.6.0: Free algebras in Haskell.

Data.Semigroup.SSet

Description

Actions of semigroup (SSet).

Synopsis

# 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 detailsDefined in Data.Semigroup.SSet Methodsact :: s -> s -> s Source # SSet s a => SSet s (IO a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> IO a -> IO a Source # SSet s a => SSet s (Down a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> Down a -> Down a Source # SSet s a => SSet s (Maybe a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> Maybe a -> Maybe a Source # SSet s a => SSet s (Identity a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> Identity a -> Identity a Source # (SSet s a, Ord a) => SSet s (Set a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> Set a -> Set a Source # SSet s a => SSet s (NonEmpty a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> NonEmpty a -> NonEmpty a Source # SSet s a => SSet s [a] Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> [a] -> [a] Source # SSet s b => SSet s (a -> b) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> (a -> b) -> a -> b Source # SSet s b => SSet s (Either a b) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> Either a b -> Either a b Source # (SSet s a, SSet s b) => SSet s (a, b) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> (a, b) -> (a, b) Source # Semigroup m => SSet m (FreeMSet m a) Source # Instance detailsDefined in Data.Monoid.MSet Methodsact :: m -> FreeMSet m a -> FreeMSet m a Source # SSet s a => SSet s (Const a b) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> Const a b -> Const a b Source # (SSet s a, SSet s b, SSet s c) => SSet s (a, b, c) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: s -> (a, b, c) -> (a, b, c) Source # (Functor f, Functor h, SSet s a) => SSet s (Sum f h a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: 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 detailsDefined in Data.Semigroup.SSet Methodsact :: 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 detailsDefined in Data.Semigroup.SSet Methodsact :: 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 detailsDefined in Data.Semigroup.SSet Methodsact :: 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 detailsDefined in Data.Semigroup.SSet Methodsact :: 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 detailsDefined in Data.Semigroup.SSet Methodsact :: 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 detailsDefined in Data.Semigroup.SSet Methodsact :: 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 detailsDefined in Data.Semigroup.SSet Methodsact :: Identity s -> a -> a Source # SSet (Endo a) a Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: Endo a -> a -> a Source # Group g => SSet (Sum Integer) g Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: Sum Integer -> g -> g Source # Num s => SSet (Sum s) s Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: Sum s -> s -> s Source # Monoid s => SSet (Sum Natural) s Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: Sum Natural -> s -> s Source # Num s => SSet (Product s) s Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: Product s -> s -> s Source # SSet s a => SSet (S s) (Endo a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: 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 FieldsrunS :: s
Instances
 Eq s => Eq (S s) Source # Instance detailsDefined in Data.Semigroup.SSet Methods(==) :: S s -> S s -> Bool #(/=) :: S s -> S s -> Bool # Ord s => Ord (S s) Source # Instance detailsDefined in Data.Semigroup.SSet Methodscompare :: 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 detailsDefined in Data.Semigroup.SSet MethodsshowsPrec :: Int -> S s -> ShowS #show :: S s -> String #showList :: [S s] -> ShowS # Semigroup m => Semigroup (S m) Source # Instance detailsDefined 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 detailsDefined in Data.Semigroup.SSet Methodsmempty :: S m #mappend :: S m -> S m -> S m #mconcat :: [S m] -> S m # SSet s a => SSet (S s) (Endo a) Source # Instance detailsDefined in Data.Semigroup.SSet Methodsact :: S s -> Endo a -> Endo a Source # MSet m b => MSet (S m) (Endo b) Source # Instance detailsDefined in Data.Monoid.MSet Methodsmact :: S m -> Endo b -> Endo b Source #