Copyright	(c) Alice Rixte 2025
License	BSD 3
Maintainer	alice.rixte@u-bordeaux.fr
Stability	unstable
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell2010

Data.Semidirect.Strict

Description

Semidirect products for left and right actions.

For a lazy version, see Lazy.

Usage :

>>> import Data.Semigroup
>>> LSemidirect (Sum 1) (Product 2) <> LSemidirect (Sum (3 :: Int)) (Product (4 :: Int))
LSemidirect {lactee = Sum {getSum = 7}, lactor = Product {getProduct = 8}}

Property checking :

There is a Semigroup instance for LSemidirect (resp. RSemidirect) only if there is a LActSgMorph (resp. RActSgMorph) instance. For example, Sum Int acting on itself is not a semigroup action by morphism and therefore the semidirect product is not associative :

>>> LSemidirect (Sum 1) (Sum 2) <> LSemidirect (Sum (3 :: Int)) (Sum (4 :: Int))
No instance for `LActDistrib (Sum Int) (Sum Int)'
  arising from a use of `<>'

Synopsis

data LSemidirect x s = LSemidirect {
- lactee :: !x
- lactor :: !s
}
lerase :: Monoid x => LSemidirect x s -> LSemidirect x s
lforget :: Monoid s => LSemidirect x s -> LSemidirect x s
lembedActee :: Monoid s => x -> LSemidirect x s
lembedActor :: Monoid x => s -> LSemidirect x s
lfromPair :: (x, s) -> LSemidirect x s
data RSemidirect x s = RSemidirect {
- ractee :: !x
- ractor :: !s
}
rerase :: Monoid x => RSemidirect x s -> RSemidirect x s
rforget :: Monoid s => RSemidirect x s -> RSemidirect x s
rembedActee :: Monoid s => x -> RSemidirect x s
rembedActor :: Monoid x => s -> RSemidirect x s
rfromPair :: (x, s) -> RSemidirect x s

Documentation

data LSemidirect x s Source #

A semi-direct product for a left action, where s acts on x

Constructors

LSemidirect
Fields lactee :: !x The value being acted on lactor :: !s The acting element

Instances

Instances details

Bifunctor LSemidirect Source #
Instance details Defined in Data.Semidirect.Strict Methods bimap :: (a -> b) -> (c -> d) -> LSemidirect a c -> LSemidirect b d # first :: (a -> b) -> LSemidirect a c -> LSemidirect b c # second :: (b -> c) -> LSemidirect a b -> LSemidirect a c #
Functor (LSemidirect x) Source #
Instance details Defined in Data.Semidirect.Strict Methods fmap :: (a -> b) -> LSemidirect x a -> LSemidirect x b # (<$) :: a -> LSemidirect x b -> LSemidirect x a #
LActMnMorph x s => Monoid (LSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods mempty :: LSemidirect x s # mappend :: LSemidirect x s -> LSemidirect x s -> LSemidirect x s # mconcat :: [LSemidirect x s] -> LSemidirect x s #
LActSgMorph x s => Semigroup (LSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods (<>) :: LSemidirect x s -> LSemidirect x s -> LSemidirect x s # sconcat :: NonEmpty (LSemidirect x s) -> LSemidirect x s # stimes :: Integral b => b -> LSemidirect x s -> LSemidirect x s #
(Read x, Read s) => Read (LSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods readsPrec :: Int -> ReadS (LSemidirect x s) # readList :: ReadS [LSemidirect x s] # readPrec :: ReadPrec (LSemidirect x s) # readListPrec :: ReadPrec [LSemidirect x s] #
(Show x, Show s) => Show (LSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods showsPrec :: Int -> LSemidirect x s -> ShowS # show :: LSemidirect x s -> String # showList :: [LSemidirect x s] -> ShowS #
(Eq x, Eq s) => Eq (LSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods (==) :: LSemidirect x s -> LSemidirect x s -> Bool # (/=) :: LSemidirect x s -> LSemidirect x s -> Bool #

lerase :: Monoid x => LSemidirect x s -> LSemidirect x s Source #

Erase the actee (i.e. replace it with mempty).

lforget :: Monoid s => LSemidirect x s -> LSemidirect x s Source #

Forget the actor (i.e. replace it with mempty).

lembedActee :: Monoid s => x -> LSemidirect x s Source #

Make a semidirect pair whose actor is mempty.

lembedActor :: Monoid x => s -> LSemidirect x s Source #

Make a semidirect pair whose actee is mempty.

lfromPair :: (x, s) -> LSemidirect x s Source #

Convert a pair into a semidirect product element.

data RSemidirect x s Source #

A semidirect product for a right action, where s acts on x

Constructors

RSemidirect
Fields ractee :: !x The value being acted on ractor :: !s The acting element

Instances

Instances details

Bifunctor RSemidirect Source #
Instance details Defined in Data.Semidirect.Strict Methods bimap :: (a -> b) -> (c -> d) -> RSemidirect a c -> RSemidirect b d # first :: (a -> b) -> RSemidirect a c -> RSemidirect b c # second :: (b -> c) -> RSemidirect a b -> RSemidirect a c #
Functor (RSemidirect x) Source #
Instance details Defined in Data.Semidirect.Strict Methods fmap :: (a -> b) -> RSemidirect x a -> RSemidirect x b # (<$) :: a -> RSemidirect x b -> RSemidirect x a #
RActMnMorph x s => Monoid (RSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods mempty :: RSemidirect x s # mappend :: RSemidirect x s -> RSemidirect x s -> RSemidirect x s # mconcat :: [RSemidirect x s] -> RSemidirect x s #
RActSgMorph x s => Semigroup (RSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods (<>) :: RSemidirect x s -> RSemidirect x s -> RSemidirect x s # sconcat :: NonEmpty (RSemidirect x s) -> RSemidirect x s # stimes :: Integral b => b -> RSemidirect x s -> RSemidirect x s #
(Read x, Read s) => Read (RSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods readsPrec :: Int -> ReadS (RSemidirect x s) # readList :: ReadS [RSemidirect x s] # readPrec :: ReadPrec (RSemidirect x s) # readListPrec :: ReadPrec [RSemidirect x s] #
(Show x, Show s) => Show (RSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods showsPrec :: Int -> RSemidirect x s -> ShowS # show :: RSemidirect x s -> String # showList :: [RSemidirect x s] -> ShowS #
(Eq x, Eq s) => Eq (RSemidirect x s) Source #
Instance details Defined in Data.Semidirect.Strict Methods (==) :: RSemidirect x s -> RSemidirect x s -> Bool # (/=) :: RSemidirect x s -> RSemidirect x s -> Bool #

rerase :: Monoid x => RSemidirect x s -> RSemidirect x s Source #

Erase the actee (i.e. replace it with mempty).

rforget :: Monoid s => RSemidirect x s -> RSemidirect x s Source #

Forget the actor (i.e. replace it with mempty).

rembedActee :: Monoid s => x -> RSemidirect x s Source #

Make a semidirect pair whose actor element is mempty .

rembedActor :: Monoid x => s -> RSemidirect x s Source #

Make a semidirect pair whose actee is mempty.

rfromPair :: (x, s) -> RSemidirect x s Source #

Convert a pair into a semidirect product element