Safe Haskell	None
Language	Haskell2010

Data.Semigroup.Involutive

Description

Semigroups with involution.

Synopsis

class Semigroup a => Involutive a where
- rev :: a -> a

Documentation

class Semigroup a => Involutive a where Source #

Involutive lies between Semigroup and Group, orthogonally to Monoid. Instances should satisfy the following:

Involution: rev (rev x) = x
Reversal: rev (x <> y) = rev y <> rev x

An Involutive Monoid should additionally satisfy:

Identity: rev mempty = mempty

Note that, in a commutative Semigroup, we could lawfully take rev = id if all else failed. This would be bad, so we have not done so here.

Methods

rev :: a -> a Source #

An "inverse-like" unary operation. Suggestively named rev because the best example (that isn't just a group inverse) is the reverse operation on a sequence type.

Instances

Involutive () Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: () -> () Source #
Involutive Void Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Void -> Void Source #
Involutive ByteString Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: ByteString -> ByteString Source #
Involutive ByteString Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: ByteString -> ByteString Source #
Involutive Text Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Text -> Text Source #
Involutive Text Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Text -> Text Source #
Involutive [a] Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: [a] -> [a] Source #
Involutive a => Involutive (Maybe a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Maybe a -> Maybe a Source #
Involutive p => Involutive (Par1 p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Par1 p -> Par1 p Source #
Involutive a => Involutive (Identity a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Identity a -> Identity a Source #
Involutive a => Involutive (Dual a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Dual a -> Dual a Source #
Num a => Involutive (Sum a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Sum a -> Sum a Source #
Involutive a => Involutive (Down a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Down a -> Down a Source #
Involutive (NonEmpty a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: NonEmpty a -> NonEmpty a Source #
Involutive (Seq a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Seq a -> Seq a Source #
Unbox a => Involutive (Vector a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Vector a -> Vector a Source #
Storable a => Involutive (Vector a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Vector a -> Vector a Source #
Prim a => Involutive (Vector a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Vector a -> Vector a Source #
Involutive (Vector a) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Vector a -> Vector a Source #
Involutive b => Involutive (a -> b) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: (a -> b) -> a -> b Source #
Involutive (V1 p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: V1 p -> V1 p Source #
Involutive (U1 p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: U1 p -> U1 p Source #
(Involutive a, Involutive b) => Involutive (a, b) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: (a, b) -> (a, b) Source #
Involutive a => Involutive (Op a b) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Op a b -> Op a b Source #
Involutive (Proxy s) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Proxy s -> Proxy s Source #
Involutive (f p) => Involutive (Rec1 f p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Rec1 f p -> Rec1 f p Source #
(Involutive a, Involutive b, Involutive c) => Involutive (a, b, c) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: (a, b, c) -> (a, b, c) Source #
Involutive a => Involutive (Const a b) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: Const a b -> Const a b Source #
Involutive c => Involutive (K1 i c p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: K1 i c p -> K1 i c p Source #
(Involutive (f p), Involutive (g p)) => Involutive ((f :*: g) p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: (f :: g) p -> (f :: g) p Source #
(Involutive a, Involutive b, Involutive c, Involutive d) => Involutive (a, b, c, d) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: (a, b, c, d) -> (a, b, c, d) Source #
Involutive (f p) => Involutive (M1 i c f p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: M1 i c f p -> M1 i c f p Source #
Involutive (f (g p)) => Involutive ((f :.: g) p) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: (f :.: g) p -> (f :.: g) p Source #
(Involutive a, Involutive b, Involutive c, Involutive d, Involutive e) => Involutive (a, b, c, d, e) Source #
Instance details Defined in Data.Semigroup.Involutive Methods rev :: (a, b, c, d, e) -> (a, b, c, d, e) Source #