Data.Semigroup.Involutive

Semigroups with involution.

Documentation

class Semigroup a => Involutive a where

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

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 ()

Defined in Data.Semigroup.Involutive

Methods

rev :: () -> ()

Involutive Void

Defined in Data.Semigroup.Involutive

Methods

rev :: Void -> Void

Involutive ByteString

Defined in Data.Semigroup.Involutive

Methods

rev :: ByteString -> ByteString

Involutive ByteString

Defined in Data.Semigroup.Involutive

Methods

rev :: ByteString -> ByteString

Involutive Text

Defined in Data.Semigroup.Involutive

Methods

rev :: Text -> Text

Involutive Text

Defined in Data.Semigroup.Involutive

Methods

rev :: Text -> Text

Involutive [a]

Defined in Data.Semigroup.Involutive

Methods

rev :: [a] -> [a]

Involutive a => Involutive (Maybe a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Maybe a -> Maybe a

Involutive p => Involutive (Par1 p)

Defined in Data.Semigroup.Involutive

Methods

rev :: Par1 p -> Par1 p

Involutive a => Involutive (Identity a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Identity a -> Identity a

Involutive a => Involutive (Dual a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Dual a -> Dual a

Num a => Involutive (Sum a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Sum a -> Sum a

Involutive a => Involutive (Down a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Down a -> Down a

Involutive (NonEmpty a)

Defined in Data.Semigroup.Involutive

Methods

rev :: NonEmpty a -> NonEmpty a

Involutive (Seq a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Seq a -> Seq a

Unbox a => Involutive (Vector a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Vector a -> Vector a

Storable a => Involutive (Vector a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Vector a -> Vector a

Prim a => Involutive (Vector a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Vector a -> Vector a

Involutive (Vector a)

Defined in Data.Semigroup.Involutive

Methods

rev :: Vector a -> Vector a

Involutive b => Involutive (a -> b)

Defined in Data.Semigroup.Involutive

Methods

rev :: (a -> b) -> a -> b

Involutive (V1 p)

Defined in Data.Semigroup.Involutive

Methods

rev :: V1 p -> V1 p

Involutive (U1 p)

Defined in Data.Semigroup.Involutive

Methods

rev :: U1 p -> U1 p

(Involutive a, Involutive b) => Involutive (a, b)

Defined in Data.Semigroup.Involutive

Methods

rev :: (a, b) -> (a, b)

Involutive a => Involutive (Op a b)

Defined in Data.Semigroup.Involutive

Methods

rev :: Op a b -> Op a b

Involutive (Proxy s)

Defined in Data.Semigroup.Involutive

Methods

rev :: Proxy s -> Proxy s

Involutive (f p) => Involutive (Rec1 f p)

Defined in Data.Semigroup.Involutive

Methods

rev :: Rec1 f p -> Rec1 f p

(Involutive a, Involutive b, Involutive c) => Involutive (a, b, c)

Defined in Data.Semigroup.Involutive

Methods

rev :: (a, b, c) -> (a, b, c)

Involutive a => Involutive (Const a b)

Defined in Data.Semigroup.Involutive

Methods

rev :: Const a b -> Const a b

Involutive c => Involutive (K1 i c p)

Defined in Data.Semigroup.Involutive

Methods

rev :: K1 i c p -> K1 i c p

(Involutive (f p), Involutive (g p)) => Involutive ((f :*: g) p)

Defined in Data.Semigroup.Involutive

Methods

rev :: (f :*: g) p -> (f :*: g) p

(Involutive a, Involutive b, Involutive c, Involutive d) => Involutive (a, b, c, d)

Defined in Data.Semigroup.Involutive

Methods

rev :: (a, b, c, d) -> (a, b, c, d)

Involutive (f p) => Involutive (M1 i c f p)

Defined in Data.Semigroup.Involutive

Methods

rev :: M1 i c f p -> M1 i c f p

Involutive (f (g p)) => Involutive ((f :.: g) p)

Defined in Data.Semigroup.Involutive

Methods

rev :: (f :.: g) p -> (f :.: g) p

(Involutive a, Involutive b, Involutive c, Involutive d, Involutive e) => Involutive (a, b, c, d, e)

Defined in Data.Semigroup.Involutive

Methods

rev :: (a, b, c, d, e) -> (a, b, c, d, e)