Algebra

Documentation

class Semigroup a => Abelian a

class Semigroup a => Idempotent a

class Monoid a => Group a where

Minimal complete definition

invert

Methods

invert :: a -> a

Instances

Group ()

Methods

invert :: () -> ()

Group a => Group (IO a)

Methods

invert :: IO a -> IO a

Group a => Group (Identity a)

Methods

invert :: Identity a -> Identity a

Group a => Group (Dual a)

Methods

invert :: Dual a -> Dual a

Group (Sum Integer)

Methods

invert :: Sum Integer -> Sum Integer

Group b => Group (a -> b)

Methods

invert :: (a -> b) -> a -> b

(Group a, Group b) => Group (a, b)

Methods

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

Group (Proxy k a)

Methods

invert :: Proxy k a -> Proxy k a

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

Methods

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

Group a => Group (Const k a b)

Methods

invert :: Const k a b -> Const k a b

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

Methods

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

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

Methods

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

(+) :: Semigroup (Sum a) => a -> a -> a

(-) :: (Semigroup (Sum a), Group (Sum a)) => a -> a -> a

(*) :: Semigroup (Product a) => a -> a -> a

(/) :: (Semigroup (Product a), Group (Product a)) => a -> a -> a