-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Haskell 98 groups
--   
--   Haskell 98 groups. A group is a monoid with invertibility.
@package groups
@version 0.3.0.0

module Data.Group

-- | A <a>Group</a> is a <a>Monoid</a> plus a function, <a>invert</a>, such
--   that:
--   
--   <pre>
--   a &lt;&gt; invert a == mempty
--   </pre>
--   
--   <pre>
--   invert a &lt;&gt; a == mempty
--   </pre>
class Monoid m => Group m
invert :: Group m => m -> m

-- | An <a>Abelian</a> group is a <a>Group</a> that follows the rule:
--   
--   <pre>
--   a &lt;&gt; b == b &lt;&gt; a
--   </pre>
class Group g => Abelian g
instance (Abelian a, Abelian b, Abelian c, Abelian d, Abelian e) => Abelian (a, b, c, d, e)
instance (Abelian a, Abelian b, Abelian c, Abelian d) => Abelian (a, b, c, d)
instance (Abelian a, Abelian b, Abelian c) => Abelian (a, b, c)
instance (Abelian a, Abelian b) => Abelian (a, b)
instance Abelian b => Abelian (a -> b)
instance Abelian a => Abelian (Dual a)
instance Fractional a => Abelian (Product a)
instance Num a => Abelian (Sum a)
instance Abelian ()
instance (Group a, Group b, Group c, Group d, Group e) => Group (a, b, c, d, e)
instance (Group a, Group b, Group c, Group d) => Group (a, b, c, d)
instance (Group a, Group b, Group c) => Group (a, b, c)
instance (Group a, Group b) => Group (a, b)
instance Group b => Group (a -> b)
instance Group a => Group (Dual a)
instance Fractional a => Group (Product a)
instance Num a => Group (Sum a)
instance Group ()