module Data.Quasigroup
    ( module Data.Magma
    , Quasigroup (..)
    ) where

import Control.Applicative
import Data.Magma

-- | A 'Quasigroup' is a nonempty 'Magma' with left and right
--   division.
class Magma q => Quasigroup q where

    -- | Left division. @y = x + (x `leftDivide` y)@ and @y = x
    --   `leftDivide` (x + y)@.
    leftDivide :: q -> q -> q

    -- | Right division. @y = (y `rightDivide` x) + x@ and @y = (y +
    --   x) `rightDivide` x@.
    rightDivide :: q -> q -> q

instance Quasigroup b => Quasigroup (a -> b) where
    leftDivide = map2 leftDivide
    rightDivide = map2 rightDivide