Module.hs

{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Ring.Module
-- Copyright   :  (c) Edward Kmett 2009
-- License     :  BSD-style
-- Maintainer  :  ekmett@gmail.com
-- Stability   :  experimental
-- Portability :  non-portable (MPTCs)
--
-- Left- and right- modules over rings, semirings, and Seminearrings.
-- To avoid a proliferation of classes. These only require that there
-- be an addition and multiplication operation for the 'Ring'
--
-----------------------------------------------------------------------------

module Data.Ring.Module 
    ( module Data.Ring
    , LeftModule
    , (*.)
    , RightModule
    , (.*)
    , Module
    ) where

import Data.Ring
-- import qualified Data.Monoid.Combinators as Monoid

-- | @ (x * y) *. m = x * (y *. m) @
class (Monoid r, Multiplicative r, Monoid m) => LeftModule r m where
    (*.) :: r -> m -> m
    
-- | @ (m .* x) * y = m .* (x * y) @
class (Monoid r, Multiplicative r, Monoid m) => RightModule r m where
    (.*) :: m -> r -> m

-- | @ (x *. m) .* y = x *. (m .* y) @
class (LeftModule r m, RightModule r m) => Module r m 

instance (LeftModule r m, LeftModule r n) => LeftModule r (m,n) where
    r *. (m,n) = (r *. m, r *. n)
instance (LeftModule r m, LeftModule r n, LeftModule r o) => LeftModule r (m,n,o) where
    r *. (m,n,o) = (r *. m, r *. n, r *. o)
instance (LeftModule r m, LeftModule r n, LeftModule r o, LeftModule r p) => LeftModule r (m,n,o,p) where
    r *. (m,n,o,p) = (r *. m, r *. n, r *. o, r *. p)
instance (LeftModule r m, LeftModule r n, LeftModule r o, LeftModule r p, LeftModule r q) => LeftModule r (m,n,o,p,q) where
    r *. (m,n,o,p,q) = (r *. m, r *. n, r *. o, r *. p, r *. q)

instance (RightModule r m, RightModule r n) => RightModule r (m,n) where
    (m,n) .* r = (m .* r, n .* r)
instance (RightModule r m, RightModule r n, RightModule r o) => RightModule r (m,n,o) where
    (m,n,o) .* r = (m .* r, n .* r, o .* r)
instance (RightModule r m, RightModule r n, RightModule r o, RightModule r p ) => RightModule r (m,n,o,p) where
    (m,n,o,p) .* r = (m .* r, n .* r, o .* r, p .* r)
instance (RightModule r m, RightModule r n, RightModule r o, RightModule r p, RightModule r q ) => RightModule r (m,n,o,p,q) where
    (m,n,o,p,q) .* r = (m .* r, n .* r, o .* r, p .* r, q .* r)

instance (Module r m, Module r n) => Module r (m,n)
instance (Module r m, Module r n, Module r o) => Module r (m,n,o)
instance (Module r m, Module r n, Module r o, Module r p) => Module r (m,n,o,p)
instance (Module r m, Module r n, Module r o, Module r p, Module r q) => Module r (m,n,o,p,q)