HLearn-algebra-1.0.0: src/HLearn/Algebra/Structures/Modules.hs

{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}

-- | Modules are a generalization of vector spaces

module HLearn.Algebra.Structures.Modules
    where

import Data.List
import HLearn.Algebra.Structures.Groups

-------------------------------------------------------------------------------
-- Modules

class (Num (Ring m)) => HasRing m where
    type Ring m

-- | Bug: The module classes have the constraint that r be of type Num.  Technically, this should be a Ring.  But creating a Ring class would be awkward because it would conflict with the Num class and require importing a different Prelude.
class (HasRing m, Abelian m, Group m) => Module m where    
    infix 7 .*
    (.*) :: (Ring m) -> m -> m
    
    {-# INLINE (*.) #-}
    infix 7 *.
    (*.) :: m -> (Ring m) -> m
    m *. r = r .* m

-------------------------------------------------------------------------------
-- Vector Spaces

class (Module m, Fractional (Ring m)) => VectorSpace m where
    infix 7 /.
    {-# INLINE (/.) #-}
    (/.) :: m -> (Ring m) -> m
    m /. r = m *. (1/r)

instance (Module m, Fractional (Ring m)) => VectorSpace m