{-# LANGUAGE ConstraintKinds        #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE MultiParamTypeClasses  #-}
{-# LANGUAGE TypeFamilies           #-}

module LinearAlgebra.TypedSpaces.Classes
       ( Isomorphism  (..)
       , CZippable    (..)
       , CIndexed     (..)
       , IsList       (..)
       , module CC ) where

import GHC.Exts (IsList (..), Constraint)
import Control.ConstraintClasses as CC

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class Isomorphism a b where
  fw :: a -> b
  bw :: b -> a

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class CFunctor f => CZippable f where

  czipWith :: (CFun f a, CFun f b, CFun f c)
          => (a -> b -> c) -> f a -> f b -> f c

  czipWith3 :: (CFun f a, CFun f b, CFun f c, CFun f d)
            => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

  czipWith4 :: (CFun f a, CFun f b, CFun f c, CFun f d, CFun f e)
            => (a -> b -> c -> d -> e) -> f a -> f b -> f c -> f d -> f e

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class CFunctor f => CIndexed f i | f -> i where
  type CInd f a :: Constraint
  type CInd f a = ()

  (!) :: (CFun f a, CInd f a) => f a -> i -> a

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