{-# LANGUAGE KindSignatures, GADTs, TypeFamilies, TypeOperators, MultiParamTypeClasses, DataKinds #-}

import Control.Applicative
import Data.Traversable (Traversable)

class (Applicative f, Traversable f) => Dim f

class Shapely (fs :: [* -> *])
instance Shapely '[]
instance (Dim f, Shapely fs) => Shapely (f ': fs)

-------------------------------------
--            Hypercuboid datatype
-------------------------------------
data Hyper :: [* -> *] -> * -> * where
    Scalar :: a -> Hyper '[] a
    Prism  :: (Dim f, Shapely fs) => 
                Hyper fs (f a) -> Hyper (f ': fs) a

instance Functor (Hyper fs) where
    fmap f (Scalar a) = Scalar $ f a
    fmap f (Prism p)  = Prism $ fmap (fmap f) p

instance Applicative (Hyper fs) where
    pure a = undefined 
{- `pure a = Scalar a` gives:
            Couldn't match type ‘fs’ with ‘'[]’
                  ‘fs’ is a rigid type variable bound by
                       the instance declaration
            Expected type: Hyper fs a
              Actual type: Hyper '[] a
-}

main = print 42