What I want is to have the «same» function for these cases: 

operation :: a -> a -> Vect k a

operation :: a -> Vect k a -> Vect k a

operation :: Vect k a -> a -> Vect k a

operation :: Vect k a -> Vect k a -> Vect k a

Her are som sample code to illustrate what I want. Do anybody have an idea to how to solve it?

{-# LANGUAGE MultiParamTypeClasses #-}

{-# LANGUAGE FlexibleInstances #-}

{-# LANGUAGE FunctionalDependencies #-}

import Math.Algebras.VectorSpace

linearExtension :: (Eq k, Num k, Ord a)

             => (a -> a -> Vect k a) -> Vect k a -> Vect k a -> Vect k a

linearExtension f xs ys = linear (\x -> linear (f x) ys) xs

data Tree t = Root t [Tree t] deriving(Eq, Show, Ord)

op :: (Eq k, Num k, Ord t) => Tree t -> Tree t -> Vect k (Tree t)

op x y = return x <+> return y

opA :: (Eq k, Num k, Ord t) => Vect k (Tree t) -> Vect k (Tree t) -> Vect k (Tree t)

opA = linearExtension op

class Operation a b c | a b -> c where

  (<.>) :: a -> b -> c

instance (Ord t) => Operation (Tree t) (Tree t) (Vect k (Tree t)) where

  (<.>)= op

instance (Ord t) => Operation (Vect k (Tree t)) (Vect k (Tree t)) (Vect k (Tree t)) where

  (<.>) = opA

instance (Ord t) => Operation (Tree t) (Vect k (Tree t)) (Vect k (Tree t)) where

  (<.>) x = opA (return x)

instance (Ord t) => Operation (Vect k (Tree t)) (Tree t) (Vect k (Tree t)) where

  (<.>) x y = opA x (return y)