I am trying to use Functional dependencies to overload a operation on Vector space and its basis (Use the Vector spaces module Math.Algebras.VectorSpace https://hackage.haskell.org/package/HaskellForMaths-0.4.8/docs/Math-Algebras...). I have tried to mimic the example for matrices and vectors from https://wiki.haskell.org/Functional_dependencies https://wiki.haskell.org/Functional_dependencies. I have tried different ways of defining classes and instances, but I do not get it to work. 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)