Internally in programs I will use the specific functions for each case. But I want some «syntactic sugar» for this functions when doing direct calculations in for example ghci. It will be more user friendly for direct interaction not to have four different functions that in practice do the same thing. Kristoffer

Date: Sun, 28 Feb 2016 21:11:20 +0000 From: Tom Ellis mailto:tom-lists-haskell-cafe-2013@jaguarpaw.co.uk> To: haskell-cafe@haskell.org mailto:haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] Functional dependencies and overloading of operation Message-ID: <20160228211120.GB23479@weber> Content-Type: text/plain; charset=iso-8859-1

On Sun, Feb 28, 2016 at 10:00:42PM +0100, Kristoffer F?llesdal wrote:

...

I am trying to use Functional dependencies to overload a operation on Vector space and its basis [...] 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

This is unlikely to be a good idea in practice. Is there a good reason you can't use four different names for these operations?

Date: Sun, 28 Feb 2016 22:00:42 +0100 From: Kristoffer F?llesdal mailto:kfollesdal@gmail.com> To: haskell-cafe@haskell.org mailto:haskell-cafe@haskell.org Subject: [Haskell-cafe] Functional dependencies and overloading of operation Message-ID: <84F1908D-05B0-4EAE-9CB7-50847BD65344@gmail.com mailto:84F1908D-05B0-4EAE-9CB7-50847BD65344@gmail.com> Content-Type: text/plain; charset="utf-8"

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... 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 <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)