Haskell: Num instance of non-concrete type

Question

data Vector a = Vector a a a deriving (Eq, Show)

instance Functor Vector where
    fmap f (Vector x y z) = Vector (f x) (f y) (f z)

So far so good.

instance Num ((Num a) => Vector a) where
    negate = fmap negate

Doesn't work. I tried many different variations on that first line but GHC keeps complaining. I want to make a Vector containing numbers an instance of Num ; surely this should be possible? Otherwise I would have to make an instance for Int , Integer , Float , Double , etc. all with the same definition.

Answer 1

instance Num a => Num (Vector a) where
   negate = fmap negate

Consider writing other methods too.

(You can write deriving (Eq, Show, Functor) if you turn on -XDeriveFunctor .)

Answer 2

It is probably a bad idea to make Vector an instance of Num . Here's the declaration of Num :

class Num a where
  (+) :: a -> a -> a
  (*) :: a -> a -> a
  (-) :: a -> a -> a
  negate :: a -> a
  abs :: a -> a
  signum :: a -> a
  fromInteger :: Integer -> a

+ and - and negate are no problem. One can define * as cross product, but only for 3-vectors, and this is really stretching it. abs , signum and fromInteger have no meaningful definitions.

In short, it is possible to shoehorn Vector into Num , but the result is not nice.

You may want to explore alternative type class hierarchies which replace the standard Prelude ones, eg the Numeric prelude .