[Haskell-beginners] class and instance question

[Walck, Scott]

Hi folks,

I'm trying to make doubles and triples act like vectors, as in

(3,4) <+> (7,8) ==> (10,12)
(3,2,1) <+> (9,8,7) ==> (12,10,8)
6 *> (1,2,3) ==> (6,12,18)

I thought I should make a type class so that I could use <+> for both double addition and triple addition,
and *> for both double and triple scalar multiplication.  (Some of this functionality is provided by
NumericPrelude, but I didn't need all of that, and I hoped this would be simple to write.)
The code below gives the error

NewVectorShort.hs:19:0:
    Type synonym `Vector2D' should have 1 argument, but has been given 0
    In the instance declaration for `BasicVector Vector2D'
Failed, modules loaded: none.

I don't understand how what I'm trying to do is different from, say, the Monad instance for Maybe.
(Maybe a) is a type, and (Vector2D a) is a type.

Thanks,

Scott



{-# LANGUAGE TypeSynonymInstances #-}

infixl 6 <+>
infixl 6 <->
infixl 7 *>
infixl 7 <*

class BasicVector v where
    (<+>) :: v a -> v a -> v a
    (<->) :: v a -> v a -> v a
    (*>)  :: Num a => a -> v a -> v a
    (<*)  :: Num a => v a -> a -> v a
    v1 <-> v2 = v1 <+> fromInteger (-1) *> v2
    v1 <* c = c *> v1
    c *> v1 = v1 <* c

type Vector2D a = (a,a)

instance BasicVector Vector2D where
    (ax,ay) <+> (bx,by) = (ax+bx,ay+by)
    c *> (ax,ay) = (c*ax,c*ay)