[Haskell-beginners] class and instance question

[Brent Yorgey]

On Thu, May 20, 2010 at 06:35:34AM -0400, Walck, Scott wrote:
> Hi folks,
> 
> 
> 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.

The problem is simply that type synonyms must always be fully applied, so given

  type Vector2D a = (a,a)

you cannot declare an instance for Vector2D, since Vector2D is not
applied to an argument.  The solution is to make Vector2D a newtype:

  newtype Vector2D a = V2D (a,a)

Of course, this means you'll need to wrap and unwrap V2D constructors
in various places, which can be a bit annoying, but such is the price
of progress.

For another take on encoding vector stuff in Haskell, see the
vector-space package on Hackage.

-Brent

> 
> 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)
> 
> 
> 
> 
> 
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