[Haskell] Instance declaration of classes with method type constraints

[Johan Holmquist]

> This type declaration for 'm' probably doesn't mean what you think it
> does.  I think what you want is "m takes an item of type 'a' and returns
> an item of a particular type in the Num class, but I'm not going to tell
> you which one", but what this declaration really means "m takes an item
> of type 'a' and will return an item of any type you wish, so long as it
> is in the Num class".
>
> In this context 'a' and 'b' are very different kinds of type variables:
> 'a' is fixed, but 'b' is universally quantified.

Thank you Mr. Dockins for pointing that out, now I understand (I think) why my 
attempts failed.

> [ ... ]
> {-# OPTIONS -fglasgow-exts #-}
> class Num b => Rect a b | a -> b where
>      width :: a -> b
>      height :: a -> b
>
> instance Rect IRect Int where
>     width  ( IRect (x1, _ ) (x2, _ ) ) = abs(x2 - x1)
>     height ( IRect ( _, y1) ( _, y2) ) = abs(y2 - y1)

This works perfectly!

Anyone:

However, I haven't been able to make PRect an instance of this class (with 
extensions). I might not have grasped this yet, but I came to think; if the 
old class declaration would say that "width" and "height" returns something 
with unfixed type in the "Num" class, then wouldn't it be possible to make 
PRect an instance of that class (since PRect has a type parameter)?

Something like this:

class Rect a where
	width  :: (Num b) => a -> b
	height :: (Num b) => a -> b

data Num a => PRect a = PRect (a, a) (a, a) deriving (Eq, Show)

instance Rect PRect a where ...

This (as well as my other attemps) fail with a "Kind error: `PRect' is not 
applied to enough type arguments" - error. Is there a way to do it, or am I 
lost here?

regards
/johan