[Haskell-beginners] Instance declaration needs more info?

[Dimitri DeFigueiredo]

Hi All,

I'm trying to write a simplified dimensional library where where 
quantities in meters, seconds and meters/second can all co-exist 
adjusting their respective units when multiplied and/or divided.

Also, meter+meter is allowed, but meter+second should cause the type 
checker to complain.

This is a bit like a *much* simplified version of the Units library. 
However, I am having trouble understanding why my instance declaration 
below appears to be under specified. Here's the code:

------------
module Dimensional where
import qualified Prelude

-- A Group allows you to add and subtract (but not multiply or divide)
class Group a where

     (+) :: a -> a -> a

     (-) :: a -> a -> a
     x - y = x + negate y

     negate              :: a -> a
     negate x             = fromInteger 0 - x

     fromInteger         :: Prelude.Integer -> a

class Unit a where

     (*) :: (Unit a, Unit b, Unit c) => a -> b -> c
     (/) :: (Unit a, Unit b, Unit c) => a -> b -> c
     toDouble :: a -> Prelude.Double

instance Unit Prelude.Double where

     (*) x y    = (Prelude.*) x (toDouble y)   -- <----- Error here
     (/) x y    = (Prelude./) x (toDouble y)
     toDouble x = x

------------
GHC complains as follows:

     Could not deduce (c ~ Prelude.Double)
     from the context (Unit Prelude.Double, Unit b, Unit c)
       bound by the type signature for
                  * :: (Unit Prelude.Double, Unit b, Unit c) =>
                       Prelude.Double -> b -> c
       at /code/haskell/dimensional.hs:25:5-43
       `c' is a rigid type variable bound by
           the type signature for
             * :: (Unit Prelude.Double, Unit b, Unit c) =>
                  Prelude.Double -> b -> c
           at /code/haskell/dimensional.hs:25:5
     In the first argument of `(Prelude.*)', namely `x'
     In the expression: (Prelude.*) x (toDouble y)
     In an equation for `*': * x y = (Prelude.*) x (toDouble y)

Any pointers would be much appreciated!

Thanks,

Dimitri