[Haskell-cafe] more generic class instances?

[Christopher Howard]

Hi. I am playing around with basic Haskell overloading. What I'm 
interested in is how to do specialization in Haskell -- i.e., functions 
that work generically on all (or many) types but work more efficiently 
on certain types. So, I am trying to make a class of functions which can 
be fed into a partial sum calculator. Maybe something like so:

class PartialSum f where
     -- params: term function, end index
     partialSum :: Integral b => f -> b -> a

The most generic instance would be any function that takes an integer 
and returns a number. The specialized instances would things like, say, 
a wrapped function which is guaranteed to be linear (through safe 
constructors or something). But I'm having trouble figuring out how even 
to make the generic version. I'm thinking something like this:

instance PartialSum (a -> b) where
     partialSum f n = foldl (\u v -> u + f v) 0 [1..n]

But the compiler complains it can't prove that the input to the "f" 
function is the same type as the "n" parameter. That makes sense, but 
I'm not sure how to fix that.