functions not in type classes

[D. Tweed]

On Fri, 18 Jan 2002, Cagdas Ozgenc wrote:

> Why does Haskell let you write functions that are not a part of type class?

[snip] Responding to the more philosophical bit rather than the concrete
type stuff snipped, I'm not a supporter of the belief that `absolutely
everything in all programs ever written in a language should be object
oriented', which appears to be what your proposal implies. (Maybe I'm
wrong, and I know that, e.g., Ruby supporters disagree with me.) I think
there are lots of components of programming where using object-orientation
ideas make sense and I use them in those areas when writing my C++ and
Haskell programs, but there are also areas where the object orientation
leaves things the same or makes them more contrived than otherwise. For
example, consider a function casually expressed like

--                      fn              derivative     init val  result
newtonRaphson :: (Float -> Float) -> (Float -> Float) -> Float-> Float

OK, it could certainly be generalised to

newtonRaphson :: Floating a=> (a->a)->(a->a)->a->a

easily enough, but to actually make it a type class method you'd need to
make something like

class DifferentiableFloatingSingleVarFn

which might be sensible for a big library, but not if I just need it just
a couple of times in a one off script.

Finally, what typeclass should main by a member of, and more importantly
what benefit does it provide? :-) 

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