functions not in type classes

[D. Tweed]

On Fri, 18 Jan 2002, Cagdas Ozgenc wrote:

> > the goal of type class is to allow overloading of function, so for example
> > id x = x     is not subject to overloading => no use to put it in a type
> class.
> 
> Because it doesn't do anything?

I believe that (assuming of course that you aren't a simplicity fanatic
who programs only using the S, K, I combinators [1]) id is useful for
interfacing with very general functions which have an a->a argument which
isn't necessary for what you're doing, e.g.,

altSumsTransformedList :: (a->a) -> a-> [a] -> a
altSumsTransfromedList f e (x:xs) = f x - altSumsTransfromedList f e xs

then you can get the simple alternating sum of the original list simply by
using

altSumsTransfromedList id

A much more commonly used example is

flip f x y = f y x

which doesn't seem to do much, but is actually very useful for things
use in things like foldr when you've already got a function which does
almost what you want but expects its arguments in the opposite order to
the one that foldr gives them in. These small functions are very useful,
and several of them have counterparts in the C++ STL binders.

[1] this is a bad joke reference to the fact that `all functional programs
(under an appropriate encoding of the data) can be converted to an
equivalent form using just three elementary combinators, S (aka succ), K
(aka const) and I (aka id)'.

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