Extensionality says that the only observable properties of functions are the outputs they give for particular inputs. Accepting extensionality as a Good Thing implies that enabling the user to define a function that can differentiate between f x = x + x and g x = 2 * x is a Bad Thing.
Note that your h does not differentiate between f and g (in fact, it does not investigate them at all), the only thing you can do with f, g, (h f), and (g f) is apply them. Accordingly, it's a fine Haskell definition. "Why is extensionality a good thing?" might be a more enlightening question. My answer would quickly be outshone by others', so I'll stop here. On Dec 18, 2007 3:00 PM, Cristian Baboi <[EMAIL PROTECTED]> wrote: > > This is what I "understand" so far ... > > Suppose we have these two values: > a) \x->x + x > b) \x->2 * x > Because these to values are equal, all functions definable in Haskell must > preserve this. > This is why I am not allowed to define a function like > > h :: (a->b) -> (a->b) > h x = x > > The reasons are very complicated, but it goes something like this: > > - when one put \x->x+x trough the function h, the compiler might change it > to \x -> 2*x > - when one put \x->2*x trough the function h, the compiler might change it > to \x -> x + x > > And we all know that \x -> 2*x is not the same as \x->x+x and this is the > reason one cannot define h in Haskell > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe > _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
