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
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