[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: dynamic vs. static typing
Peter van Rooijen writes:
> From: "Joe Marshall" <firstname.lastname@example.org>
> > I was just pointing out that lists of unknown objects are
> > interesting in and of themselves.
> It seems to me that they are as interesting as natural numbers.
> After all, that's what they are, right?
Not quite: you can reverse a list without knowing its contents.
Reynold's abstraction theorem says that parametrically polymorphic
functions do not perform any operations on the values at polymorphic
type. Phillip Wadler wrote a paper on how you can turn this around and
use it to deduce specific theorems about functions without actually
having to do a proof. For example, because reverse has the type
reverse: List a -> List a
we know that it can't modify the values of the list. It can only
delete, copy, or permute the cons cells, all without looking at the
inside of its contents.