Re: [DotGNU]flexible for users, or flexible for developers? (wasRe:User Interfaces)

[BioChem333]

On Wed, 2002-07-10 at 15:47, Timothy Rue wrote:
> In other words all things
> are not possible in any one language. I believe the most logical example
> is that of the mathmatical Turning Haulting Problem.

Turing's halting problem isn't about language limitation, but about the
limits of what is and is not computable, no matter the language. You
simply can't know for certain whether a program will halt or not when
halting depends on the values of variables which are not known at the
time of halt testing. The proof I learned was one by contradiction;
assume program A tests for halting, and program B halts if and only if
program A's output says that its input program will not halt. Feed
program B into program A and you have a paradox. There is, of course,
program slicing, so you could know what the possibilities are for a
specific set of circumstances by tracking a specific variable or set of
variables. This would not violate Turing's proof, but it still doesn't
give an absolute yes or no answer (only an answer for one possible
scenario that may or may not occur). Saying that the halting problem is
a language limitation is like saying Einstein's c-limit is really a
limitation of calculus rather than physical law. The language of
mathematical reasoning has no limits, afaik, when it comes to expressing
and analyzing what is and is not computable. Also, afaik, most
programming languages are capable of expressing all that is technically
computable, although with varying degrees of difficulty for the
developer and compiler.