Surely you agree that it's possible to prove x>0 is true after executing this program:
if(x
People have come up with techniques for reasoning about loops and recursion. Not in
general, of course, but for some specific property (e.g., x > 0) and some specific loop (e.g., while(x
> I regularly see similar claims about software validationValidation and verification are very different things. Verification is "my program meets these formal specs". Validation is "my specs accurately encodes the whole problem". Indeed, there's no way to do validation in a provably correct way. (But, of course, mathematics and statistics can help :-) ). The good news is that a lot of security and other bugs arise even once you have the correct spec. So verification can be useful even if it's impossible to perfectly validate.
> by people who either do not know, or who don't want to acknowledge, that this problem cannot be solved in the general case.
It's somehow ironic that you invoke the Talking problem since Turing himself -- AFTER having proven the Halting problem -- basically conjectured the creation of formal methods.