Why can't programs be proven?

Question

Why can\'t a computer program be proven just as a mathematical statement can? A mathematical proof is built up on other proofs, which are built up from yet more proofs and

Answer 1

Of course they can, as others have posted.

Proving a very small subroutine correct is a good exercise that IMHO every undergraduate in a programming-related degree program ought to be required to do. It gives you great insight into thinking about how to make your code clear, easily reviewable and maintainable.

However, in the real world it is of limited practical use.

First, just as programs have bugs, so do mathematical proofs. How do prove that a mathematical proof is really correct and doesn't have any errors? You can't. And for counter-example, any number of published mathematical proofs have had errors discovered in them, sometimes years later.

Second, you can't prove that a program is correct without having 'a priori' an unambiguous definition of what the program is supposed to do. But any unambiguous definition of what a program is supposed to do is a program. (Although it may be a program in some sort of specification language that you don't have a compiler for.) Therefore, before you can prove that a program is correct, you must first have another program that is equivalent and is known in advance to be correct. So QED the whole thing is futile.

I would recommend tracking down the classic "No Silver Bullet" article by Brooks.