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

Theres much research in this area.. as others have said, the constructs within a program language are complex, and this only gets worse, when trying to validate or prove for any given inputs.

However, many languages allow for specifications, on what inputs are acceptable (preconditions), and also allow for specifying the end result (post conditions).

Such languages include: B, Event B, Ada, fortran.

And of course, there are many tools which are designed to help us prove certain properties about programs. For example, to prove deadlock freedom , one could crunch their program through SPIN.

There are also many tools out there that also help us detect logic errors. This can be done via static analysis (goanna, satabs) or actual execution of code (gnu valgrind?).

However, there is no one tool which really allows one to prove an entire program, from inception (specification), implementation and deployment. The B method comes close, but its implementation checking is very very weak. (It assumes that humans are infalible in the translation of speicficaiton into implmentation).

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As a side note, when using the B method, you'll frequently find yourself building complex proofs from smaller axioms. (And the same applies for other exhasustive theorem provers).