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

They can. I spent many, many hours as a college freshman doing program correctness proofs.

The reason it's not practical on a macro scale is that writing a proof of a program tends to be a lot harder than writing the program. Also, programmers today tend to build systems, not write functions or programs.

On a micro scale, I sometimes do it mentally for individual functions, and tend to organize my code to make them easy to verify.

There's a famous article about the space shuttle software. They do proofs, or something equivalent. It's incredibly costly and time-consuming. That level of verification may be necessary for them, but for any kind of consumer or commercial software company, with current techniques, you'll get your lunch eaten by a competitor who delivers a 99.9% solution at 1% of the cost. Nobody's going to pay $5000 for an MS Office that's marginally more stable.