Social Processes and Proofs of Theorems and Programs

Abstract

Many people have argued that computer programming should strive to become more like mathematics. Maybe so, but not in the way they seem to think. The aim of program verification, an attempt to make programming more mathematics-like, is to increase dramatically one’s confidence in the correct functioning of a piece of software, and the device that verifiers use to achieve this goal is a long chain of formal, deductive logic. In mathematics, the aim is to increase one’s confidence in the correctness of a theorem, and it’s true that one of the devices mathematicians could in theory use to achieve this goal is a long chain of formal logic. But in fact they don’t. What they use is a proof, a very different animal. Nor does the proof settle the matter; contrary to what its name suggests, a proof is only one step in the direction of confidence. We believe that, in the end, it is a social process that determines whether mathematicians feel confident about a theorem — and we believe that, because no comparable social process can take place among program verifiers, program verification is bound to fail. We can’t see how it’s going to be able to affect anyone’s confidence about programs.