Logic for software verification

Question

I'm looking at the requirements for automated software verification, i.e. a program that takes in code (ordinary procedural code written in languages like C and Java), generates a bunch of theorems saying that each loop must eventually halt, no assertion will be violated, there will never be a dereference of a null pointer etc., then passes same to a theorem prover to prove they are actually true (or else find a counterexample indicating a bug in the code).

The question is what kind of logic to use. The two major positions seem to be:

1. First-order logic is just fine.

2. First-order logic isn't expressive enough, you need higher order logic.

Problem is, there seems to be a lot of support for both positions. So which one is right? If it's the second one, are there any available examples of things you want to do, that verifiers based on first-order logic have trouble with?

Answer 1

You can do everything you need in FOL, but it's a lot of extra work - a LOT! Most existing systems were developed by academics / people with not a lot of time, so they are tempted to take short cuts to save time / effort, and thus are attracted to HOLs, functional languages, etc. However, if you want to build a system that is to be used by hundreds of thousands of people, rather than merely hundreds, we believe that FOL is the way to go because it is far more accessible to a wider audience. There's just no substitute for doing the work; we've been at this for 25 years now! Please take a look at our project (http://www.manmademinions.com)

Regards, Aaron.