Theories for Mechanical Proofs of Imperative Programs

For convenient application of a first-order theorem prover to verification of imperative programs, it is important to encapsulate the operational semantics in generic theories. The possibility to do so is illustrated by two theories for the Boyer-Moore theorem prover Nqthm. The first theory is an Nqthm version of the classical while-theorem. Here the main interest is to show how one can use Nqthm's facilities to constrain and to functionally instantiate for the development and application of a generic theory. The theory is illustrated by a linear search program. The second theory is a finitary approach to progress for shared-memory concurrent programs. It is illustrated by Peterson's algorithm for mutual exclusion of two processes. The proof of progress for Peterson's algorithm is new. The assertion of bounded fairness is slightly stronger than the conventional notion of weak fairness. This new concept may have other applications