Proving total correctness of nondeterministic programs in infinitary logic

Abstract

It is shown how the weakest precondition approach to proving total correctness of nondeterministic programs can be formalized in infinitary logic. The weakest precondition technique is extended to hierarchically structured programs by adding a new primitive statement for operational abstraction, the nondeterministic assignment statement, to the guarded commands of Dijkstra. The infinitary logic L ?1? is shown to be strong enough to express the weakest preconditions for Dijkstra's guarded commands, but too weak for the extended guarded commands. Two possible solutions are considered: going to the essentially stronger infinitary logic L ?1?1 and restricting the power of the nondeterministic assignment statement in a way which allows the weakest preconditions to be expressed in L ?1?.