Rob Gerth

A proof system for concurrent ADA programs

Abstract A subset of ADA is introduced, ADA-CF , to study the basic synchronization and communication primitive of ADA , the rendezvous. Basing ourselves on the techniques introduced by Apt, Francez and de Roever for their CSP proof system, we develop a Hoare-style proof system for proving partial correctness properties which is sound and relatively complete. The proof system is then extended to deal with safety, deadlock, termination and failure. No prior exposure of the reader to parallel program proving techniques is presupposed. Two non-trivial example proofs are given of ADA-CF programs; the first one concerns a buffered producer-consumer algorithm, the second one a parallel sorting algorithm due to Brinch Hansen. Features of ADA expressing dynamic process creation and realtime constraints are not covered by our proof methods. Consequently, we do not claim that the methods described can be extended to full ADA without serious additional further research.

Compositional Semantics for Real-time Distributed Computing

We give a compositional denotational semantics for a real-time distributed language, based on the linear history semantics for CSP of Francez et al. Concurrent execution is not modelled by interleaving but by an extension of the maximal parallelism model of Salwicki, that allows the modelling of transmission time for communications. The importance of constructing a semantics (and in general a proof theory) for real-time is stressed by such different sources as the problem of formalizing the real-time aspects of Ada and the elimination of errors in real-time flight control software ([Sunday Times 7-22-84]).

A Sound and Complete Hoare Axiomatization of the Ada-Rendevous

A HOARE-axiomatization is constructed for the ADA rendezvous, embedded in a subset of the ADA concurrency section. The well-known CSP proof system of Apt, Francez and de Roever is taken as a starting point. We prove the axiomatization to be sound and relatively complete.

A Proof System for Brinch Hansen's Distributed Processes

A DP program consists of a fixed number of concurrent and persistent processes, that are started simultaneously. We assume the processes as being numbered, hence the program is denoted as (P1 ||... || Pn), n≥ 2. A process does not contain parallel statements, nor shared variables. The syntax of a process is as follows: n n nprocess