Proof methods and pragmatics for parallel programming

We define a parallel extension of a standard imperative programming language, which we call CIMP. This language has a semantics in the process calculus CCS. In order to demonstrate that a sub-language of CIMP is deterministic the notion of a semi-confluent process is defined. This process structure is shown to be preserved by the appropriate equivalences of CCS, and to have a set of operators which conserve it. We show that a simple syntactic condition on the parallel components of a program is sufficient to ensure its determinacy. Furthermore we demonstrate that the deterministic sub-language of CIMP has a simple functional semantics. We also show that there is a set of simple transformation rules that can manipulate parallelism whilst maintaining determinism. Two proof systems for the language CIMP are studied, they are based respectively on the approaches of Owicki-Gries and Jones. These systems are shown to be sound with respect to an interpretation of the proof rules in Hennessey—Milner logic. We demonstrate that a knowledge of determinism can greatly ease the proof burden in both of these methods. We define a calculus, based on CCS, which permits reasoning about the temporal properties of concurrent systems. This calculus is shown to have natural notions of equality and order. Some example systems are included, in particular a temporal analysis of an alternating bit protocol. We use this calculus to provide a timed semantics for the language CIMP, and examine a timed proof system based on the system for sequential programs presented by Nielson.