A temporal-logic based compositional proof system for real-time message passing

Abstract

A compositional proof system is formulated to verify that a distributed system meets a real-time temporal logic specification. The specifications use linear temporal logic extended with a quantitative notion of time to express real-time properties. The programming language is a real-time version of CSP, akin to OCCAM, including nested parallelism with synchronous communication via channels. Concurrency is modelled as maximal parallelism, implying that no process waits unnecessarily. A denotational semantics of the programming language is formulated in which communications are represented by (possibly overlapping) intervals along a (possibly dense) time scale. The proof system is sound with respect to this semantics. Compositionality of our proof system makes it possible to verify design steps while developing a program. An example demonstrates our specifications and the use of the formalism during program development. Finally, the axiomatic system is shown to be complete relative to provability of valid formulae in real-time temporal logic.KeywordsTemporal LogicInference RuleProof SystemLinear Temporal LogicParallel CompositionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.