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P — A logic — a compositional proof system for distributed programs

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Summary

This paper describes a compositional proof system called P-A logic for establishing weak total correctness and weak divergence correctness of CSP-like distributed programs with synchronous and asynchronous communication. Each process in a network is specified using logical assertions in terms of a presuppositionPre and an affirmationAff as a triple {Pre}S{Aff}. For purely sequential programs, these triples reduce to the familiar Hoare triples. In distributed programs, P-A triples allow the behaviour of a process to be specified in the context of assumptions about its communications with the other processes in the network. Safety properties of process communications, and progress properties such as finiteness and freedom from divergence can be proved. An extension of P-A logic allowing proof of deadlock freedom is outlined. Finally, proof rules for deriving some liveness properties of a program from its P-A logic specification are discussed; these properties have the form “Q untilR”, whereQ, R are assertions over communication traces. Other liveness properties may be derived from these properties using the rules of temporal logic.

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Author notes

  1. Mathai Joseph

    Present address: Programming Research Group, 11 Keble Road, OX1 3QD, Oxford

Authors and Affiliations

  1. Tata Institute of Fundamental Research, University of Warwick, CV4 7AL, Coventry, UK

    Partosh K. Pandya

  2. Department of Computer Science, University of Warwick, CV4 7AL, Coventry, UK

    Mathai Joseph

Authors
  1. Partosh K. Pandya
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  2. Mathai Joseph
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Additional information

Paritosh Kulin Pandya received his Master's degree in Computer Science from the Indian Institute of Technology, Kanpur in 1982, and a Ph.D. from the Tata Institute of Fundamental Research in 1988 where he is currently employed. He has worked as a Research Officer in the Programming Research Group of the Oxford University from 1988 to 1991.

Mathai Joseph has since 1985 been professor of Computer Science at the University of Warwick where he leads a group working on developing formal techniques for specifying and implementing realtime and fault-tolerant systems.

Supported in part by Visiting Fellowships awarded by the Science and Engineering Research Council (research grant GR/D 90918) and the British Council

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Pandya, P.K., Joseph, M. P — A logic — a compositional proof system for distributed programs. Distrib Comput 5, 37–54 (1991). https://doi.org/10.1007/BF02311231

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  • DOI: https://doi.org/10.1007/BF02311231

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