A complete modal proof system for a subset of SCCS

  • Colin Stirling
Colloquium On Trees In Algebra And Programming Concurrency
Part of the Lecture Notes in Computer Science book series (LNCS, volume 185)


Logical proof systems for concurrent programs are notoriously complex, often involving arbitrary restrictions. One of the main reasons for this is that unlike other major programming concepts parallelism does not appear to have a logical correlate. Here using a simple semantic strategy we tentatively propose one and offer an example modal proof system for a subset of Milner's SCCS. The proof rules are reminiscent of Gentzen introduction rules except that there are also introduction rules for the operators of the program language.


  1. [Ab]
    S. Abramsky. ‘Experiments, powerdomains and fully abstract models for applicative multiprogramming', LNCS Vol.158, pp.1–13 (1983).Google Scholar
  2. [AFR]
    K. Apt, N. Francez and W. de Roever. ‘A proof system for communicating sequential processes', TOPLAS pp. 359–385 (1980).Google Scholar
  3. [BK]
    H. Barringer and R. Kuiper. ‘Towards the hierarchical, Temporal logic, specification of concurrent systems',presented at STL/SERC Workshop on the Analysis of Concurrent Systems, Cambridge. (1983).Google Scholar
  4. [BKP]
    H. Barringer, R. Kuiper and A. Pnueli. ‘Now you may compose temporal logic specifications', Proceedings STOC (1984).Google Scholar
  5. [BR]
    S. Brookes and W. Rounds. ‘Behavioural equivalence relations induced by programming logics', LNCS Vol.154 pp. 97–108 (1983).Google Scholar
  6. [DeH]
    R. de Nicola and M. Hennessy. ‘Testing equivalences for processes', in LNCS Vol. 154 pp. 548–560 (1983).Google Scholar
  7. [EH]
    E. Emerson and J. Halpern. 'sometimes and not never revisited: on branching versus linear time', pp. 127–140 POPL Proceedings (1983).Google Scholar
  8. [G]
    G. Gentzen. ‘Investigations into logic deduction', in ‘The Collected Works of Gerhard Gentzen’ ed. Szabo, North-Holland (1969).Google Scholar
  9. [GS]
    S. Graf and J. Sifakis. ‘A modal characterization of observational congruence on finite terms of CCS', IMAG Technical Report No. 402 (and to appear in ICALP '84) (1983).Google Scholar
  10. [Ha]
    D. Harel. ‘First-Order Dynamic Logic’ LNCS Vol.68 (1979).Google Scholar
  11. [HBR]
    C. Hoare, S. Brookes and A. Roscoe. ‘A theory of communicating sequential processes', Technical Monograph Prg-16, Computing Lab, University of Oxford (1981).Google Scholar
  12. [He1]
    M. Hennessy. ‘Axiomatizing finite delay operators', Acta Informatioca 21, pp. 61–88 (1984).CrossRefGoogle Scholar
  13. [He2]
    M. Hennessy. ‘Modelling finite delay operators'. Technical Report CSR-153-83 Dept. of Computer Science, Edinburgh (1983).Google Scholar
  14. [HM1]
    M. Hennessy and R. Milner. ‘On observing nondeterminism and concurrency', LNCS Vol.85, pp. 299–309 (1980).Google Scholar
  15. [HM2]
    M. Hennessy and R. Milner. ‘Algebraic laws for nondeterminism and concurrency’ Technical Report CSR-133-83 (and to appear in JACM) (1983).Google Scholar
  16. [Ho]
    C. Hoare. ‘A model for communicating sequential processes'. Technical Monograph, Prg-22, Computing Lab University of Oxford (1982).Google Scholar
  17. [HS]
    M. Hennessy and C. Stirling. ‘The power of the future perfect in program logics', LNCS Vol.176 pp.301–311 (1984).Google Scholar
  18. [K]
    R. Keller. ‘A fundamental theorem of asynchronous parallel computation’, in Parallel Processing ed. T. Feng, Springer-Verlag (1975).Google Scholar
  19. [L]
    L. Lamport. ‘The ‘Hoare logic’ of concurrent programs', Acta Informatica pp. 21–37 (1980).Google Scholar
  20. [La]
    K. Larsen. ‘A context dependent equivalence between processes'. To appear.Google Scholar
  21. [LG]
    G. Levin and D. Gries. ‘A proof technique for communicating sequential processes', Acta Informatica pp. 281–302 (1981).Google Scholar
  22. [Mi1]
    R. Milner. ‘A modal characterisation of observable machine-behaviour', LNCS Vol. 112 pp. 25–34 (1981).Google Scholar
  23. [Mi2]
    R. Milner. ‘A finite delay operator in synchronous CCS', Technical Report CSR-116-82, Dept. of Computer Science, Edinburgh (1982).Google Scholar
  24. [Mi3]
    R. Milner. ‘Calculi for synchrony and asynchrony', Theoretical Computer Science, pp. 267–310 (1983).Google Scholar
  25. [Mo]
    E. Moore. ‘Gedanken-experiments on sequential machines', in ‘Automata Studies’ ed. C. Shannon and J. McCarthy, Princeton University Press, pp. 129–153 (1956).Google Scholar
  26. [MP1]
    Z. Manna and A. Pnueli. ‘Temporal verification of concurrent programs: the temporal framework for concurrent programs', in ‘The Correctness Problem in Computer Science', ed. R. Boyer and J. Moore, Academic Press, pp. 215–273 (198 ).Google Scholar
  27. [MP2]
    Z. Manna and A. Pnueli. ‘How to cook a temporal proof system for your pet language', POPL Proceedings pp. 141–154 (1983).Google Scholar
  28. [OG]
    S. Owicki and D. Gries. ‘An axiomatic proof technique for parallel programs I’ Acta Informatica pp. 319–340 (1976).Google Scholar
  29. [Pa]
    D. Park. ‘Concurrency and automata on infinite sequences', LNCS Vol.104 (1981).Google Scholar
  30. [P]
    G. Plotkin. ‘A structural approach to operational semantics'. Lecture Notes, Aarhus University (1981).Google Scholar
  31. [QS]
    J. Queille and J. Sifakis. ‘Fairness and related properties in transition systems — a temporal logic to deal with fairness', Acta Informatica 19, pp. 195–220 (1983).CrossRefGoogle Scholar
  32. [RB]
    W. Rounds and S. Brookes. ‘Possible futures, acceptances, refusals and communicating processes', in Proc. FOCS pp. 140–149 (1981).Google Scholar
  33. [Si1]
    J. Sifakis. ‘Unified approach for studyng the properties of transition systems', Theoretical Computer Science, pp. 227–258 (1982).Google Scholar
  34. [Si2]
    J. Sifakis. ‘Property preserving homomorphisms of transition systems', Technical Report, IMAG (1982).Google Scholar
  35. [St1]
    C. Stirling. ‘A proof theoretic characterization of observational equivalence’ in Procs. FCT-TCS Bangalore (1983) (and to appear in TCS).Google Scholar
  36. [St2]
    C. Stirling. ‘A compositional modal proof system for a subset of CCS'. To appear.Google Scholar
  37. [ZBR]
    J. Zwiers, A. de Bruin and W. de Roever. ‘A proof system for partial correctness of dynamic networks of processes', Technical Report RUU-CS-83-15, Dept. of Computer Science, University of Utrecht (1983).Google Scholar
  38. [Wi]
    G. Winskel. ‘Complete proof systems for SCCS with modal assertions'. To appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Colin Stirling
    • 1
  1. 1.Dept. of Computer ScienceEdinburgh UniversityEdinburghU.K.

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