Skip to main content
Springer Nature Link
Log in

Metric predicate transformers: Towards a notion of refinement for concurrency

  • Session: Refinement Theory
  • Conference paper
  • First Online:
CONCUR '95: Concurrency Theory (CONCUR 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 962))

Included in the following conference series:

  • 146 Accesses

Abstract

A compositional weakest precondition semantics is given for a parallel language with recursion using a new metric resumption domain. By extending the classical duality of predicate vs. state transformers, the weakest precondition semantics for the parallel language is shown to be isomorphic to the standard metric state transformer semantics. Moreover, a notion of refinement for predicate transformers is proposed which corresponds to the familiar notion of simulation for state transformers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. P. America and J.J.M.M. Rutten. Solving Reflexive Domain Equations in a Category of Complete Metric Spaces. Journal of Computer and System Sciences, 39(3):343–375, 1989.

    Article  Google Scholar 

  2. R.-J.R. Back. Correctness Preserving Program Refinements: Proof Theory and Applications, volume 131 of Mathematical Centre Tracts. CWI, Amsterdam, 1980.

    Google Scholar 

  3. E. Best. Towards Compositional Predicate Transformer Semantics for Concurrent Programs. In J.W. de Bakker, 25 jaar Semantiek, pages 111–117, CWI, Amsterdam, 1989.

    Google Scholar 

  4. M.M. Bonsangue and J.N. Kok. Relating Multifunctions and Predicate Transformers through Closure Operators. pages 822–843. LNCS 789, 1994.

    Google Scholar 

  5. M.M. Bonsangue, J.N. Kok, and E.P. de Vink. Metric Predicate Transformers: Towards a Notion of Refinement for Concurrent Programs. Report IR-371, Vrije Universiteit Amsterdam, 1994. Available through anonymous ftp from ftp.cs.vu.nl as pub/papers/theory/IR-371.ps.Z.

    Google Scholar 

  6. R. J.R. Back and K. Sere. Action Systems with Synchronous Communication. In E.-R. Olderog, editor, Proc. Programming Concepts, Methods and Calculi, pages 107–126. IFIP, North Holland, 1994.

    Google Scholar 

  7. J.W. de Bakker and J.I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54:70–120, 1982.

    Article  Google Scholar 

  8. K.M. Chandy and J. Misra. Parallel Program Design: A Foundation. Addison-Wesley, 1988.

    Google Scholar 

  9. E.W. Dijkstra. A Discipline of Programming. Prentice-Hall, 1976.

    Google Scholar 

  10. W.H. Hesselink. Deadlock and fairness in morphisms of transition systems. Theoretical Computer Science, 59:235–257, 1988.

    Article  Google Scholar 

  11. L. Lamport. Win and sin: Predicate Transformers for Concurrency. ACM Transaction on Programming Languages and Systems, 12(3):396–428, 1990.

    Article  Google Scholar 

  12. N.A. Lynch and F.W. Vaandrager. Forward and Backward Simulation — Part I: Untimed Systems. Report CS-R9313, CWI, Amsterdam, 1993. To appear in Information and Computation.

    Google Scholar 

  13. G.D. Plotkin. Dijkstra's Predicate Transformer and Smyth's Powerdomain. pages 527–553. LNCS 86, 1979.

    Google Scholar 

  14. D. Scholefield and H.S.M. Zedan. Weakest Precondition Semantics for Time and Concurrency. Information Processing Letters, 43(6):301–308, 1992.

    Google Scholar 

  15. A. Udaya Shankar. An Introduction to Assertional Reasoning for Concurrent Systems. ACM Computing Surveys, 25:225–262, 1993.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1081a, NL-1081, HV Amsterdam, The Netherlands

    Marcello M. Bonsangue & Erik de Vink

  2. Department of Computer Science, Leiden University, P.O. Box 9512, NL-2300, RA Leiden, The Netherlands

    Joost N. Kok

Authors
  1. Marcello M. Bonsangue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joost N. Kok
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erik de Vink
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Insup Lee Scott A. Smolka

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bonsangue, M.M., Kok, J.N., de Vink, E. (1995). Metric predicate transformers: Towards a notion of refinement for concurrency. In: Lee, I., Smolka, S.A. (eds) CONCUR '95: Concurrency Theory. CONCUR 1995. Lecture Notes in Computer Science, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60218-6_27

Download citation

  • DOI: https://doi.org/10.1007/3-540-60218-6_27

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60218-7

  • Online ISBN: 978-3-540-44738-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics