Skip to main content
SpringerLink
Log in

A simple fixpoint argument without the restriction to continuity

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

In programming language semantics, the introduction of unbounded nondeterminacy, which amounts to the introduction of noncontinuous predicate transformers, is needed for dealing with such concepts as fair interleaving. With the semantics of the repetition given as the strongest solution of a fixpoint equation, the weakest precondition expressed in closed form would then require transfinite ordinals. Here, however, it is shown that, even in the case of unbounded nondeterminacy, the fundamental theorem about the repetition can be proved by a simple and quite elementary argument.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Back, R.J.R.: Correctness preserving program refinements: proof theory and applications. Math. Cent. Tracts 131, (1980)

  2. Back, R.J.R.: Proving Total Correctness of Nondeterministic Programs in Infinitary Logic. Acta Inf. 15, 233–249 (1981)

    MATH  MathSciNet  Google Scholar 

  3. Boom, H.J.: A Weaker Precondition for Loops. ACM Trans. Program. Lang. Syst. 4, 668–677 (1982)

    Article  MATH  Google Scholar 

  4. Dijkstra, E.W.: A discipline of programming. Englewood Cliffs. Prentice-Hall 1976

    Google Scholar 

  5. Floyd, R.W.: Assigning meanings to programs. Amer. Math. Soc. Symposia Appl. Math. 19, 19–31 (1967)

    MATH  MathSciNet  Google Scholar 

  6. Park, D.: On the semantics of fair parallelism. Lect. Notes Comput. Sci. Vol. 86, pp. 504–526. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  7. Park, D.: Concurrency and automata on infinite sequences. Lect. Notes Comput. Sci. Vol. 104, Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  8. Stoy, J.: Denotational Semantics. In: The Scott-Strachey Approach to Programming. Cambridge: MIT Press 1977

    Google Scholar 

  9. Tarski, A.: A Lattice-theoretical Fixpoint Theorem and its Applications. Pac. J. Math. 5, 285–309 (1955)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Sciences, The University of Texas at Austin, 78712-1188, Austin, TX, USA

    Edsger W. Dijkstra

  2. BP Venture Research Fellow, Department of Mathematics and Computing Science, University of Technology, NL-5600, MB Eindhoven, Netherlands

    A. J. M. van Gasteren

Authors
  1. Edsger W. Dijkstra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. J. M. van Gasteren
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dijkstra, E.W., van Gasteren, A.J.M. A simple fixpoint argument without the restriction to continuity. Acta Informatica 23, 1–7 (1986). https://doi.org/10.1007/BF00268074

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00268074

Keywords

Search

Navigation