Acta Informatica

, Volume 23, Issue 1, pp 1–7 | Cite as

A simple fixpoint argument without the restriction to continuity

  • Edsger W. Dijkstra
  • A. J. M. van Gasteren


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.


Information System Operating System Data Structure Communication Network Information Theory 
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  1. 1.
    Back, R.J.R.: Correctness preserving program refinements: proof theory and applications. Math. Cent. Tracts 131, (1980)Google Scholar
  2. 2.
    Back, R.J.R.: Proving Total Correctness of Nondeterministic Programs in Infinitary Logic. Acta Inf. 15, 233–249 (1981)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Boom, H.J.: A Weaker Precondition for Loops. ACM Trans. Program. Lang. Syst. 4, 668–677 (1982)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dijkstra, E.W.: A discipline of programming. Englewood Cliffs. Prentice-Hall 1976Google Scholar
  5. 5.
    Floyd, R.W.: Assigning meanings to programs. Amer. Math. Soc. Symposia Appl. Math. 19, 19–31 (1967)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Park, D.: On the semantics of fair parallelism. Lect. Notes Comput. Sci. Vol. 86, pp. 504–526. Berlin, Heidelberg, New York: Springer 1980Google Scholar
  7. 7.
    Park, D.: Concurrency and automata on infinite sequences. Lect. Notes Comput. Sci. Vol. 104, Berlin, Heidelberg, New York: Springer 1981Google Scholar
  8. 8.
    Stoy, J.: Denotational Semantics. In: The Scott-Strachey Approach to Programming. Cambridge: MIT Press 1977Google Scholar
  9. 9.
    Tarski, A.: A Lattice-theoretical Fixpoint Theorem and its Applications. Pac. J. Math. 5, 285–309 (1955)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Edsger W. Dijkstra
    • 1
  • A. J. M. van Gasteren
    • 2
  1. 1.Department of Computer SciencesThe University of Texas at AustinAustinUSA
  2. 2.BP Venture Research Fellow, Department of Mathematics and Computing ScienceUniversity of TechnologyMB EindhovenNetherlands

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