Acta Informatica

, Volume 23, Issue 1, pp 1–7

A simple fixpoint argument without the restriction to continuity


  • Edsger W. Dijkstra
    • Department of Computer SciencesThe University of Texas at Austin
  • A. J. M. van Gasteren
    • BP Venture Research Fellow, Department of Mathematics and Computing ScienceUniversity of Technology

DOI: 10.1007/BF00268074

Cite this article as:
Dijkstra, E.W. & van Gasteren, A.J.M. Acta Informatica (1986) 23: 1. doi:10.1007/BF00268074


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.

Copyright information

© Springer-Verlag 1986