Acta Informatica

, Volume 23, Issue 1, pp 1-7

First online:

A simple fixpoint argument without the restriction to continuity

  • Edsger W. DijkstraAffiliated withDepartment of Computer Sciences, The University of Texas at Austin
  • , A. J. M. van GasterenAffiliated withBP Venture Research Fellow, Department of Mathematics and Computing Science, University of Technology

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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.