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A cook's tour of countable nondeterminism

  • K. R. Apt
  • G. D. Plotkin
Session 15: A. Pnueci, Chairman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 115)

Abstract

We provide four semantics for a small programming language involving unbounded (but countable) nondeterminism. These comprise an operational one, two denotational ones based on the Egli-Milner and Smyth orders, respectively, and a weakest precondition semantics. Their equivalence is proved. We also introduce a Hoare-like proof system for total correctness and show its soundness and completeness in an appropriate sense. Admission of countable nondeterminism results in a lack of continuity of various semantic functions; moreover some of the partial orders considered are in general not cpo's and in proofs of total correctness one has to resort to the use of (countable) ordinals. Proofs will appear in the full version of the paper.

Keywords

Operational Semantic Proof System Semantic Function Completeness Theorem Total Correctness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • K. R. Apt
    • 1
  • G. D. Plotkin
    • 2
  1. 1.Faculty of EconomicsErasmus UniversityRotterdam
  2. 2.Dept. of Computer ScienceUniversity of EdinburghUK

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