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wp Is wlp

  • Bernhard Möller
  • Georg Struth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3929)

Abstract

Using only a simple transition relation one cannot model commands that may or may not terminate in a given state. In a more general approach commands are relations enriched with termination vectors. We reconstruct this model in modal Kleene algebra. This links the recursive definition of the do od loop with a combination of the Kleene star and a convergence operator. Moreover, the standard wp operator coincides with the wlp operator in the modal Kleene algebra of commands. Therefore our earlier general soundness and relative completeness proof for Hoare logic in modal Kleene algebra can be re-used for wp. Although the definition of the loop semantics is motivated via the standard Egli-Milner ordering, the actual construction does not depend on Egli-Milner-isotony of the constructs involved.

Keywords

Relation Algebra Algebraic Semantic Hoare Logic General Soundness Idempotent Semiring 
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 2006

Authors and Affiliations

  • Bernhard Möller
    • 1
  • Georg Struth
    • 2
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany
  2. 2.Fakultät für InformatikUniversität der Bundeswehr MünchenNeubibergGermany

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