Reformulate Dynamic Properties during B Refinement and Forget Variants and Loop Invariants

  • Authors:
  • Françoise Bellegarde;C. Darlot;Jacques Julliand;Olga Kouchnarenko

  • Affiliations:
  • -;-;-;-

  • Venue:
  • ZB '00 Proceedings of the First International Conference of B and Z Users on Formal Specification and Development in Z and B
  • Year:
  • 2000

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Abstract

We propose a way to introduce dynamic properties into a B refinement design which differs from the approach used by J.R. Abrial and L. Mussat. First, the properties are expressed in the Propositional Linear Temporal Logic PLTL. Second, the user directs the evolution of properties through the refinement, so that a property P expressed by a formula F1 in the abstract system, is expressed again by a formula F2 in the refined system. Third, the verification combines proof and model-checking. In particular, F1 is model-checked, and, then, to ensure F2 it suffices to prove some propositions depending on the shapes of F1 and F2. In this paper, we show how to obtain these "sufficient propositions" from a refinement relation and the semantics of PLTL formulae. The main advantage is that the user does not need a variant or a loop invariant to achieve an automatic proof for finite state event systems. Our approach is illustrated on a protocol between a chip card and a card reader, called protocol T=1.