Refinement and Reachability in Event_B

  • Jean-Raymond Abrial
  • Dominique Cansell
  • Dominique Méry
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3455)


Since the early 90’s (after the seminal article of R. Back [4]), the refinement of stuttering steps [5] are performed by means of new actions (called here events) refining skip. It is shown in this article that such a refinement method is not always possible in the development of large systems. We shall instead use events refining some kind of non-deterministic actions maintaining the invariant (sometimes called keep). We show that such new refinements are completely safe. In a second part, we explain how such a mechanism can be used to express some reachability conditions that were otherwise expressed using some special temporal logic statements à la TLA [5] in a previous article [2]. Examples will be used to illustrate our proposals.


Refinement Stuttering Reachability B Method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abrial, J.-R.: The B Book - Assigning Programs to Meanings. Cambridge University Press, Cambridge (1996) ISBN 0-521-49619-5zbMATHCrossRefGoogle Scholar
  2. 2.
    Abrial, J.-R., Mussat, L.: Introducing dynamic constraints in B. In: Bert, D. (ed.) B 1998. LNCS, vol. 1393, p. 83. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  3. 3.
    Abrial, J.R.: Event Based Sequential Program Development: Application to Constructing a Pointer Program. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 51–74. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Back, R.J.R.: Refinement calculus, part 2: Parallel and reactive systems. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1989. LNCS, vol. 430, pp. 67–93. Springer, Heidelberg (1990)Google Scholar
  5. 5.
    Lamport, L.: The temporal logic of actions. ACM Transactions on Programming Languages and Systems 16(3), 872–923 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jean-Raymond Abrial
    • 1
  • Dominique Cansell
    • 2
  • Dominique Méry
    • 3
  1. 1.ETHZ ZurichSwitzerland
  2. 2.LORIA, Université de MetzFrance
  3. 3.LORIA, Université Henri Poincaré Nancy 1France

Personalised recommendations