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Refinement and Reachability in Event_B

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Book cover ZB 2005: Formal Specification and Development in Z and B (ZB 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3455))

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Abstract

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.

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References

  1. Abrial, J.-R.: The B Book - Assigning Programs to Meanings. Cambridge University Press, Cambridge (1996) ISBN 0-521-49619-5

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  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)

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  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)

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  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)

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  5. Lamport, L.: The temporal logic of actions. ACM Transactions on Programming Languages and Systems 16(3), 872–923 (1994)

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© 2005 Springer-Verlag Berlin Heidelberg

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Abrial, JR., Cansell, D., Méry, D. (2005). Refinement and Reachability in Event_B. In: Treharne, H., King, S., Henson, M., Schneider, S. (eds) ZB 2005: Formal Specification and Development in Z and B. ZB 2005. Lecture Notes in Computer Science, vol 3455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11415787_14

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  • DOI: https://doi.org/10.1007/11415787_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25559-8

  • Online ISBN: 978-3-540-32007-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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