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Structured Event-B Models and Proofs

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Abstract State Machines, Alloy, B and Z (ABZ 2010)

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Abstract

Event-B does not provide specific support for the modelling of problems that require some structuring, such as, local variables or sequential ordering of events. All variables need to be declared globally and sequential ordering of events can only be achieved by abstract program counters. This has two unfortunate consequences: such models become less comprehensible — we have to infer sequential ordering from the use of program counters; proof obligation generation does not consider ordering — generating too many proof obligations (although these are usually trivially discharged).

In this article we propose a method for specifying structured models avoiding, in particular, the use of abstract program counters. It uses a notation that mainly serves to drive proof obligation generation. However, the notation also describes the structure of a model explicitly. A corresponding graphical notation is introduced that visualises the structure of a model.

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References

  1. Abrial, J.-R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press, Cambridge (2009) (to appear)

    Google Scholar 

  2. Abrial, J.-R., Butler, M., Hallerstede, S., Voisin, L.: An open extensible tool environment for Event-B. In: Liu, Z., He, J. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 588–605. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Abrial, J.-R., Hallerstede, S.: Refinement, Decomposition and Instantiation of Discrete Models: Application to Event-B. Fundam. Inform 77(1-2), 1–28 (2007)

    MATH  MathSciNet  Google Scholar 

  4. Apt, K.R., de Boer, F.S., Olderog, E.-R.: Verification of Sequential and Concurrent Programs. Springer, Heidelberg (2009)

    Book  MATH  Google Scholar 

  5. Börger, E., Stärk, R.: Abstract State Machines: A Method for High-Level System Design and Analysis. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  6. Butler, M.: Decomposition Structures for Event-B. In: Leuschel, M., Wehrheim, H. (eds.) IFM 2009. LNCS, vol. 5423, pp. 20–38. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Cansell, D., Méry, D., Merz, S.: Diagram refinements for the design of reactive systems. J. UCS 7(2), 159–174 (2001)

    MATH  Google Scholar 

  8. de Alfaro, L., Manna, Z., Sipma, H.B., Uribe, T.E.: Visual verification of reactive systems. In: Brinksma, E. (ed.) TACAS 1997. LNCS, vol. 1217, pp. 334–350. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  9. Hallerstede, S.: Justifications for the Event-B Modelling Notation. In: Julliand, J., Kouchnarenko, O. (eds.) B 2007. LNCS, vol. 4355, pp. 49–63. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Hallerstede, S.: On the Purpose of Event-B Proof Obligations. In: Börger, E., Butler, M., Bowen, J.P., Boca, P. (eds.) ABZ 2008. LNCS, vol. 5238, pp. 125–138. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Hallerstede, S.: Proving Quicksort Correct in Event-B. In: Refine 2009, 16 pages (2009)

    Google Scholar 

  12. Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12, 576–580 (1969)

    Article  MATH  Google Scholar 

  13. Ifill, W., Schneider, S.A., Treharne, H.: Augmenting B with control annotations. In: Julliand, J., Kouchnarenko, O. (eds.) B 2007. LNCS, vol. 4355, pp. 34–48. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Manna, Z., Pnueli, A.: Temporal verification diagrams. In: Hagiya, M., Mitchell, J.C. (eds.) TACS 1994. LNCS, vol. 789, pp. 726–765. Springer, Heidelberg (1994)

    Google Scholar 

  15. Morgan, C.: Programming from Specifications, 2nd edn. Prentice Hall, Englewood Cliffs (1994)

    MATH  Google Scholar 

  16. Owicki, S., Gries, D.: An axiomatic proof technique for parallel programs. Acta Informatica 6(4), 319–340 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  17. Said, M.Y., Butler, M.J., Snook, C.F.: Language and tool support for class and state machine refinement in UML-B. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 579–595. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

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Hallerstede, S. (2010). Structured Event-B Models and Proofs. In: Frappier, M., Glässer, U., Khurshid, S., Laleau, R., Reeves, S. (eds) Abstract State Machines, Alloy, B and Z. ABZ 2010. Lecture Notes in Computer Science, vol 5977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11811-1_21

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  • DOI: https://doi.org/10.1007/978-3-642-11811-1_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11810-4

  • Online ISBN: 978-3-642-11811-1

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