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Automatic Refinement Checking for B

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Formal Methods and Software Engineering (ICFEM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3785))

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Abstract

Refinement is a key concept in the B-Method. While refinement is at the heart of the B Method, so far no automatic refinement checker has been developed for it. In this paper we present a refinement checking algorithm and implementation for B. It is based on using an operational semantics of B, obtained in practice by the ProB animator. The refinement checker has been integrated into ProB toolset and we present various case studies and empirical results in the paper, showing the algorithm to be surprisingly effective. The algorithm checks that a refinement preserves the trace properties of a specification. We also compare our tool against the refinement checker FDR for CSP and discuss an extension for singleton failure refinement.

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References

  1. Abrial, J.-R.: The B-Book. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  2. Abrial, J.-R.: Case study of a complete reactive system in Event-B: A mechanical press controller. In: Tutorial at ZB 2005(2005), Available at http://www.zb2005.org/

  3. Abrial, J.-R., Cansell, D.: Click’n prove: Interactive proofs within set theory. In: Basin, D., Wolff, B. (eds.) TPHOLs 2003. LNCS, vol. 2758, pp. 1–24. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Abrial, J.-R., Mussat, L.: Introducing dynamic constraints in B. In: Bert, D. (ed.) B 1998. LNCS, vol. 1393, p. 83. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  5. Basu, S., Mukund, M., Ramakrishnan, C.R., Ramakrishnan, I.V., Verma, R.M.: Local and symbolic bisimulation using tabled constraint logic programming. In: Codognet, P. (ed.) ICLP 2001. LNCS, vol. 2237, pp. 166–180. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Bolton, C., Davies, J.: A comparison of refinement orderings and their associated simulation rules. Electr. Notes Theor. Comput. Sci. 70(3), 440–453 (2002)

    Article  Google Scholar 

  7. Butler, M., Leuschel, M.: Combining CSP and B for specification and property verification. In: Fitzgerald, J.S., Hayes, I.J., Tarlecki, A. (eds.) FM 2005. LNCS, vol. 3582, pp. 221–236. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Butler, M.J.: An approach to the design of distributed systems with B AMN. In: Till, D., Bowen, P.J., Hinchey, M.G. (eds.) ZUM 1997. LNCS, vol. 1212, pp. 223–241. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  9. Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)

    Google Scholar 

  10. Dunne, S., Conroy, S.: Process refinement in B. In: Treharne, H., King, S., C. Henson, M., Schneider, S. (eds.) ZB 2005. LNCS, vol. 3455, pp. 45–64. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Farwer, B., Leuschel, M.: Model checking object Petri nets in Prolog. In: Proceedings PPDP 2004, pp. 20–31. ACM Press, New York (2004)

    Chapter  Google Scholar 

  12. Formal Systems (Europe) Ltd. Failures-Divergence Refinement — FDR2 User Manual

    Google Scholar 

  13. Gardiner, P.H.B., Morgan, C.: A single complete rule for data refinement. Formal Asp. Comput. 5(4), 367–382 (1993)

    Article  MATH  Google Scholar 

  14. He, J., Hoare, C.A.R., Sanders, J.W.: Data refinement refined. In: Robinet, B., Wilhelm, R. (eds.) ESOP 1986. LNCS, vol. 213, pp. 187–196. Springer, Heidelberg (1986)

    Google Scholar 

  15. Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)

    MATH  Google Scholar 

  16. Leuschel, M., Butler, M.: ProB: A Model Checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. Leuschel, M., Massart, T.: Infinite state model checking by abstract interpretation and program specialisation. In: Bossi, A. (ed.) LOPSTR 1999. LNCS, vol. 1817, pp. 63–82. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  18. Leuschel, M., Turner, E.: Visualizing larger states spaces in ProB. In: Treharne, H., King, S., Henson, M.C., Schneider, S. (eds.) ZB 2005. LNCS, vol. 3455, pp. 6–23. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  19. B-Core. B-toolkit manuals (1999)

    Google Scholar 

  20. Robinson, N.J.: Checking z data refinements using an animation tool. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 62–81. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. Roscoe, A.: The Theory and Practice of Concurrency. Prentice-Hall, Englewood Cliffs (1998)

    Google Scholar 

  22. Sagonas, K., Swift, T., Warren, D.S.: XSB as an efficient deductive database engine. In: Proceedings SIGMOD 1994, Minneapolis, pp. 442–453. ACM, New York (1994)

    Chapter  Google Scholar 

  23. Schneider, S., Treharne, H.: Communicating B machines. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 416–435. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  24. Steria. Atelier B, user and reference manuals (1997)

    Google Scholar 

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Leuschel, M., Butler, M. (2005). Automatic Refinement Checking for B. In: Lau, KK., Banach, R. (eds) Formal Methods and Software Engineering. ICFEM 2005. Lecture Notes in Computer Science, vol 3785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11576280_24

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  • DOI: https://doi.org/10.1007/11576280_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29797-0

  • Online ISBN: 978-3-540-32250-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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