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Shared Event Composition/Decomposition in Event-B

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Formal Methods for Components and Objects (FMCO 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6957))

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Abstract

The construction of specifications is often a combination of smaller sub-components. Composition and decomposition are techniques supporting reuse and allowing formal combination of sub-components through refinement steps. Sub-components can result from a design or architectural goal and a refinement framework should allow them to be further developed, possibly in parallel. We propose the definition of composition and decomposition in the Event-B formalism following a shared event approach where sub-components interact via synchronised shared events and shared states are not allowed. We define the necessary proof obligations to ensure valid compositions and decompositions. We also show that shared event composition preserves refinement proofs, that is, in order to maintain refinement of compositions, it is sufficient to prove refinement between corresponding sub-components. A case study applying these two techniques is illustrated using Rodin, the Event-B toolset.

Part of this research was carried out within the European Commission ICT project 214158 DEPLOY ( http://www.deploy-project.eu .

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References

  1. Jackson, D.: Structuring Z specifications with views. ACM Trans. Softw. Eng. Methodol. 4(4), 365–389 (1995)

    Article  Google Scholar 

  2. Zave, P., Jackson, M.: Conjunction as Composition. ACM Trans. Softw. Eng. Methodol. 2(4), 379–411 (1993)

    Article  Google Scholar 

  3. Jones, C.B.: Wanted: a compositional approach to concurrency. In: Programming Methodology, pp. 5–15. Springer-Verlag New York, Inc, New York (2003)

    Chapter  Google Scholar 

  4. Poppleton, M.: The Composition of Event-B Models. In: Börger, E., Butler, M., Bowen, J.P., Boca, P. (eds.) ABZ 2008. LNCS, vol. 5238, pp. 209–222. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Abrial, J.R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  7. Butler, M.: An Approach to the Design of Distributed Systems with B AMN. In: Till, D., P. Bowen, J., Hinchey, M.G. (eds.) ZUM 1997. LNCS, vol. 1212, pp. 221–241. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  8. Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall International Series in Computer Science (1985)

    Google Scholar 

  9. Morgan, C.: Of wp and CSP. In: Beauty is our Business: a Birthday Salute to Edsger W. Dijkstra, pp. 319–326. Springer-Verlag New York, Inc., New York (1990)

    Chapter  Google Scholar 

  10. Back, R.-J.R., Kurki-Suonio, R.: Decentralization of Process Nets with Centralized Control. In: PODC 1983: Proceedings of the Second Annual ACM Symposium on Principles of Distributed Computing, pp. 131–142. ACM, New York (1983)

    Chapter  Google Scholar 

  11. Abrial, J.R.: The B-Book: Assigning programs to meanings. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  12. Rodin: RODIN project Homepage (September 2008), http://rodin.cs.ncl.ac.uk (accessed July 27, 2010)

  13. Abrial, J.R., Butler, M.J., Hallerstede, S., Voisin, L.: An Open Extensible Tool Environment for Event-B. In: Liu, Z., Kleinberg, R.D. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 588–605. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Spivey, J.M.: The Z Notation: a Reference Manual. Prentice-Hall, Inc., Englewood Cliffs (1989)

    MATH  Google Scholar 

  15. Butler, M.J.: A CSP Approach to Action Systems. PhD thesis, Oxford University (1992)

    Google Scholar 

  16. Butler, M.: Stepwise Refinement of Communicating Systems. Science of Computer Programming 27(2), 139–173 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Butler, M.: Synchronisation-Based Decomposition for Event-B. In: RODIN Deliverable D19 Intermediate Report on Methodology, pp. 47–57 (2006)

    Google Scholar 

  18. Abrial, J.R., Butler, M., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: An Open Toolset for Modelling and Reasoning in Event-B. International Journal on Software Tools for Technology Transfer, STTT (April 2010)

    Google Scholar 

  19. Silva, R., Pascal, C., Hoang, T.S., Butler, M.: Decomposition Tool for Event-B. Software: Practice and Experience 41(2), 199–208 (2011)

    Google Scholar 

  20. Silva, R., Butler, M.: Parallel Composition Using Event-B (July 2009), http://wiki.event-b.org/index.php/Parallel_Composition_using_Event-B (accessed July 27, 2010)

  21. Back, R.-J.R.: Refinement Calculus, part II: Parallel and Reactive Programs. 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 

  22. Abadi, M., Lamport, L.: Composing Specifications. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds.) REX 1989. LNCS, vol. 430, pp. 1–41. Springer, Heidelberg (1990)

    Google Scholar 

  23. Woodcock, J., Dickinson, B.: Using VDM with Rely and Guarantee-Conditions. In: Bloomfield, R.E., Jones, R.B., Marshall, L.S. (eds.) VDM 1988. LNCS, vol. 328, pp. 434–458. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  24. Bellegarde, F., Julliand, J., Kouchnarenko, O.: Synchronized Parallel Composition of Event Systems in B. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 436–457. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  25. Butler, M., Waldén, M.: Distributed System Development in B. Technical Report TUCS-TR-53, Turku Centre for Computer Science, 14 (1996)

    Google Scholar 

  26. Hoang, T., Abrial, J.R.: Event-B Decomposition for Parallel Programs. In: Frappier, M., Glässer, U., Khurshid, S., Laleau, R., Reeves, S. (eds.) ABZ 2010. LNCS, vol. 5977, pp. 319–333. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

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Silva, R., Butler, M. (2011). Shared Event Composition/Decomposition in Event-B. In: Aichernig, B.K., de Boer, F.S., Bonsangue, M.M. (eds) Formal Methods for Components and Objects. FMCO 2010. Lecture Notes in Computer Science, vol 6957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25271-6_7

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  • DOI: https://doi.org/10.1007/978-3-642-25271-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25270-9

  • Online ISBN: 978-3-642-25271-6

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