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Refactoring Refinement Structure of Event-B Machines

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FM 2016: Formal Methods (FM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9995))

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Abstract

Refinement in formal specifications has received significant attention as a method to gradually construct a rigorous model. Although refactoring methods for formal specifications have been proposed, there are no methods for refactoring of refinement structures in formal specifications. In this paper, we describe a method to restructure refinements in specifications of Event-B, a formal specification method with supports for refinement. The core of our method is decomposition of refinements. Namely, when an abstract Event-B machine A, a concrete machine C refining A, and a slicing strategy are provided, our method constructs a consistent intermediate machine B, which refines A and is refined by C. We show effectiveness of our methods through two case studies on representative usages of our method: decomposition of large-scale refinements and extraction of reusable parts of specifications.

This work is partially supported by JSPS KAKENHI Grant Number 26700005.

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Notes

  1. 1.

    Assume that a function \(\mathrm {mod2}(n)\) that returns \(n \, \mathrm {modulo} \, 2\) is defined in a context.

  2. 2.

    Actually static predicates (axioms) and predicates of event parameters are also included in POs. We will omit them for the sake of simplicity.

  3. 3.

    BAPs that are expressible by \(V_{\mathrm {B}}\cup V_{\mathrm {B}}'\) are also specified, where \(V_{\mathrm {B}}'\) represents the set of after-state variables of \(V_{\mathrm {B}}\).

  4. 4.

    Available at http://tkoba.jp/software/slice_and_merge/.

  5. 5.

    For the sake of simplicity we did not count invariants for typing.

  6. 6.

    There were differences in the actual specifications, because several invariants were moved in order to abstract the intermediate machines and the refinement structures of the events were changed.

  7. 7.

    Models of this case study are at http://tkoba.jp/publications/fm2016/

References

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

    Book  MATH  Google Scholar 

  2. Abrial, J.R., Hallerstede, S.: Refinement, decomposition, and instantiation of discrete models: application to Event-B. Fundamenta Informaticae 77(1–2), 1–28 (2007)

    MathSciNet  MATH  Google Scholar 

  3. Butler, M.: Decomposition structures for Event-B. In: Leuschel, M., Wehrheim, H. (eds.) IFM 2009. LNCS, vol. 5423, pp. 20–38. Springer, Heidelberg (2009). doi:10.1007/978-3-642-00255-7_2

    Chapter  Google Scholar 

  4. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). doi:10.1007/10722167_15

    Chapter  Google Scholar 

  5. Correa, A., Werner, C., Barros, M.: An empirical study of the impact of OCL smells and refactorings on the understandability of OCL specifications. In: Engels, G., Opdyke, B., Schmidt, D.C., Weil, F. (eds.) MODELS 2007. LNCS, vol. 4735, pp. 76–90. Springer, Heidelberg (2007). doi:10.1007/978-3-540-75209-7_6

    Chapter  Google Scholar 

  6. Degiovanni, R., Alrajeh, D., Aguirre, N., Uchitel, S.: Automated goal operationalisation based on interpolation and SAT solving. In: Proceedings of the 36th International Conference on Software Engineering, pp. 129–139. ACM, New York (2014)

    Google Scholar 

  7. Gheyi, R., Borba, P.: Refactoring alloy specifications. Electron. Notes Theoret. Comput. Sci. 95, 227–243 (2004)

    Article  Google Scholar 

  8. Marković, S., Baar, T.: Refactoring OCL annotated UML class diagrams. In: Briand, L., Williams, C. (eds.) MODELS 2005. LNCS, vol. 3713, pp. 280–294. Springer, Heidelberg (2005). doi:10.1007/11557432_21

    Chapter  Google Scholar 

  9. Matichuk, D., Murray, T., Andronick, J., Jeffery, R., Klein, G., Staples, M.: Empirical Study Towards a Leading Indicator for Cost of Formal Software Verification. In: Proceedings of the 37th International Conference on Software Engineering. pp. 722–732. ACM, New York (2015)

    Google Scholar 

  10. McComb, T., Smith, G.: A minimal set of refactoring rules for object-Z. In: Barthe, G., Boer, F.S. (eds.) FMOODS 2008. LNCS, vol. 5051, pp. 170–184. Springer, Heidelberg (2008). doi:10.1007/978-3-540-68863-1_11

    Chapter  Google Scholar 

  11. Stepney, S., Polack, F., Toyn, I.: Refactoring in maintenance and development of Z specifications and proofs. ENTCS 70(3), 50–69 (2002)

    MATH  Google Scholar 

  12. Tarasyuk, A., Pereverzeva, I., Troubitsyna, E., Latvala, T.: The formal derivation of mode logic for autonomous satellite flight formation. In: Koornneef, F., Gulijk, C. (eds.) SAFECOMP 2015. LNCS, vol. 9337, pp. 29–43. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24255-2_4

    Chapter  Google Scholar 

  13. Whiteside, I.J.: Refactoring Proofs. Ph.D. thesis, The University of Edinburgh (2013)

    Google Scholar 

  14. Yaghoubi Shahir, H., Farahbod, R., Glässer, U.: Refactoring abstract state machine models. In: Derrick, J., Fitzgerald, J., Gnesi, S., Khurshid, S., Leuschel, M., Reeves, S., Riccobene, E. (eds.) ABZ 2012. LNCS, vol. 7316, pp. 345–348. Springer, Heidelberg (2012). doi:10.1007/978-3-642-30885-7_28

    Chapter  Google Scholar 

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Authors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Tsutomu Kobayashi & Shinichi Honiden

  2. National Institute of Informatics, Tokyo, Japan

    Fuyuki Ishikawa & Shinichi Honiden

Authors
  1. Tsutomu Kobayashi
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  2. Fuyuki Ishikawa
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  3. Shinichi Honiden
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Corresponding author

Correspondence to Tsutomu Kobayashi .

Editor information

Editors and Affiliations

  1. Newcastle University, Newcastle upon Tyne, United Kingdom

    John Fitzgerald

  2. US Naval Research Laboratory, Washington, District of Columbia, USA

    Constance Heitmeyer

  3. ISTI-CNR, Pisa, Italy

    Stefania Gnesi

  4. University of Cyprus, Nicosia, Cyprus

    Anna Philippou

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Kobayashi, T., Ishikawa, F., Honiden, S. (2016). Refactoring Refinement Structure of Event-B Machines. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds) FM 2016: Formal Methods. FM 2016. Lecture Notes in Computer Science(), vol 9995. Springer, Cham. https://doi.org/10.1007/978-3-319-48989-6_27

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  • DOI: https://doi.org/10.1007/978-3-319-48989-6_27

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  • Print ISBN: 978-3-319-48988-9

  • Online ISBN: 978-3-319-48989-6

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