The Use of Rippling to Automate Event-B Invariant Preservation Proofs

  • Yuhui Lin
  • Alan Bundy
  • Gudmund Grov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7226)


Proof automation is a common bottleneck for industrial adoption of formal methods. In Event-B, a significant proportion of proof obligations which require human interaction fall into a family called invariant preservation. In this paper we show that a rewriting technique called rippling can increase the automation of proofs in this family, and extend this technique by combining two existing approaches.


Event-B automated reasoning rippling lemma conjecture 


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  1. 1.
    Abrial, J.R.: Formal methods in industry: achievements, problems, future. In: Proceedings of the 28th International Conference on Software Engineering, pp. 761–768. ACM (2006)Google Scholar
  2. 2.
    Abrial, J.R.: Modeling in Event-B - System and Software Engineering. Cambridge University Press (2010)Google Scholar
  3. 3.
    Abrial, J.R., Butler, M.J., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: an open toolset for modelling and reasoning in event-B. STTT 12(6), 447–466 (2010)CrossRefGoogle Scholar
  4. 4.
    Armando, A., Smaill, A., Green, I.: Automatic synthesis of recursive programs: The proof-planning paradigm. Autom. Softw. Eng. 6(4), 329–356 (1999)CrossRefGoogle Scholar
  5. 5.
    Bundy, A.: A Science of Reasoning. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 633–640. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  6. 6.
    Bundy, A.: Rippling: meta-level guidance for mathematical reasoning, vol. 56. Cambridge Univ. Pr. (2005)Google Scholar
  7. 7.
    Ireland, A.: Productive use of failure in inductive proof. Journal of Automated Reasoning 16(1-2), 79–111 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Jones, C.B., Grov, G., Bundy, A.: Ideas for a high-level proof strategy language. Tech. Rep. CS-TR-1210, School of Computing Science, Newcastle University (2010)Google Scholar
  9. 9.
    Kraan, I., Basin, D., Bundy, A.: Middle-out reasoning for synthesis and induction. Journal of Automated Reasoning 16(1), 113–145 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Montano-Rivas, O., McCasland, R.L., Dixon, L., Bundy, A.: Scheme-Based Synthesis of Inductive Theories. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds.) MICAI 2010, Part I. LNCS, vol. 6437, pp. 348–361. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yuhui Lin
    • 1
  • Alan Bundy
    • 1
  • Gudmund Grov
    • 1
  1. 1.School of InformaticsUniversity of EdinburghUK

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