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Automating Event-B invariant proofs by rippling and proof patching

Formal Aspects of Computing volume 31, pages 95–129 (2019)Cite this article

Abstract

The use of formal method techniques can contribute to the production of more reliable and dependable systems. However, a common bottleneck for industrial adoption of such techniques is the needs for interactive proofs. We use a popular formal method, called Event-B, as our working domain, and set invariant preservation (INV) proofs as targets, because INV proofs can account for a significant proportion of the proofs requiring human interactions. We apply an inductive theorem proving technique, called rippling, for Event-B INV proofs. Rippling automates proofs using meta-level guidance. The guidance is in particular useful to develop proof patches to recover failed proof attempts. We are interested in the case when a missing lemma is required. We combine a scheme-based theory-exploration system, called IsaScheme [MRMDB10], with rippling to develop a proof patch via lemma discovery. We also develop two new proof patches to unfold operator definitions and to suggest case-splits, respectively. The combined use of rippling with these three proof patches as a proof method significantly improves the proof automation for our evaluation set.

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Acknowledgements

This work is supported by EPSRC Grants EP/H024204/1, EP/E005713/1, EP/M018407/1 and EP/J001058/1.We warmly thank OmarMontano Rivas for his support on IsaScheme.We also thank anonymous referees for their helpful suggestions.

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Authors and Affiliations

  1. School of Informatics, University of Edinburgh, Edinburgh, UK

    Yuhui Lin, Alan Bundy & Ewen Maclean

  2. School of Computer Science, University of St Andrews, St Andrews, UK

    Yuhui Lin

  3. Norwegian Defence Research Establishment(FFI), Kjeller, Norway

    Gudmund Grov

  4. School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK

    Yuhui Lin & Gudmund Grov

Authors
  1. Yuhui Lin
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  2. Alan Bundy
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  3. Gudmund Grov
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  4. Ewen Maclean
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Correspondence to Yuhui Lin.

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Communicated by Michael Butler

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Lin, Y., Bundy, A., Grov, G. et al. Automating Event-B invariant proofs by rippling and proof patching. Form Asp Comp 31, 95–129 (2019). https://doi.org/10.1007/s00165-018-00476-7

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  • DOI: https://doi.org/10.1007/s00165-018-00476-7

Keywords

  • Formal verification
  • Event-B
  • Automated reasoning
  • Rippling
  • Lemma conjecturing