Abstract
The ProB disprover uses constraint solving to find counter-examples for B proof obligations. As the ProB kernel is now capable of determining whether a search was exhaustive, one can also use the disprover as a prover. In this paper, we explain how ProB has been embedded as a prover into Rodin and Atelier B. Furthermore, we compare ProB with the standard automatic provers and SMT solvers used in Rodin. We demonstrate that constraint solving in general and ProB in particular are able to deal with classes of proof obligations that are not easily discharged by other provers and solvers. As benchmarks we use medium sized specifications such as landing gear systems, a CAN bus specification and a railway system. We also present a new method to check proof obligations for inconsistencies, which has helped uncover various issues in existing (sometimes fully proven) models.
Parts of this research have been sponsored by the EU funded FP7 project 287563 (ADVANCE) and by an industrial project funded by Alstom.
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Notes
- 1.
Deferred sets are sets which are not given upfront by enumerating their elements.
- 2.
This includes quantification, negation and arbitrarily nested combinations of them.
- 3.
Which ProB can find if we enlarge the default search space, e.g., by adding \(i<10000\) as additional constraint.
- 4.
This work was conducted in a joint project with ClearSy (Lilian Burdy, Etienne Prun) and funded by Alstom (Fernando Mejia).
- 5.
Deeper within a proof, contradicting hypotheses can occur “naturally”.
- 6.
See https://github.com/wysiib/ProverEvaluationPlugin for sources and instructions.
- 7.
For a standalone version of ProB see http://www.prob2.de.
- 8.
For technical reasons this axiom is not yet included in the unsat core; partition axioms are never removed from the core by the current algorithm.
- 9.
In LPN4 of [26]: treat_hndl_up_122, treat_hndl_up_132, treat_hndl_dn_112, treat_hndl_dn_122, treat_hndl_dn_132.
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Acknowledgements
We would like to thank the various developers for giving us access to their Event-B models, and for discussions and feedback: Jean-Raymond Abrial, Andre, Attiogbe, John Colley, Régine Laleau, Luis-Fernando Mejia, Lanoix, Amel Mammar, Dominique Méry, Neeraj Kumar Singh, Wen Su.
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Krings, S., Bendisposto, J., Leuschel, M. (2015). From Failure to Proof: The ProB Disprover for B and Event-B. In: Calinescu, R., Rumpe, B. (eds) Software Engineering and Formal Methods. SEFM 2015. Lecture Notes in Computer Science(), vol 9276. Springer, Cham. https://doi.org/10.1007/978-3-319-22969-0_15
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