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Verifying B proof rules using deep embedding and automated theorem proving

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Abstract

We propose a formal and mechanized framework which consists in verifying proof rules of the B method, which cannot be automatically proved by the elementary prover of Atelier B and using an external automated theorem prover called Zenon. This framework contains in particular a set of tools, named BCARe and developed by Siemens IC-MOL, which relies on a deep embedding of the B theory within the logic of the Coq proof assistant. This toolkit allows us to automatically generate the required properties to be checked for a given proof rule. Currently, this tool chain is able to automatically verify a part of the derived rules of the B-Book, as well as some added rules coming from Atelier B and the rule database maintained by Siemens IC-MOL.

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Acknowledgments

The authors wish to thank the anonymous reviewers for their helpful comments and suggestions. They also thank Éric Dubois for his help in the production of the graphics for the benchmarks, as well as Hélène and Dalton Nelson for their careful reading.

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Authors and Affiliations

  1. Siemens IC-MOL, Châtillon, France

    Mélanie Jacquel & Karim Berkani

  2. CEDRIC/CNAM, Paris, France

    David Delahaye

  3. INRIA/CEDRIC/ENSIIE, Paris, France

    Catherine Dubois

Authors
  1. Mélanie Jacquel
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  2. Karim Berkani
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  3. David Delahaye
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  4. Catherine Dubois
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Corresponding author

Correspondence to David Delahaye.

Additional information

Communicated by Dr. Gerardo Schneider, Gilles Barthe, and Alberto Pardo.

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Jacquel, M., Berkani, K., Delahaye, D. et al. Verifying B proof rules using deep embedding and automated theorem proving. Softw Syst Model 14, 101–119 (2015). https://doi.org/10.1007/s10270-013-0322-z

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  • DOI: https://doi.org/10.1007/s10270-013-0322-z

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