Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving

摘要

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 SAS I MO, which relies on a deep embedding of the B theory within the logic of the Coq proof assistant and 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 SAS I MO.