Section: Application Domains

B-set theory

The B method allows the user to develop software correct by construction, going from abstract models to implementations via refinement. During the development process, proof obligations are generated. The formalism underlying B is based on predicate logic and B-set theory. Atelier B that supports the B method provides interactive and automatic provers. To increase automation the user may add proof rules which, if not correct, may corrupt the process. Siemens has developed a tool chain to verify such added proof rules. In particular we have to verify that any proof rule derives from B logic. This step has to be as automatic as possible. Furthermore confidence in these verification proofs is required. A first attempt using the first order prover Zenon allowed the verification of a large number of proof rules [10] . To go further we have experimented techniques such as super deduction and deduction modulo. B-set theory is an interesting benchmark for the tools developed by Deducteam since this theory contains numerous operators and predicates defined by equations or rewrite rules.