Soundly Proving B Method Formulæ Using Typed Sequent Calculus

Abstract

Abstract. The B Method is a formal method mainly used in the railway industry to specify and develop safety-critical software. To guarantee the consistency of a B project, one decisive challenge is to show correct a large amount of proof obligations, which are mathematical formulae expressed in a classical set theory extended with a specific type system. To improve automated theorem proving in the B Method, we propose to use a firstorder sequent calculus extended with a polymorphic type system, which is in particular the output proof-format of the tableau-based automated theorem prover Zenon. After stating some modifications of the B syntax and defining a sound elimination of comprehension sets, we propose a translation of B formulae into a polymorphic first-order logic format. Then, we introduce the typed sequent calculus used by Zenon, and show that Zenon proofs can be translated to proofs of the initial B formulae in the B proof system.

First-Order Automated Reasoning with Theories: When Deduction Modulo Theory Meets Practice

“…The main distinctive feature of the B set theory compared to usual set theories, like Zermelo-Frankel's set theory, is the addition of typing constraints to expressions. Since the type system of the B method can be interpreted as a polymorphic type system [69], an encoding of the B set theory in an ML-like language called WhyML has been proposed in BWare. WhyML is the native language of Why3 [26], a platform dedicated to program verification and used in BWare to manage several automated reasoning tools like Zenon Modulo in particular.…”