Soundly Proving B Method Formulae Using Typed Sequent Calculus

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 first-order 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.
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Pierre Halmagrand. Soundly Proving B Method Formulae Using Typed Sequent Calculus. 13th International Colloquium on Theoretical Aspects of Computing (ICTAC), Oct 2016, Taipei, Taiwan. pp 196-213, ⟨10.1007/978-3-319-46750-4_12⟩. ⟨hal-01342849⟩



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