An Automation-Friendly Set Theory for the B Method

Guillaume Bury; Simon Cruanes; David Delahaye; Pierre-Louis Euvrard

An Automation-Friendly Set Theory for the B Method

Guillaume Bury ¹ Simon Cruanes ² David Delahaye ³ Pierre-Louis Euvrard ⁴

1 LSV - Laboratoire Spécification et Vérification [Cachan]

2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems

MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods

3 MAREL - Models And Reuse Engineering, Languages

LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier

4 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier

Abstract : We propose an automation-friendly set theory for the B method. This theory is expressed using first order logic extended to poly-morphic types and rewriting. Rewriting is introduced along the lines of deduction modulo theory, where axioms are turned into rewrite rules over both propositions and terms. We also provide experimental results of several tools able to deal with polymorphism and rewriting over a benchmark of problems in pure set theory (i.e. without arithmetic).

Keywords : B Method Set Theory Automated Deduction Polymorphic Types Rewriting

Document type :

Conference papers

Domain :

Computer Science [cs] / Logic in Computer Science [cs.LO]

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https://hal.archives-ouvertes.fr/hal-02082755
Contributor : David Delahaye <>
Submitted on : Thursday, March 28, 2019 - 2:09:47 PM
Last modification on : Saturday, July 13, 2019 - 11:44:37 AM
Long-term archiving on : Saturday, June 29, 2019 - 2:31:30 PM

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