An Automation-Friendly Set Theory for the B Method

Guillaume Bury 1 Simon Cruanes 2 David Delahaye 3 Pierre-Louis Euvrard 4
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
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).
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Guillaume Bury, Simon Cruanes, David Delahaye, Pierre-Louis Euvrard. An Automation-Friendly Set Theory for the B Method. ABZ: Abstract State Machines, Alloy, B, TLA, VDM, and Z, Jun 2018, Southampton, United Kingdom. pp.409-414, ⟨10.1007/978-3-319-91271-4_32⟩. ⟨hal-02082755⟩

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