An Automation-Friendly Set Theory for the B Method

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).