Scalable automated proving and debugging of set-based specifications

Abstract

We present a technique to prove invariants of model-based specifications in a fragment of set theory. Proof obligations containing set theory constructs are translated to first-order logic with equality augmented with (an extension of) the theory of arrays with extensionality. The idea underlying the translation is that sets are represented by their characteristic function which, in turn, is encoded by an array of Booleans indexed on the elements of the set. A theorem proving procedure automating the verification of the proof obligations obtained by the translation is described. Furthermore, we discuss how a sub-formula can be extracted from a failed proof attempt and used by a model finder to build a counter-example. To be concrete, we use a B specification of a simple process scheduler on which we illustrate our technique.