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.

Combining Data Structures with Nonstably Infinite Theories Using Many-Sorted Logic

“…We also wish to implement our combination method in haRVey [5], and apply it to the verification of set-based specifications of smart-cards [4].…”

Distributing the Workload in a Lazy Theorem-Prover

“…provers providing a high-degree of automation for selected classes of formulae in decidable theories of first-order logic (FOL). Lightweight theorem provers have also been used successfully to check consistency of formal specification artifacts [9] and extended static checking of software code [14]. The construction of such provers has been made possible by recent advances in the integration of highly efficient Boolean solvers (e.g.…”

A prototype implementation of a distributed Satisfiability Modulo Theories solver in the ToolBus framework

“…A peculiarity of haRVey is that the implementation of the function unsat T is done by an automated (first-order) theorem prover, called the E prover [28], which is combined with a decision procedure for a fragment of Linear Arithmetic via the Nelson-Oppen combination schema [24]. The availability of an automated prover for full first-order logic makes it possible to handle also formulas containing quantifiers, as shown in [11], and this is particularly useful for software verification. So far, haRVey has been successfully applied to the verification of pointer-based programs [27], B specifications [11], static checking of automatically generated code for aerospatial applications [16] as well as array programs [14].…”

“…As benchmark problems, we have selected 50 proof obligations requiring several interactions between the Boolean solver and the satisfiability procedure from previous experiences with the sequential version of haRVey (namely, proof obligations generated from the B methodology [11], the verification of pointer-manipulating programs and Burns protocol [27]). The goal of our experiments was to understand if it were possible to significantly reduce the overall running time by invoking several instances of the satisfiability procedure concurrently.…”

“…After the implementation of the distributed version of haRVey was completed, its behavior was tested on a set of problems which are representative of those generated by software verification techniques, where the sequential version of the solver was already successfully used (see [15,11]). The main contribution of this work is to show the possibility to obtain super-linear speed-ups for the distributed version of the SMT solver with respect to its sequential version.…”