Tuning the Alt-Ergo SMT Solver for B Proof Obligations

Abstract

Abstract. In this paper, we present recent developments in the AltErgo SMT-solver to e ciently discharge proof obligations (POs) generated by Atelier B. This includes a new plugin architecture to facilitate experiments with di erent SAT engines, new heuristics to handle quantied formulas, and important modi cations in its internal data structures to boost performances of core decision procedures. Experiments realized on more than 10,000 POs generated from industrial B projects show signi cant improvements. Alt-Ergo is an open-source SMT solver capable of reasoning in a combination of several built-in theories such as uninterpreted equality, integer and rational arithmetic, arrays, records, enumerated data types and AC symbols. It is the unique SMT solver that natively handles polymorphic rst-order quanti ed formulas, which makes it particularly suitable for program veri cation. For instance, AltErgo is used as a back-end of SPARK and Frama-C to discharge proof obligations generated from Ada and C programs, respectively. Recently, we started using Alt-Ergo in the context of the ANR project BWare [8] which aims at integrating SMT solvers as back-ends of Atelier B.The proof obligations sent to Alt-Ergo are extracted from Atelier B as logical formulas that are combined with a (polymorphic) model of B's set theory [7]. This process relies on the Why3 platform [6] which can target a wide range of SMT solvers. However, we show (Section 2) on a large benchmark of industrial B projects that it is not immediate to obtain a substantial gain of performances by using SMT solvers. Without a speci c tunning for B, Alt-Ergo together with other SMT solvers compete just equally with Atelier B's prover on those industrial benchmarks.In this paper, we report on recent developments in Alt-Ergo that signi cantly improve its capacities to handle POs coming from Atelier B. Our improvements are: (1) better heuristics for instantiating polymorphic quanti ed formulas from B model; (2) new e cient internal data structures; (3) a plugin architecture to facilitate experiments with di erent SAT engines; and (4) the implementation of a new CDCL-based SAT solver.

Encoding TLA+ into unsorted and many-sorted first-order logic

“…Function application is represented using a binary operator and then axiomatized. In the context of the BWare project, Conchon et al [10] proposed many internal optimizations to improve the performance of Alt-Ergo, in order to discharge Atelier-B proof obligations obtained from industrial settings.…”

Applying a Formal Method in Industry: A 25-Year Trajectory

“…Each PO thus includes a prelude where the logic of the B expression language is formalized in Why3 [14]. The axiomatization of the B operators in Why3 has been fine tuned based on an industrial benchmark, resulting in significant improvement of the automatic proving capabilities in Atelier B on that benchmark [6]. As the proof obligations are produced automatically, they include all the hypotheses that are in scope at the point the PO is concerned about.…”

Software Component Design with the B Method — A Formalization in Isabelle/HOL

“…However these rules have not been verified, and the resulting artifacts must be submitted to formal verification. Verification of proof obligations also benefits from advancement in automated theorem proving such as the use of SMT solvers [3,4]. One missing step in the verification aspect of the B method is the code generation from the implementation artifacts.…”