CC(X): Semantic Combination of Congruence Closure with Solvable Theories

Conchon, Sylvain; Contejean, Evelyne; Kanig, Johannes; Lescuyer, Stéphane

doi:10.1016/j.entcs.2008.04.080

Cited by 22 publications

(13 citation statements)

References 7 publications

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“…Such provers range from interactive proof assistants, such as Coq, to general-purpose automated theorem provers, such as Alt-Ergo, Z3, or CVC3, and even to dedicated theorem provers, such as Gappa. Using Why3, this goal is proved valid with any of Alt-Ergo [12], Z3 [13], or CVC3 [4].…”

Section: 2mentioning

confidence: 99%

Discharging Proof Obligations from Atelier B Using Multiple Automated Provers

Mentré

Marché

Filliâtre

et al. 2012

Abstract State Machines, Alloy, B, VDM, and Z

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Section: 2mentioning

confidence: 99%

Discharging Proof Obligations from Atelier B Using Multiple Automated Provers

Mentré

Marché

Filliâtre

et al. 2012

Abstract State Machines, Alloy, B, VDM, and Z

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“…These are logical formulas whose validity implies the soundness of the code with respect to the given specification. Finally, the VCs are discharged using one or several theorem provers, which range from interactive proof assistants such as Coq to purely automatic theorem provers such as Alt-Ergo [8]. The workflow is illustrated on Figure 1.…”

Section: Verification Of C Programsmentioning

confidence: 99%

Combining Coq and Gappa for Certifying Floating-Point Programs

Boldo

Filliâtre

Melquiond

2009

Lecture Notes in Computer Science

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Abstract. Formal verification of numerical programs is notoriously difficult. On the one hand, there exist automatic tools specialized in floatingpoint arithmetic, such as Gappa, but they target very restrictive logics. On the other hand, there are interactive theorem provers based on the LCF approach, such as Coq, that handle a general-purpose logic but that lack proof automation for floating-point properties. To alleviate these issues, we have implemented a mechanism for calling Gappa from a Coq interactive proof. This paper presents this combination and shows on several examples how this approach offers a significant speedup in the process of verifying floating-point programs.

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“…as conditional rewriting rules. For that, we are studying the design of a new combination algorithm which will extend our parametrized algorithms AC(X) [2] and CC(X) [3] to handle, in a uniform way, user-de ned rewriting systems. This would allow us to handle a fragment of the set theory of B in a built-in way.…”

Section: Alt-ergomentioning

confidence: 99%

Tuning the Alt-Ergo SMT Solver for B Proof Obligations

Conchon

Iguernelala

2014

Lecture Notes in Computer Science

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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.

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CC(X): Semantic Combination of Congruence Closure with Solvable Theories

Cited by 22 publications

References 7 publications

Discharging Proof Obligations from Atelier B Using Multiple Automated Provers

Discharging Proof Obligations from Atelier B Using Multiple Automated Provers

Combining Coq and Gappa for Certifying Floating-Point Programs

Tuning the Alt-Ergo SMT Solver for B Proof Obligations

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