Experimenting with Deduction Modulo

Burel, Guillaume

doi:10.1007/978-3-642-22438-6_14

Cited by 18 publications

(17 citation statements)

References 13 publications

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“…In the deduction-modulo approach to theorem proving (Dowek et al, 2003), a first-order presentation of (intensional) higher-order logic can be exploited to automate higher-order reasoning . A recent implementation of the deduction modulo approach (still restricted to first-order) has been presented by Burel (2011b); see also the Dedukti proof checker (Boespflug et al, 2012).…”

Section: Early Systemsmentioning

confidence: 99%

Automation of Higher-Order Logic

Benzmüller¹,

Miller²

2014

Handbook of the History of Logic

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Section: Early Systemsmentioning

confidence: 99%

Automation of Higher-Order Logic

Benzmüller¹,

Miller²

2014

Handbook of the History of Logic

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“…We also plan to investigate whether deduction modulo techniques, like those in Zenon Modulo [4,5] and iProver Modulo [1], would be helpful to e ciently handle quanti ed formulas in the SMT world. Another line of research would be the generation of veri able traces for external proof checkers in order to augment our con dence in the SMT solver.…”

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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“…The satisfiability of this formula can be proved by reducing it to effectively propositional case [8], where the sub-formula ∀xA is replaced by A(s 1 /x) ∧ · · · ∧ A(s n /x), and ∃xA by A(s 1 /x)∨· · ·∨A(s n /x), in which s 1 , ..., s n are the constants for all the vertices of a graph. By representing the theory of the graph as a set of rewrite rules [7], these problems can be proved by some off-the-shelf automated theorem provers, such as iProver Modulo [2]. As these problems can be expressed with temporal formulae [3], they can also be solved by model checking tools.…”

Section: Introductionmentioning

confidence: 99%

Resolution in Solving Graph Problems

2016

Lecture Notes in Computer Science

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Experimenting with Deduction Modulo

Cited by 18 publications

References 13 publications

Automation of Higher-Order Logic

Automation of Higher-Order Logic

Tuning the Alt-Ergo SMT Solver for B Proof Obligations

Resolution in Solving Graph Problems

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