Modular SMT Proofs for Fast Reflexive Checking Inside Coq

Besson, Frédéric; Cornilleau, Pierre-Emmanuel; Pichardie, David

doi:10.1007/978-3-642-25379-9_13

Cited by 15 publications

(18 citation statements)

References 25 publications

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“…This tactic combines equational reasoning on Qc field with a bit of congruence. 4 Let us detail how it works on this example. First, in backward reasoning, H5 is applied to eliminate False from the conclusion.…”

Section: Using the Vpl Tacticmentioning

confidence: 99%

“…It is much less powerful than Coq SMT tactics [1,4] and than the famous sledgehammer of Isabelle [6,5]. But, it may help users to progress on goals that do not exactly fit into the scope of existing SMT-solving procedures.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

“…As detailed below, equality learning plays a crucial role in this proof: the rewriting of a learned equality inside a non-linear term (because under symbol f) is interleaved between deduction steps in linear arithmetic. Of course, such a goal is also provable in Z by SMT-solving tactics: the verit tactic of SMTCoq [1] or the one of Besson et al [4]. However, such a SMT-tactic is also a "prove-or-fail" tactic that do not simplify the goal when it cannot prove it.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Coq Tactic for Equality Learning in Linear Arithmetic

Boulmé

Maréchal

2018

Interactive Theorem Proving

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Abstract. Coq provides linear arithmetic tactics like omega or lia. Currently, these tactics either fully prove the goal in progress, or fail. We propose to improve this behavior: when the goal is not provable in linear arithmetic, we inject in hypotheses new equalities discovered from the linear inequalities. These equalities may help other Coq tactics to discharge the goal. In other words, we apply -in interactive proofsone of the seminal idea of SMT-solving: combining tactics by exchanging equalities. The paper describes how we have implemented equality learning in a new Coq tactic, dealing with linear arithmetic over rationals. It also illustrates how this tactic interacts with other Coq tactics.

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Section: Using the Vpl Tacticmentioning

confidence: 99%

Section: Conclusion and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Coq Tactic for Equality Learning in Linear Arithmetic

Boulmé

Maréchal

2018

Interactive Theorem Proving

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“…Our approach is more automatic and capture a family of analyses at the cost of integrating provers in the TCB. However, generating foundational proofs for provers is also an active research area [11,8,3]. These works pave the way for foundational proofs of family of static analysis results.…”

Section: Related Workmentioning

confidence: 99%

Result Certification of Static Program Analysers with Automated Theorem Provers

Besson

Cornilleau

Jensen

2014

Verified Software: Theories, Tools, Experiments

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Abstract. The automation of the deductive approach to program verification crucially depends on the ability to efficiently infer and discharge program invariants. In an ideal world, user-provided invariants would be strengthened by incorporating the result of static analysers as untrusted annotations and discharged by automated theorem provers. However, the results of object-oriented analyses are heavily quantified and cannot be discharged, within reasonable time limits, by state-of-the-art automated theorem provers. In the present work, we investigate an original approach for verifying automatically and efficiently the result of certain classes of object-oriented static analyses using off-the-shelf automated theorem provers. We propose to generate verification conditions that are generic enough to capture, not a single, but a family of analyses which encompasses Java bytecode verification and Fähndrich and Leino typesystem for checking null pointers. For those analyses, we show how to generate tractable verification conditions that are still quantified but fall in a decidable logic fragment that is reducible to the Effectively Propositional logic. Our experiments confirm that such verification conditions are efficiently discharged by off-the-shelf automated theorem provers.

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“…For instance, several proof assistants propose an infrastructure allowing the user to call an external SMT-solver as a blackbox and re-interpret its output to reconstruct a proof within the system [2,8,9,35]. This blackbox infrastructure is natural, given the available tools, their development history, and the communities that designed their techniques.…”

mentioning

confidence: 99%

A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus

Farooque

Graham-Lengrand

Mahboubi

2013

Proceedings of the Eighth ACM SIGPLAN International Workshop on Logical Frameworks &Amp; Meta-Languages: Theory &Amp; Practice

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We describe how the Davis-Putnam-Logemann-Loveland procedure DPLL is bisimilar to the goal-directed proof-search mechanism described by a standard but carefully chosen sequent calculus. We thus relate a procedure described as a transition system on states to the gradual completion of incomplete proof-trees.For this we use a focused sequent calculus for polarised classical logic, for which we allow analytic cuts. The focusing mechanisms, together with an appropriate management of polarities, then allows the bisimulation to hold: The class of sequent calculus proofs that are the images of the DPLL runs finishing on UNSAT, is identified with a simple criterion involving polarities.We actually provide those results for a version DPLL(T ) of the procedure that is parameterised by a background theory T for which we can decide whether conjunctions of literals are consistent. This procedure is used for Satisfiability Modulo Theories (SMT) generalising propositional SAT. For this, we extend the standard focused sequent calculus for propositional logic in the same way DPLL(T ) extends DPLL: with the ability to call the decision procedure for T . DPLL(T ) is implemented as a plugin for PSYCHE, a proofsearch engine for this sequent calculus, to provide a sequentcalculus based SMT-solver.

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Modular SMT Proofs for Fast Reflexive Checking Inside Coq

Cited by 15 publications

References 25 publications

A Coq Tactic for Equality Learning in Linear Arithmetic

A Coq Tactic for Equality Learning in Linear Arithmetic

Result Certification of Static Program Analysers with Automated Theorem Provers

A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus

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