Language and Proofs for Higher-Order SMT (Work in Progress)

Barbosa, Haniel; Blanchette, Jasmin Christian; Cruanes, Simon; Ouraoui, Daniel El; Fontaine, Pascal

doi:10.4204/eptcs.262.3

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…Furthermore, there are efforts to extend SMT solvers to higher-order logic [34], [35] but the techniques seem to be incomplete even for Henkin semantics.…”

Section: A Combining the Bernays-schönfinkel-ramsey Fragment Of Hochc...mentioning

confidence: 99%

HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories

Ong¹,

Wagner²

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC)-a system of higher-order logic modulo theories-and prove its soundness and refutational completeness w.r.t. both standard and Henkin semantics. As corollaries, we obtain the compactness theorem and semi-decidability of HoCHC for semi-decidable background theories, and we prove that HoCHC satisfies a canonical model property. Moreover a variant of the well-known translation from higher-order to 1st-order logic is shown to be sound and complete for HoCHC in both semantics. We illustrate how to transfer decidability results for (fragments of) 1st-order logic modulo theories to our higher-order setting, using as example the Bernays-Schönfinkel-Ramsey fragment of HoCHC modulo a restricted form of Linear Integer Arithmetic.

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“…Furthermore, there are efforts to extend SMT solvers to higher-order logic [34], [35] but the techniques seem to be incomplete even for Henkin semantics.…”

Section: A Combining the Bernays-schönfinkel-ramsey Fragment Of Hochc...mentioning

confidence: 99%

HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories

Ong¹,

Wagner²

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…Increasingly, however, SMT solvers also support quantified formulas. Hence there is overlap between SMT solving and automated theorem proving for quantified Boolean formulas (QBF), first-order logic, and even higher-order logic [2].…”

Section: Introductionmentioning

confidence: 99%

The SMT Competition 2015–2018

Weber

Conchon

Déharbe³

et al. 2019

SAT

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The International Satisfiability Modulo Theories Competition is an annual competition between Satisfiability Modulo Theories (SMT) solvers. The 2018 edition of the competition was part of the FLoC Olympic Games, which comprised 14 competitions in various areas of computational logic. We report on the design and selected results of the SMT Competition during the last FLoC Olympiad, from 2015 to 2018. These competitions set several new records regarding the number of participants, number of benchmarks used, and amount of computation performed.

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“…http://matryoshka.gforge.inria.fr/pubs/hosmt/ 2 Since veriT does not parse TPTP, its reported results are on the equivalent benchmarks as translated by CVC4 into the HOSMT language[3].…”

mentioning

confidence: 99%

Extending SMT Solvers to Higher-Order Logic

Barbosa

Reynolds

Ouraoui

et al. 2019

Lecture Notes in Computer Science

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SMT solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic (FOL). In contrast, the extension of SMT solvers to higher-order logic (HOL) is mostly unexplored. We propose a pragmatic extension for SMT solvers to support HOL reasoning natively without compromising performance on FOL reasoning, thus leveraging the extensive research and implementation efforts dedicated to efficient SMT solving. We show how to generalize data structures and the ground decision procedure to support partial applications and extensionality, as well as how to reconcile quantifier instantiation techniques with higher-order variables. We also discuss a separate approach for redesigning an HOL SMT solver from the ground up via new data structures and algorithms. We apply our pragmatic extension to the CVC4 SMT solver and discuss a redesign of the veriT SMT solver. Our evaluation shows they are competitive with state-of-the-art HOL provers and often outperform the traditional encoding into FOL.

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Language and Proofs for Higher-Order SMT (Work in Progress)

Cited by 4 publications

References 10 publications

HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories

HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories

The SMT Competition 2015–2018

Extending SMT Solvers to Higher-Order Logic

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