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Extending SMT solvers to higher-order logic. (English) Zbl 07178968
Fontaine, Pascal (ed.), Automated deduction – CADE 27. 27th international conference on automated deduction, Natal, Brazil, August 27–30, 2019. Proceedings. Cham: Springer (ISBN 978-3-030-29435-9/pbk; 978-3-030-29436-6/ebook). Lecture Notes in Computer Science 11716. Lecture Notes in Artificial Intelligence, 35-54 (2019).
Summary: 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.
For the entire collection see [Zbl 1428.68018].
MSC:
03B35 Mechanization of proofs and logical operations
68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)
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