Congruence Closure with Free Variables

Barbosa, Haniel; Fontaine, Pascal; Reynolds, Andrew

doi:10.1007/978-3-662-54580-5_13

Cited by 15 publications

(13 citation statements)

References 24 publications

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“…The main quantifier instantiation techniques in SMT solving are trigger-based [22], conflict-based [4,38], model-based [26,40], and enumerative [37]. Lifting any of them to HOSMT presents its own challenges.…”

Section: Extending the Quantifier Instantiation Module To Homstmentioning

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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Section: Extending the Quantifier Instantiation Module To Homstmentioning

confidence: 99%

Extending SMT Solvers to Higher-Order Logic

Barbosa

Reynolds

Ouraoui

et al. 2019

Lecture Notes in Computer Science

Self Cite

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“…Following the publication of our CADE-26 paper [3], we developed a usable integration of veriT proofs, including a parser and efficient reconstruction. It is part of the development version of Isabelle 4 and is expected to be included in the next official release (Isabelle2019).…”

Section: Isabellementioning

confidence: 99%

“…We implemented the approach in veriT (Sect. 6), an SMT solver that is competitive on problems combining equality, linear arithmetic, and quantifiers [4]. Compared with other SMT solvers, veriT is known for its very detailed proofs [9], which are reconstructed in the proof assistants Coq [1] and Isabelle/HOL [10] and in the GAPT system [18].…”

mentioning

confidence: 99%

Scalable Fine-Grained Proofs for Formula Processing

et al. 2019

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We present a framework for processing formulas in automatic theorem provers, with generation of detailed proofs. The main components are a generic contextual recursion algorithm and an extensible set of inference rules. Clausification, skolemization, theoryspecific simplifications, and expansion of 'let' expressions are instances of this framework. With suitable data structures, proof generation adds only a linear-time overhead, and proofs can be checked in linear time. We implemented the approach in the SMT solver veriT. This allowed us to dramatically simplify the code base while increasing the number of problems for which detailed proofs can be produced, which is important for independent checking and reconstruction in proof assistants. To validate the framework, we implemented proof reconstruction in Isabelle/HOL. 1 Introduction An increasing number of automatic theorem provers can generate certificates, or proofs, that justify the formulas they derive. These proofs can be checked by other programs and shared across reasoning systems. It might also happen that a human user would want to inspect

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“…We implemented the contextual recursion framework in the SMT solver veriT, 2 replacing large parts of the previous non-proof-producing, hard-to-maintain code. Even though it offers more functionality (proof generation), the preprocessing module is about 20% smaller than before and consists of about 3000 lines of code.…”

Section: Veritmentioning

confidence: 99%

“…We implemented the approach in veriT (Sect. 6), an SMT solver that is competitive on problems combining equality, linear arithmetic, and quantifiers [2]. Compared with other SMT solvers, veriT is known for its very detailed proofs [6], which are reconstructed in the proof assistants Coq [1] and Isabelle/HOL [7] and in the GAPT system [14].…”

Section: Introductionmentioning

confidence: 99%