Premise Selection and External Provers for HOL4

Gauthier, Thibault; Kaliszyk, Cezary

doi:10.1145/2676724.2693173

Cited by 31 publications

(37 citation statements)

References 35 publications

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“…Hence, some additional work is needed when constructing from to ensure that p_def pI and p_def pE. An alternative concept of visibility, as implemented in HOL y Hammer, would be to linearize the partial order to obtain a total order [39]. The proof suggested by the tool can then refer to lemmas that are not currently available, requiring the user to add some directives to import background theories.…”

Section: Learning From and For Isabellementioning

confidence: 99%

A Learning-Based Fact Selector for Isabelle/HOL

et al. 2016

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Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the fact selector, heuristically ranks the thousands of facts (lemmas, definitions, or axioms) available and selects a subset, based on syntactic similarity to the current proof goal. We introduce MaSh, an alternative that learns from successful proofs. New challenges arose from our "zero click" vision: MaSh integrates seamlessly with the users' workflow, so that they benefit from machine learning without having to install software, set up servers, or guide the learning. MaSh outperforms the old fact selector on large formalizations.

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Section: Learning From and For Isabellementioning

confidence: 99%

A Learning-Based Fact Selector for Isabelle/HOL

et al. 2016

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“…Finally, we briefly show how the conjecture can be proven from these lemmas. More detailed descriptions of these steps are presented in [15,7].…”

Section: Hol(y)hammermentioning

confidence: 99%

Sharing HOL4 and HOL Light Proof Knowledge

Gauthier

Kaliszyk

2015

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers. Certain conjectures can be proved directly from the dependencies induced by similar proofs in the other library. Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises. Such external help can be further combined with internal advice. We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4.

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“…On the other hand, with small exceptions, ATPs are still significantly weaker than trained mathematicians in finding proofs in most research domains.Recently, machine learning over large formal corpora created from ITP libraries [37,28,19] has started to be used to develop guidance of ATP systems [39,25,2]. This has already produced strong systems for selecting relevant facts for proving new conjectures over large formal libraries [1,4,9]. More recently, machine learning has also started to be used to guide the internal search of the ATP systems.…”

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confidence: 99%

ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E

Chvalovský

Jakubův

Suda

et al. 2019

Lecture Notes in Computer Science

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We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach. Unlike in the first ENIGMA implementation where fast linear classifier is trained and used together with manually engineered features, we have started to experiment with more sophisticated state-of-the-art machine learning methods such as gradient boosted trees and recursive neural networks. In particular the latter approach poses challenges in terms of efficiency of clause evaluation, however, we show that deep integration of the neural evaluation with the ATP data-structures can largely amortize this cost and lead to competitive real-time results. Both methods are evaluated on a large dataset of theorem proving problems and compared with the previous approaches. The resulting methods improve on the manually designed clause guidance, providing the first practically convincing application of gradient-boosted and neural clause guidance in saturation-style automated theorem provers. IntroductionAutomated theorem provers (ATPs) [32] have been developed for decades by manually designing proof calculi and search heuristics. Their power has been growing and they are already very useful, e.g., as parts of large interactive theorem proving (ITP) verification toolchains (hammers) [5]. On the other hand, with small exceptions, ATPs are still significantly weaker than trained mathematicians in finding proofs in most research domains.Recently, machine learning over large formal corpora created from ITP libraries [37,28,19] has started to be used to develop guidance of ATP systems [39,25,2]. This has already produced strong systems for selecting relevant facts for proving new conjectures over large formal libraries [1,4,9]. More recently, machine learning has also started to be used to guide the internal search of the ATP systems. In sophisticated saturation-style provers this has been done by feedback loops for strategy invention [38,16,33] and by using supervised learning [14,26] to select the next given clause [27]. In the simpler connection tableau systems such as leancop [29], supervised learning has been used to choose ⋆ Supported by the ERC Consolidator grant no. 649043 AI4REASON, and by the Czech project AI&Reasoning CZ.02.1.01/0.0/0.0/15 003/0000466 and the European Regional Development Fund.

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Premise Selection and External Provers for HOL4

Cited by 31 publications

References 35 publications

A Learning-Based Fact Selector for Isabelle/HOL

A Learning-Based Fact Selector for Isabelle/HOL

Sharing HOL4 and HOL Light Proof Knowledge

ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E

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