Aligning concepts across proof assistant libraries

Gauthier, Thibault; Kaliszyk, Cezary

doi:10.1016/j.jsc.2018.04.005

Cited by 13 publications

(21 citation statements)

References 14 publications

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“…Our use of symbol-independent arity-based features for GBDTs differs from Schulz's anonymous clause patterns [23,24] (CPs) used in E for proof guidance and from Gauthier and Kaliszyk's (GK) anonymous abstractions used for their concept alignments between ITP libraries [10] in two ways:…”

Section: B Discussion Of Anonymizationmentioning

confidence: 99%

“…With ATPs being increasingly used and trained on large ITP libraries [2,3,6,8,16,18], it is more and more rewarding to develop methods that learn to reason without relying on the particular terminology adopted in a single project. Initial experiments in this direction using concept alignment [10] methods have already shown performance improvements by transferring knowledge between the HOL libraries [9]. Structural analogies (or even terminology duplications) are however common already in a single large ITP library [17] and their automated detection can lead to new proof ideas and a number of other interesting applications [11].…”

Section: Introduction: Symbol Independent Inference Guidancementioning

confidence: 99%

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ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

Jakubův

Chvalovský

Olšák

et al. 2020

Lecture Notes in Computer Science

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We describe an implementation of gradient boosting and neural guidance of saturation-style automated theorem provers that does not depend on consistent symbol names across problems. For the gradient-boosting guidance, we manually create abstracted features by considering arity-based encodings of formulas. For the neural guidance, we use symbol-independent graph neural networks (GNNs) and their embedding of the terms and clauses. The two methods are efficiently implemented in the E prover and its ENIGMA learning-guided framework.To provide competitive real-time performance of the GNNs, we have developed a new context-based approach to evaluation of generated clauses in E. Clauses are evaluated jointly in larger batches and with respect to a large number of already selected clauses (context) by the GNN that estimates their collectively most useful subset in several rounds of message passing. This means that approximative inference rounds done by the GNN are efficiently interleaved with precise symbolic inference rounds done inside E. The methods are evaluated on the MPTP large-theory benchmark and shown to achieve comparable realtime performance to state-of-the-art symbol-based methods. The methods also show high complementarity, solving a large number of hard Mizar problems.

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Section: B Discussion Of Anonymizationmentioning

confidence: 99%

Section: Introduction: Symbol Independent Inference Guidancementioning

confidence: 99%

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

Jakubův

Chvalovský

Olšák

et al. 2020

Lecture Notes in Computer Science

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show abstract

“…Even though the alignment problem was recognized in [50] already, which also gives the first solution in a practical setting, it has remained difficult. Major case studies so far are [61] for aligning many different small libraries and [18] for aligning two large ones. We gave a survey of issues in [28], and if anything, we see a longer list of difficulties by now.…”

Section: Future Workmentioning

confidence: 99%

Experiences from Exporting Major Proof Assistant Libraries

Kohlhase

Rabe

2021

J Autom Reasoning

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The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc/MMT. Each translation presented great theoretical, technical, and social challenges, some universal and some system-specific, some solvable and some still open. In this paper, we survey these challenges and compare and evaluate the solutions we chose. We believe similar library translations will be an essential part of any future system interoperability solution, and our experiences will prove valuable to others undertaking such efforts.

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“…To improve the ability to distinguish different anonymized clauses, we add the following features. Variable statistics of clause C containing (1) the number of variables in C without repetitions, (2) the number of variables with repetitions, (3) the number of variables with exactly one occurrence, (4) the number of variables with more than one occurrence, (5)(6)(7)(8)(9)(10) the number of occurrences of the most/least (and second/third most/least) occurring variable. Symbol statistics do the same for symbols instead of variables.…”

Section: New Statistics and Problem Featuresmentioning

confidence: 99%

“…With ATPs being increasingly used and trained on large ITP libraries [3,2,16,18,6,8], it is more and more rewarding to develop methods that learn to reason without relying on the particular terminology adopted in a single project. Initial experiments in this direction using concept alignment [10] methods have already shown performance improvements by transferring knowledge between the HOL libraries [9]. Structural analogies (or even terminology duplications) are however common already in a single large ITP library [17] and their automated detection can lead to new proof ideas and a number of other interesting applications [11].…”

Section: Introduction: Symbol Independent Inference Guidancementioning

confidence: 99%

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (system description)

Jakubův¹,

Chvalovský²,

Olšák³

et al. 2020

Preprint

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We describe an implementation of gradient boosting and neural guidance of saturation-style automated theorem provers that does not depend on consistent symbol names across problems. For the gradientboosting guidance, we manually create abstracted features by considering arity-based encodings of formulas. For the neural guidance, we use symbol-independent graph neural networks (GNNs) and their embedding of the terms and clauses. The two methods are efficiently implemented in the E prover and its ENIGMA learning-guided framework. To provide competitive real-time performance of the GNNs, we have developed a new context-based approach to evaluation of generated clauses in E. Clauses are evaluated jointly in larger batches and with respect to a large number of already selected clauses (context) by the GNN that estimates their collectively most useful subset in several rounds of message passing. This means that approximative inference rounds done by the GNN are efficiently interleaved with precise symbolic inference rounds done inside E. The methods are evaluated on the MPTP largetheory benchmark and shown to achieve comparable real-time performance to state-of-the-art symbol-based methods. The methods also show high complementarity, solving a large number of hard Mizar problems.

show abstract

Aligning concepts across proof assistant libraries

Cited by 13 publications

References 14 publications

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

Experiences from Exporting Major Proof Assistant Libraries

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (system description)

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