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Sharing HOL4 and HOL Light Proof Knowledge

  • Thibault GauthierEmail author
  • Cezary Kaliszyk
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9450)

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.

Keywords

Proof Assistant Standard Library Type Constructor Concept Match Interactive Theorem Prover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgments

This work has been supported by the Austrian Science Fund (FWF): P26201.

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of InnsbruckInnsbruckAustria

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