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International Conference on Interactive Theorem Proving

ITP 2015: Interactive Theorem Proving pp 227–233Cite as

Learning to Parse on Aligned Corpora (Rough Diamond)

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9236))

Abstract

One of the first big hurdles that mathematicians encounter when considering writing formal proofs is the necessity to get acquainted with the formal terminology and the parsing mechanisms used in the large ITP libraries. This includes the large number of formal symbols, the grammar of the formal languages and the advanced mechanisms instrumenting the proof assistants to correctly understand the formal expressions in the presence of ubiquitous overloading.

In this work we start to address this problem by developing approximate probabilistic parsing techniques that autonomously train disambiguation on large corpora. Unlike in standard natural language processing, we can filter the resulting parse trees by strong ITP and AR semantic methods such as typechecking and automated theorem proving, and even let the probabilistic methods self-improve based on such semantic feedback. We describe the general motivation and our first experiments, and build an online system for parsing ambiguous formulas over the Flyspeck library.

C. Kaliszyk—Supported by the Austrian Science Fund (FWF): P26201.

J. Urban—Supported by NWO grant nr. 612.001.208.

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Notes

  1. 1.

    Approximate results of an opinion poll run by the second author since 2000.

  2. 2.

    http://colo12-c703.uibk.ac.at/hh/parse.html.

  3. 3.

    Exactly, the theorems containing substrings sin, cos and tan.

  4. 4.

    http://nlp.stanford.edu/software/lex-parser.shtml.

  5. 5.

    http://colo12-c703.uibk.ac.at/hh/parse.html.

  6. 6.

    http://colo12-c703.uibk.ac.at/hh/parseimg.html.

  7. 7.

    The exact list is at http://mizar.cs.ualberta.ca/~mptp/i2f/00proved2.

References

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Author information

Authors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  2. Radboud University Nijmegen, Nijmegen, The Netherlands

    Josef Urban

  3. Czech Technical University, Prague, Czech Republic

    Jiří Vyskočil

Authors
  1. Cezary Kaliszyk
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  2. Josef Urban
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  3. Jiří Vyskočil
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Corresponding author

Correspondence to Josef Urban .

Editor information

Editors and Affiliations

  1. Department of Informatics, King's College London, London, United Kingdom

    Christian Urban

  2. PLA University of Science and Technology, Nanjing, China

    Xingyuan Zhang

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© 2015 Springer International Publishing Switzerland

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Kaliszyk, C., Urban, J., Vyskočil, J. (2015). Learning to Parse on Aligned Corpora (Rough Diamond). In: Urban, C., Zhang, X. (eds) Interactive Theorem Proving. ITP 2015. Lecture Notes in Computer Science(), vol 9236. Springer, Cham. https://doi.org/10.1007/978-3-319-22102-1_15

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  • DOI: https://doi.org/10.1007/978-3-319-22102-1_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22101-4

  • Online ISBN: 978-3-319-22102-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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