Skip to main content
SpringerLink
Log in

A New Export of the Mizar Mathematical Library

  • Conference paper
  • First Online:
Intelligent Computer Mathematics (CICM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12833))

Included in the following conference series:

Abstract

The Mizar Mathematical Library (MML) is a prime target of library exports, i.e., translations of proof assistant libraries that make the libraries available to knowledge management systems or other deduction systems. The MML has been exported multiple times in the past, including our own export from Mizar to OMDoc done in 2011. But the exporters tend to be very difficult and expensive to maintain.

We present a complete reimplementation of our previous export. It incorporates many lessons learned and leverages improvements made both on the Mizar and the OMDoc side.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bylinski, C., Alama, J.: New developments in parsing Mizar. In: Jeuring, J., Campbell, J.A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M., Sorge, V. (eds.) CICM 2012. LNCS (LNAI), vol. 7362, pp. 427–431. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31374-5_30

    Chapter  Google Scholar 

  2. Bancerek, G., et al.: The role of the Mizar Mathematical Library for interactive proof development in Mizar. J. Autom. Reason. 61(1), 9–32 (2018). https://doi.org/10.1007/s10817-017-9440-6

    Article  MathSciNet  MATH  Google Scholar 

  3. Horozal, F., Kohlhase, M., Rabe, F.: Extending MKM formats at the statement level. In: Jeuring, J., et al. (eds.) CICM 2012. LNCS (LNAI), vol. 7362, pp. 65–80. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31374-5_5

    Chapter  Google Scholar 

  4. Horozal, F., Rabe, F.: Formal logic definitions for interchange languages. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS (LNAI), vol. 9150, pp. 171–186. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20615-8_11

    Chapter  Google Scholar 

  5. Iancu, M., Kohlhase, M., Rabe, F., Urban, J.: The Mizar Mathematical Library in OMDoc: translation and applications. J. Autom. Reason. 50(2), 191–202 (2013). https://doi.org/10.1007/s10817-012-9271-4

    Article  MathSciNet  MATH  Google Scholar 

  6. Kohlhase, M.: OMDoc – An Open Markup Format for Mathematical Documents [version 1.2]. LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006). https://doi.org/10.1007/11826095

    Book  Google Scholar 

  7. Kaliszyk, C., Pak, K.: Semantics of Mizar as an Isabelle object logic. J. Autom. Reason. 63(3), 557–595 (2019). https://doi.org/10.1007/s10817-018-9479-z

    Article  MathSciNet  MATH  Google Scholar 

  8. Kohlhase, M., Rabe, F.: Experiences from exporting major proof assistant libraries (2020). see https://kwarc.info/people/frabe/Research/KR_oafexp_20.pdf

  9. Müller, D., Rabe, F., Rothgang, C., Kohlhase, M.: Representing structural language features in formal meta-languages. In: Benzmüller, C., Miller, B. (eds.) CICM 2020. LNCS (LNAI), vol. 12236, pp. 206–221. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-53518-6_13

    Chapter  Google Scholar 

  10. Naumowicz, A., Piliszek, R.: Accessing the Mizar library with a weakly strict Mizar parser. In: Kohlhase, M., Johansson, M., Miller, B., de de Moura, L., Tompa, F. (eds.) CICM 2016. LNCS (LNAI), vol. 9791, pp. 77–82. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42547-4_6

    Chapter  Google Scholar 

  11. Rabe, F., Kohlhase, M.: A scalable module system. Inf. Comput. 230(1), 1–54 (2013)

    Article  MathSciNet  Google Scholar 

  12. Urban, J.: Translating Mizar for first order theorem provers. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 203–215. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36469-2_16

    Chapter  Google Scholar 

  13. Urban, J.: XML-izing Mizar: making semantic processing and presentation of MML easy. In: Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, pp. 346–360. Springer, Heidelberg (2006). https://doi.org/10.1007/11618027_23

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics, TU Berlin, Berlin, Germany

    Colin Rothgang

  2. Institute of Computer Science, Bialystok, Poland

    Artur Korniłowicz

  3. Computer Science, FAU Erlangen-Nürnberg, Erlangen, Germany

    Florian Rabe

Authors
  1. Colin Rothgang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Artur Korniłowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Florian Rabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Colin Rothgang .

Editor information

Editors and Affiliations

  1. Heriot-Watt University, Edinburgh, UK

    Fairouz Kamareddine

  2. University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rothgang, C., Korniłowicz, A., Rabe, F. (2021). A New Export of the Mizar Mathematical Library. In: Kamareddine, F., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2021. Lecture Notes in Computer Science(), vol 12833. Springer, Cham. https://doi.org/10.1007/978-3-030-81097-9_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-81097-9_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81096-2

  • Online ISBN: 978-3-030-81097-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation