Skip to main content
SpringerLink
Log in

Accessing the Mizar Library with a Weakly Strict Mizar Parser

  • Conference paper
  • First Online:
Book cover Intelligent Computer Mathematics (CICM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9791))

Included in the following conference series:

Abstract

Our work is focused on the Mizar proof assistant and accessing the contents of its library in a machine readable and easily accessible form. The main result of the work described here is the implementation of an independent parser of the Weakly Strict Mizar language (WS-Mizar) along with a formal specification of its grammar and a program simulating an existing Mizar utility but using the new parser. The WS-Mizar language is less complex than the original Mizar language from a programmer’s point of view, while there is a software tool available that can translate any text written in Mizar into its WS-Mizar representation for easier access to the library. This is the key step towards developing various external utilities for processing mathematical data contained in Mizar articles.

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 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 44.99
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

Notes

  1. 1.

    http://mizar.org.

  2. 2.

    http://mizar.org/language/mizar-grammar.xml.

  3. 3.

    https://github.com/MizarProject/wsm-tools.

References

  1. Grabowski, A., Korniłowicz, A., Naumowicz, A.: Four decades of Mizar. J. Autom. Reason. 55(3), 191–198 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bancerek, G., Byliński, C., Grabowski, A., Korniłowicz, A., Matuszewski, R., Naumowicz, A., Pąk, K., Urban, J.: Mizar: state-of-the-art and beyond. In: Kerber, M., et al. [29], pp. 261–279

    Google Scholar 

  3. Korniłowicz, A.: Flexary connectives in Mizar. Comput. Lang. Syst. Struct. 44, 238–250 (2015)

    Google Scholar 

  4. Korniłowicz, A.: Definitional expansions in Mizar. J. Autom. Reason. 55(3), 257–268 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Korniłowicz, A.: On rewriting rules in Mizar. J. Autom. Reason. 50(2), 203–210 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Naumowicz, A.: Interfacing external CA systems for Gröbner bases computation in Mizar proof checking. Int. J. Comput. Math. 87(1), 1–11 (2010)

    Article  MATH  Google Scholar 

  7. Pąk, K.: Readable formalization of Euler’s partition theorem in Mizar. In: Kerber, M., et al. [29], pp. 211–226

    Google Scholar 

  8. Grabowski, A.: Mechanizing complemented lattices within Mizar type system. J. Autom. Reason. 55(3), 211–221 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Grabowski, A.: Efficient rough set theory merging. Fundamenta Informaticae 135(4), 371–385 (2014)

    MathSciNet  MATH  Google Scholar 

  10. Grabowski, A.: Automated discovery of properties of rough sets. Fundamenta Informaticae 128(1–2), 65–79 (2013)

    MathSciNet  MATH  Google Scholar 

  11. Grabowski, A., Korniłowicz, A., Schwarzweller, C.: Equality in computer proof-assistants. In: Ganzha, M., Maciaszek, L.A., Paprzycki, M. (eds.) Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, pp. 45–54. IEEE (2015). doi:10.15439/2015F229

  12. Naumowicz, A.: Automating Boolean set operations in Mizar proof checking with the aid of an external SAT solver. J. Autom. Reason. 55(3), 285–294 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Grabowski, A., Schwarzweller, C.: Towards automatically categorizing mathematical knowledge. In: Ganzha, M., Maciaszek, L.A., Paprzycki, M. (eds.) Proceedings of Federated Conference on Computer Science and Information Systems - FedCSIS 2012, Wroclaw, 9–12 September 2012, pp. 63–68 (2012)

    Google Scholar 

  14. Grabowski, A., Schwarzweller, C.: Revisions as an essential tool to maintain mathematical repositories. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 235–249. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Pąk, K.: Methods of lemma extraction in natural deduction proofs. J. Autom. Reason. 50(2), 217–228 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Grabowski, A., Schwarzweller, C.: On duplication in mathematical repositories. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) AISC 2010. LNCS, vol. 6167, pp. 300–314. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Pąk, K.: Improving legibility of formal proofs based on the close reference principle is NP-hard. J. Autom. Reason. 55(3), 295–306 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Pąk, K.: Improving legibility of natural deduction proofs is not trivial. Log. Methods Comput. Sci. 10(3), 1–30 (2014)

    MathSciNet  Google Scholar 

  19. Alama, J.: \(\sf Mizar\)-\(\sf items\): exploring fine-grained dependencies in the \(\sf Mizar\) mathematical library. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) MKM 2011 and Calculemus 2011. LNCS, vol. 6824, pp. 276–277. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Naumowicz, A.: Tools for MML environment analysis. In: Kerber, M., et al. [29], pp. 348–352

    Google Scholar 

  21. Cairns, P.A., Gow, J.: Using and parsing the Mizar language. Electr. Notes Theor. Comput. Sci. 93, 60–69 (2004)

    Article  MATH  Google Scholar 

  22. Bylinski, C., Alama, J.: New developments in parsing \(\sf Mizar\). In: Jeuring, J., Campbell, J.A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M., Sorge, V. (eds.) CICM 2012. LNCS, vol. 7362, pp. 427–431. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Wenzel, M., Wiedijk, F.: A comparison of Mizar and Isar. J. Autom. Reason. 29(3–4), 389–411 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. 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)

    Chapter  Google Scholar 

  25. Levine, J.: Flex & Bison. O’Reilly Media, Sebastopol (2009)

    Google Scholar 

  26. Alama, J., Kohlhase, M., Mamane, L., Naumowicz, A., Rudnicki, P., Urban, J.: Licensing the \(\sf Mizar\) mathematical library. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) MKM 2011 and Calculemus 2011. LNCS, vol. 6824, pp. 149–163. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  27. Trybulec, A.: Some features of the Mizar language. In: ESPRIT Workshop, Torino (1993)

    Google Scholar 

  28. Grabowski, A., Kornilowicz, A., Naumowicz, A.: Mizar in a nutshell. J. Formaliz. Reason. 3(2), 153–245 (2010)

    MathSciNet  MATH  Google Scholar 

  29. Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.): CICM 2015. LNCS, vol. 9150, pp. 261–279. Springer, Heidelberg (2015)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Informatics, University of Białystok, Konstantego Ciołkowskiego 1M, 15-245, Białystok, Poland

    Adam Naumowicz & Radosław Piliszek

  2. High Performance Computing Center, University of Białystok, Konstantego Ciołkowskiego 1M, 15-245, Białystok, Poland

    Radosław Piliszek

Authors
  1. Adam Naumowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Radosław Piliszek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adam Naumowicz .

Editor information

Editors and Affiliations

  1. Jacobs University Bremen, Bremen, Germany

    Michael Kohlhase

  2. Chalmers University, Göteborg, Sweden

    Moa Johansson

  3. National Institute of Standards and Technology, Gaithersburg, Maryland, USA

    Bruce Miller

  4. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

  5. University of Waterloo, Waterloo, Ontario, Canada

    Frank Tompa

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Naumowicz, A., Piliszek, R. (2016). Accessing the Mizar Library with a Weakly Strict Mizar Parser. In: Kohlhase, M., Johansson, M., Miller, B., de Moura, L., Tompa, F. (eds) Intelligent Computer Mathematics. CICM 2016. Lecture Notes in Computer Science(), vol 9791. Springer, Cham. https://doi.org/10.1007/978-3-319-42547-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42547-4_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42546-7

  • Online ISBN: 978-3-319-42547-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation