Skip to main content
Springer Nature Link
Log in

On the Integrity of a Repository of Formalized Mathematics

  • Conference paper
  • First Online:
Mathematical Knowledge Management (MKM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2594))

Included in the following conference series:

  • 370 Accesses

Abstract

Mizar ,a proof-checking system,is used to build the Mizar Mathematical Library (MML ).This is a long term project aiming at building a comprehensive library of mathematical knowledge. The language and the checking software evolve, and the evolution is driven by the growing library. We discuss the issues of maintaining integrity of an electronic repository of formal mathematics, based on our experience with MML .

Partially supported by NSERC grant OGP9207.

Partially supported by FP5 grant HPRN-CT-2000-00102.

http://mizar.org

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Grzegorz Bancerek.The ordinal numbers.Formalized Mathematics,1(1 ):91–96, 1990.

    Google Scholar 

  2. Grzegorz Bancerek. König’s theorem.Formalized Mathematics,1(3 ):589–593, 1990.

    Google Scholar 

  3. Grzegorz Bancerek.Cartesian product of functions.Formalized Mathematics, 2(4 ):547–552,1991.

    Google Scholar 

  4. Grzegorz Bancerek.Reduction relations.Formalized Mathematics,5(4 ):469–478, 1996.

    Google Scholar 

  5. Grzegorz Bancerek.Continuous lattices of maps between T 0 spaces.Formalized Mathematics,9(1 ):111–117,2001.

    MATH  Google Scholar 

  6. Grzegorz Bancerek and Krzysztof Hryniewiecki.Segments of natural numbers and finite sequences.Formalized Mathematics,1(1 ):107–114,1990.

    Google Scholar 

  7. Czesław Byliński.Some basic properties of sets.Formalized Mathematics,1(1 ):47–53,1990.

    Google Scholar 

  8. Czesław Byliński.Functions from a set to a set.Formalized Mathematics ,1(1 ):153–164,1990.

    Google Scholar 

  9. Czesław Byliński.Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics,1(3 ):529–536,1990.

    Google Scholar 

  10. Czesław Byliński and Piotr Rudnicki.Bounding boxes for compact sets in ⌉2. Formalized Mathematics ,6(3 ):427–440,1997.

    Google Scholar 

  11. Agata Darmochwał.The Euclidean space.Formalized Mathematics,2(4 ):599–603, 1991.

    Google Scholar 

  12. Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics,1(3 ):607–610,1990.

    Google Scholar 

  13. Artur Korniłowicz.Cartesian products of relations and relational structures.For-malized Mathematics,6(1 ):145–152,1997.

    Google Scholar 

  14. Jarosław Kotowicz.Convergent real sequences.Upper and lower bound of sets of real numbers.Formalized Mathematics,1(3 ):477–481,1990.

    Google Scholar 

  15. Mizar Manuals .http://mizar.org/project/bibliography.html.

  16. Yatsuka Nakamura and Adam Grabowski.Bounding boxes for special sequences in ⌉2.Formalized Mathematics,7(1 ):115–121,1998.

    Google Scholar 

  17. Yatsuka Nakamura and Piotr Rudnicki.Vertex sequences induced by chains.For-malized Mathematics,5(3 ):297–304,1996.

    Google Scholar 

  18. Adam Naumowicz and Czesław Byliński.Basic Elements of Computer Algebra in Mizar.Mechanized Mathematics and Its Applications,2 (1):9–16,2002.

    Google Scholar 

  19. Beata Padlewska and Agata Darmochwał.Topological spaces and continuous func-tions.Formalized Mathematics,1(1 ):223–230,1990.

    Google Scholar 

  20. P. Rudnicki, Ch. Schwarzweller and A. Trybulec.Commutative Algebra in the Mizar System.Journal of Symbolic Computation,32 :143–169,2001.

    Article  MathSciNet  Google Scholar 

  21. Piotr Rudnicki and Andrzej Trybulec.On equivalents of well-foundedness.Journal of Automated Reasoning ,23 (3-4):197–234,1999.

    Article  MathSciNet  Google Scholar 

  22. Piotr Rudnicki and Andrzej Trybulec.Mathematical Knowledge Management in Mizar.1st Int.Workshop on MKM ,Sept.24–26,2001, http://www.risc.uni-linz.ac.at/institute/conferences/MKM2001.

  23. Agnieszka Sakowicz, Jarosław Gryko, and Adam Grabowski. Sequences in⌉n tFormalized Mathematics,5(1 ):93–96,1996.

    Google Scholar 

  24. Andrzej Trybulec.Tarski Grothendieck set theory.Formalized Mathematics , 1(1 ):9–11,1990.

    Google Scholar 

  25. Wojciech A. Trybulec.Non-contiguous substrings and one-to-one.nite sequences. Formalized Mathematics,1(3 ):569–573,1990.

    Google Scholar 

  26. Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-Based Finite Sequences. Formalized Mathematics,9(4):825–829,2001.

    Google Scholar 

  27. Freek Wiedijk.Mizar:An Impression.http://www.cs.kun.nl/~freek/notes.

Download references

Author information

Authors and Affiliations

  1. Dept.of Computing Science, University of Alberta, Edmonton, Canada

    Piotr Rudnicki

  2. Institute of Informatics, University in Białystok, Białystok, Poland

    Andrzej Trybulec

Authors
  1. Piotr Rudnicki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrzej Trybulec
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Bologna, Mura Anteo Zamboni, 7, 40127, Bologna, Italy

    Andrea Asperti

  2. Research Institute for Symbolic Computation, Johannes Kepler University, 4232 Castle of Hagenberg, Austria

    Bruno Buchberger

  3. Departments of Mathematical Sciences and Computer Science, University of Bath, BA2 7AY, Bath, England

    James Harold Davenport

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rudnicki, P., Trybulec, A. (2003). On the Integrity of a Repository of Formalized Mathematics. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds) Mathematical Knowledge Management. MKM 2003. Lecture Notes in Computer Science, vol 2594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36469-2_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-36469-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00568-1

  • Online ISBN: 978-3-540-36469-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics