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Mizar: State-of-the-art and Beyond

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Intelligent Computer Mathematics (CICM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9150))

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Abstract

Mizar is one of the pioneering systems for mathematics formalization, which still has an active user community. The project has been in constant development since 1973, when Andrzej Trybulec designed the fundamentals of a language capable of rigorously encoding mathematical knowledge in a computerized environment which guarantees its full logical correctness. Since then, the system with its feature-rich language devised to approximate mathematics writing has influenced other formalization projects and has given rise to a number of Mizar modes implemented on top of other systems. However, the information about the system as a whole is not readily available to developers of other systems. Various papers describing Mizar features have been rather incremental and focused only on particular newly implemented Mizar aspects. The objective of the current paper is to give a survey of the most important Mizar features that distinguish it from other popular proof checkers. We also go a step further and describe most important current trends and lines of development that go beyond the state-of-the-art system.

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Notes

  1. 1.

    http://www.cl.cam.ac.uk/~jrh13/hol-light/.

  2. 2.

    http://www.cl.cam.ac.uk/research/hvg/Isabelle/.

  3. 3.

    http://coq.inria.fr.

  4. 4.

    http://us.metamath.org.

  5. 5.

    http://www.lemma-one.com/ProofPower/index/.

  6. 6.

    http://www.cs.utexas.edu/users/moore/acl2/.

  7. 7.

    http://pvs.csl.sri.com.

  8. 8.

    http://www.nuprl.org.

  9. 9.

    Generated with MML Query, http://mmlquery.mizar.org.

  10. 10.

    The description of the Mizar  grammar can be found at http://mizar.uwb.edu.pl/language/.

  11. 11.

    http://github.com/JUrban/xsl4mizar.

  12. 12.

    http://mizar.cs.ualberta.ca/~mptp/MizAR.html.

  13. 13.

    http://fm.uwb.edu.pl/proof-read/.

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Author information

Authors and Affiliations

  1. Association of Mizar Users, Białystok, Poland

    Grzegorz Bancerek

  2. Section of Computer Systems and Teleinformatic Networks, University of Białystok, Białystok, Poland

    Czesław Byliński

  3. Institute of Informatics, University of Białystok, Białystok, Poland

    Adam Grabowski, Artur Korniłowicz, Adam Naumowicz & Karol Pa̧k

  4. Department of Applied Linguistics, Faculty of Philology, University of Białystok, Białystok, Poland

    Roman Matuszewski

  5. Radboud University, Nijmegen, The Netherlands

    Josef Urban

Authors
  1. Grzegorz Bancerek
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  3. Adam Grabowski
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  6. Adam Naumowicz
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Correspondence to Adam Naumowicz .

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Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham, United Kingdom

    Manfred Kerber

  2. McMaster University, Hamilton, Ontario, Canada

    Jacques Carette

  3. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. University of Birmingham, Birmingham, United Kingdom

    Volker Sorge

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Bancerek, G. et al. (2015). Mizar: State-of-the-art and Beyond. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds) Intelligent Computer Mathematics. CICM 2015. Lecture Notes in Computer Science(), vol 9150. Springer, Cham. https://doi.org/10.1007/978-3-319-20615-8_17

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