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DOI: 10.4230/LIPIcs.ITP.2023.37

Implementing More Explicit Definitional Expansions in Mizar (Short Paper)

Authors: Adam Grabowski and Artur Korniłowicz

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract

The Mizar language and its corresponding proof-checker offers the tactic of definitional expansions in proof skeletons. This apparatus is rather fragile in the case of intensive overloading of notions (which is widely observed e.g. in the field of algebra, but it is also present in the more fundamental set-theory contexts). We propose the extension of this mechanism: the change should offer users the more precise control over expansions via choosing the right definitional variant for the proof under consideration, still letting the authors to retain the more conservative approach. As a rule, the change will affect new Mizar texts, but obviously, it allows also for solving some context conflicts caused by the original approach in the Mizar repository. The usefulness of our approach is shown by a number of experiments carried out within MML, which is also affected by the change.

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Adam Grabowski and Artur Korniłowicz. Implementing More Explicit Definitional Expansions in Mizar (Short Paper). In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 37:1-37:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{grabowski_et_al:LIPIcs.ITP.2023.37,
  author =	{Grabowski, Adam and Korni{\l}owicz, Artur},
  title =	{{Implementing More Explicit Definitional Expansions in Mizar}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{37:1--37:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.37},
  URN =		{urn:nbn:de:0030-drops-184121},
  doi =		{10.4230/LIPIcs.ITP.2023.37},
  annote =	{Keywords: Mizar, definitions, proof assistants, mechanization of proof}
}

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DOI: 10.4230/LIPIcs.ITP.2021.11

Syntactic-Semantic Form of Mizar Articles

Authors: Czesław Byliński, Artur Korniłowicz, and Adam Naumowicz

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract

Mizar Mathematical Library is most appreciated for the wealth of mathematical knowledge it contains. However, accessing this publicly available huge corpus of formalized data is not straightforward due to the complexity of the underlying Mizar language, which has been designed to resemble informal mathematical papers. For this reason, most systems exploring the library are based on an internal XML representation format used by semantic modules of Mizar. This representation is easily accessible, but it lacks certain syntactic information available only in the original human-readable Mizar source files. In this paper we propose a new XML-based format which combines both syntactic and semantic data. It is intended to facilitate various applications of the Mizar library requiring fullest possible information to be retrieved from the formalization files.

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Czesław Byliński, Artur Korniłowicz, and Adam Naumowicz. Syntactic-Semantic Form of Mizar Articles. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bylinski_et_al:LIPIcs.ITP.2021.11,
  author =	{Byli\'{n}ski, Czes{\l}aw and Korni{\l}owicz, Artur and Naumowicz, Adam},
  title =	{{Syntactic-Semantic Form of Mizar Articles}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.11},
  URN =		{urn:nbn:de:0030-drops-139064},
  doi =		{10.4230/LIPIcs.ITP.2021.11},
  annote =	{Keywords: Mizar system, mathematical knowledge representation, XML representation}
}

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Documents authored by Korniłowicz, Artur

Implementing More Explicit Definitional Expansions in Mizar (Short Paper)

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Syntactic-Semantic Form of Mizar Articles

Abstract

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