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Documents authored by Baanen, Anne

Document
DOI: 10.4230/LIPIcs.ITP.2024.28
Lean Formalization of Completeness Proof for Coalition Logic with Common Knowledge

Authors: Kai Obendrauf, Anne Baanen, Patrick Koopmann, and Vera Stebletsova

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Coalition Logic (CL) is a well-known formalism for reasoning about the strategic abilities of groups of agents in multi-agent systems. Coalition Logic with Common Knowledge (CLC) extends CL with operators from epistic logics, and thus with the ability to model the individual and common knowledge of agents. We have formalized the syntax and semantics of both logics in the interactive theorem prover Lean 4, and used it to prove soundness and completeness of its axiomatization. Our formalization uses the type class system to generalize over different aspects of CLC, thus allowing us to reuse some of to prove properties in related logics such as CL and CLK (CL with individual knowledge).
Cite as

Kai Obendrauf, Anne Baanen, Patrick Koopmann, and Vera Stebletsova. Lean Formalization of Completeness Proof for Coalition Logic with Common Knowledge. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{obendrauf_et_al:LIPIcs.ITP.2024.28,
  author =	{Obendrauf, Kai and Baanen, Anne and Koopmann, Patrick and Stebletsova, Vera},
  title =	{{Lean Formalization of Completeness Proof for Coalition Logic with Common Knowledge}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.28},
  URN =		{urn:nbn:de:0030-drops-207560},
  doi =		{10.4230/LIPIcs.ITP.2024.28},
  annote =	{Keywords: Multi-agent systems, Coalition Logic, Epistemic Logic, common knowledge, completeness, formal methods, Lean prover}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.4
Use and Abuse of Instance Parameters in the Lean Mathematical Library

Authors: Anne Baanen

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
The Lean mathematical library mathlib features extensive use of the typeclass pattern for organising mathematical structures, based on Lean’s mechanism of instance parameters. Related mechanisms for typeclasses are available in other provers including Agda, Coq and Isabelle with varying degrees of adoption. This paper analyses representative examples of design patterns involving instance parameters in the current Lean 3 version of mathlib, focussing on complications arising at scale and how the mathlib community deals with them.
Cite as

Anne Baanen. Use and Abuse of Instance Parameters in the Lean Mathematical Library. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{baanen:LIPIcs.ITP.2022.4,
  author =	{Baanen, Anne},
  title =	{{Use and Abuse of Instance Parameters in the Lean Mathematical Library}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.4},
  URN =		{urn:nbn:de:0030-drops-167131},
  doi =		{10.4230/LIPIcs.ITP.2022.4},
  annote =	{Keywords: formalization of mathematics, dependent type theory, typeclasses, algebraic hierarchy, Lean prover}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.5
A Formalization of Dedekind Domains and Class Groups of Global Fields

Authors: Anne Baanen, Sander R. Dahmen, Ashvni Narayanan, and Filippo A. E. Nuccio Mortarino Majno di Capriglio

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

Abstract
Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number theoretic finiteness results for class groups, in the Lean prover as part of the mathlib mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and mathlib’s decentralized collaboration processes involved in this project.
Cite as

Anne Baanen, Sander R. Dahmen, Ashvni Narayanan, and Filippo A. E. Nuccio Mortarino Majno di Capriglio. A Formalization of Dedekind Domains and Class Groups of Global Fields. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baanen_et_al:LIPIcs.ITP.2021.5,
  author =	{Baanen, Anne and Dahmen, Sander R. and Narayanan, Ashvni and Nuccio Mortarino Majno di Capriglio, Filippo A. E.},
  title =	{{A Formalization of Dedekind Domains and Class Groups of Global Fields}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{5:1--5:19},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.5},
  URN =		{urn:nbn:de:0030-drops-139004},
  doi =		{10.4230/LIPIcs.ITP.2021.5},
  annote =	{Keywords: formal math, algebraic number theory, commutative algebra, Lean, mathlib}
}
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