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Documents authored by Mellendijk, Arend


Artifact
Software
algebra-tactic

Authors: Arend Mellendijk


Abstract

Cite as

Arend Mellendijk. algebra-tactic (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@misc{dagstuhl-artifact-27124,
   title = {{algebra-tactic}}, 
   author = {Mellendijk, Arend},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:c939acdbc385233836c284ca55f264661c444c36;origin=https://github.com/amellendijk/algebra-tactic;visit=swh:1:snp:1ae7b2d2024fcbb577fe915ce6e3e8268ea25d74;anchor=swh:1:rev:3372ce1dc459f56e8de10abdfd51f3deaa4b0411}{\texttt{swh:1:dir:c939acdbc385233836c284ca55f264661c444c36}} (visited on 2026-07-16)},
   url = {https://github.com/amellendijk/algebra-tactic},
   doi = {10.4230/artifacts.27124},
}
Document
Short Paper
A Lean Tactic for Normalizing Expressions in an Algebra over a Ring (Short Paper)

Authors: Arend Mellendijk

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)


Abstract
This paper introduces the algebra normalizing tactic for the Lean theorem prover. This tactic expands on the existing ring tactic by additionally supporting a scalar multiplication action over a fixed commutative (semi)ring. It supports rational constants in the base ring even when the main ring is not a field, which lets us implement a suite of tactics for manipulating both univariate and multivariate polynomials. These features are implemented by adapting the existing implementation of ring while retaining support for variable exponents.

Cite as

Arend Mellendijk. A Lean Tactic for Normalizing Expressions in an Algebra over a Ring (Short Paper). In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 35:1-35:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{mellendijk:LIPIcs.ITP.2026.35,
  author =	{Mellendijk, Arend},
  title =	{{A Lean Tactic for Normalizing Expressions in an Algebra over a Ring}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{35:1--35:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.35},
  URN =		{urn:nbn:de:0030-drops-270099},
  doi =		{10.4230/LIPIcs.ITP.2026.35},
  annote =	{Keywords: Lean, Mathlib, algebraic structures, proof algorithms}
}
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