2 Search Results for "Paulson, Lawrence C."

Document
Invited Talk
DOI: 10.4230/LIPIcs.ITP.2023.1
Formalisation of Additive Combinatorics in Isabelle/HOL (Invited Talk)

Authors: Angeliki Koutsoukou-Argyraki

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

Abstract
In this talk, I will present an overview of recent formalisations, in the interactive theorem prover Isabelle/HOL, of significant theorems in additive combinatorics, an area of combinatorial number theory. The formalisations of these theorems were the first in any proof assistant to my knowledge. For each of these theorems, I will discuss selected aspects of the formalisation process, focussing on observations on our treatment of certain mathematical arguments when translated into Isabelle/HOL and our overall formalisation experience with Isabelle/HOL for this area of mathematics.
Cite as

Angeliki Koutsoukou-Argyraki. Formalisation of Additive Combinatorics in Isabelle/HOL (Invited Talk). In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{koutsoukouargyraki:LIPIcs.ITP.2023.1,
  author =	{Koutsoukou-Argyraki, Angeliki},
  title =	{{Formalisation of Additive Combinatorics in Isabelle/HOL}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{1:1--1:2},
  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.2023.1},
  URN =		{urn:nbn:de:0030-drops-183760},
  doi =		{10.4230/LIPIcs.ITP.2023.1},
  annote =	{Keywords: Additive combinatorics, additive number theory, combinatorial number theory, formalisation of mathematics, interactive theorem proving, proof assistants, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.11
Formalising Fisher’s Inequality: Formal Linear Algebraic Proof Techniques in Combinatorics

Authors: Chelsea Edmonds and Lawrence C. Paulson

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

Abstract
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents formal linear algebraic techniques for proofs on incidence structures in Isabelle/HOL, and their application to the first formalisation of Fisher’s inequality. In addition to formalising incidence matrices and simple techniques for reasoning on linear algebraic representations, the formalisation focuses on the linear algebra bound and rank arguments. These techniques can easily be adapted for future formalisations in combinatorics, as we demonstrate through further application to proofs of variations on Fisher’s inequality.
Cite as

Chelsea Edmonds and Lawrence C. Paulson. Formalising Fisher’s Inequality: Formal Linear Algebraic Proof Techniques in Combinatorics. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{edmonds_et_al:LIPIcs.ITP.2022.11,
  author =	{Edmonds, Chelsea and Paulson, Lawrence C.},
  title =	{{Formalising Fisher’s Inequality: Formal Linear Algebraic Proof Techniques in Combinatorics}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{11:1--11:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.11},
  URN =		{urn:nbn:de:0030-drops-167204},
  doi =		{10.4230/LIPIcs.ITP.2022.11},
  annote =	{Keywords: Isabelle/HOL, Mathematical Formalisation, Fisher’s Inequality, Linear Algebra, Formal Proof Techniques, Combinatorics}
}
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