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DOI: 10.4230/LIPIcs.ITP.2023.5

Formalizing Functions as Processes

Authors: Beniamino Accattoli, Horace Blanc, and Claudio Sacerdoti Coen

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

Abstract

We present the first formalization of Milner’s classic translation of the λ-calculus into the π-calculus. It is a challenging result with respect to variables, names, and binders, as it requires one to relate variables and binders of the λ-calculus with names and binders in the π-calculus. We formalize it in Abella, merging the set of variables and the set of names, thus circumventing the challenge and obtaining a neat formalization. About the translation, we follow Accattoli’s factoring of Milner’s result via the linear substitution calculus, which is a λ-calculus with explicit substitutions and contextual rewriting rules, mediating between the λ-calculus and the π-calculus. Another aim of the formalization is to investigate to which extent the use of contexts in Accattoli’s refinement can be formalized.

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Beniamino Accattoli, Horace Blanc, and Claudio Sacerdoti Coen. Formalizing Functions as Processes. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{accattoli_et_al:LIPIcs.ITP.2023.5,
  author =	{Accattoli, Beniamino and Blanc, Horace and Sacerdoti Coen, Claudio},
  title =	{{Formalizing Functions as Processes}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{5:1--5:21},
  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.2023.5},
  URN =		{urn:nbn:de:0030-drops-183800},
  doi =		{10.4230/LIPIcs.ITP.2023.5},
  annote =	{Keywords: Lambda calculus, pi calculus, proof assistants, binders, Abella}
}

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DOI: 10.4230/LIPIcs.RTA.2012.38

A Term Rewriting System for Kuratowski's Closure-Complement Problem

Authors: Osama Al-Hassani, Quratul-ain Mahesar, Claudio Sacerdoti Coen, and Volker Sorge

Published in: LIPIcs, Volume 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12) (2012)

Abstract

We present a term rewriting system to solve a class of open problems that are generalisations of Kuratowski's closure-complement theorem. The problems are concerned with finding the number of distinct sets that can be obtained by applying combinations of axiomatically defined set operators. While the original problem considers only closure and complement of a topological space as operators, it can be generalised by adding operators and varying axiomatisation. We model these axioms as rewrite rules and construct a rewriting system that allows us to close some so far open variants of Kuratowski's problem by analysing several million inference steps on a typical personal computer.

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Osama Al-Hassani, Quratul-ain Mahesar, Claudio Sacerdoti Coen, and Volker Sorge. A Term Rewriting System for Kuratowski's Closure-Complement Problem. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 38-52, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{alhassani_et_al:LIPIcs.RTA.2012.38,
  author =	{Al-Hassani, Osama and Mahesar, Quratul-ain and Sacerdoti Coen, Claudio and Sorge, Volker},
  title =	{{A Term Rewriting System for Kuratowski's Closure-Complement Problem}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12)},
  pages =	{38--52},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-38-5},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{15},
  editor =	{Tiwari, Ashish},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2012.38},
  URN =		{urn:nbn:de:0030-drops-34838},
  doi =		{10.4230/LIPIcs.RTA.2012.38},
  annote =	{Keywords: Kuratowski's closure-complement problem, Rewriting system}
}

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Documents authored by Sacerdoti Coen, Claudio

Formalizing Functions as Processes

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A Term Rewriting System for Kuratowski's Closure-Complement Problem

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