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DOI: 10.4230/LIPIcs.CSL.2023.13

A Curry-Howard Correspondence for Linear, Reversible Computation

Authors: Kostia Chardonnet, Alexis Saurin, and Benoît Valiron

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract

In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of clauses is enough to ensure reversibility. The language allows to represent any Primitive Recursive Function. We then give a Curry-Howard correspondence with the logic μMALL: linear logic extended with least fixed points allowing inductive statements. The critical part of our work is to show how primitive recursion yields circular proofs that satisfy μMALL validity criterion and how the language simulates the cut-elimination procedure of μMALL.

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Kostia Chardonnet, Alexis Saurin, and Benoît Valiron. A Curry-Howard Correspondence for Linear, Reversible Computation. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chardonnet_et_al:LIPIcs.CSL.2023.13,
  author =	{Chardonnet, Kostia and Saurin, Alexis and Valiron, Beno\^{i}t},
  title =	{{A Curry-Howard Correspondence for Linear, Reversible Computation}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.13},
  URN =		{urn:nbn:de:0030-drops-174747},
  doi =		{10.4230/LIPIcs.CSL.2023.13},
  annote =	{Keywords: Reversible Computation, Linear Logic, Curry-Howard}
}

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DOI: 10.4230/LIPIcs.MFCS.2021.30

Geometry of Interaction for ZX-Diagrams

Authors: Kostia Chardonnet, Benoît Valiron, and Renaud Vilmart

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure ZX-Calculus and its extension to mixed processes. We also show how to connect this new semantics to the usual standard interpretation of ZX-diagrams. This model allows us to have a new look at what ZX-diagrams compute, and give a more local, operational view of the semantics of ZX-diagrams.

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Kostia Chardonnet, Benoît Valiron, and Renaud Vilmart. Geometry of Interaction for ZX-Diagrams. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chardonnet_et_al:LIPIcs.MFCS.2021.30,
  author =	{Chardonnet, Kostia and Valiron, Beno\^{i}t and Vilmart, Renaud},
  title =	{{Geometry of Interaction for ZX-Diagrams}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.30},
  URN =		{urn:nbn:de:0030-drops-144701},
  doi =		{10.4230/LIPIcs.MFCS.2021.30},
  annote =	{Keywords: Quantum Computation, Linear Logic, ZX-Calculus, Geometry of Interaction}
}

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Documents authored by Chardonnet, Kostia

A Curry-Howard Correspondence for Linear, Reversible Computation

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Geometry of Interaction for ZX-Diagrams

Abstract

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