License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2023.13
URN: urn:nbn:de:0030-drops-174747
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17474/
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Chardonnet, Kostia ; Saurin, Alexis ; Valiron, Benoît

A Curry-Howard Correspondence for Linear, Reversible Computation

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LIPIcs-CSL-2023-13.pdf (0.9 MB)

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.

BibTeX - Entry

@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.dagstuhl.de/opus/volltexte/2023/17474},
  URN =		{urn:nbn:de:0030-drops-174747},
  doi =		{10.4230/LIPIcs.CSL.2023.13},
  annote =	{Keywords: Reversible Computation, Linear Logic, Curry-Howard}
}

Keywords: Reversible Computation, Linear Logic, Curry-Howard
Collection: 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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