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DOI: 10.4230/LIPIcs.CONCUR.2024.30

Around Classical and Intuitionistic Linear Processes

Authors: Juan C. Jaramillo, Dan Frumin, and Jorge A. Pérez

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract

Curry-Howard correspondences between Linear Logic (LL) and session types provide a firm foundation for concurrent processes. As the correspondences hold for intuitionistic and classical versions of LL (ILL and CLL), we obtain two different families of type systems for concurrency. An open question remains: how do these two families exactly relate to each other? Based upon a translation from CLL to ILL due to Laurent, we provide two complementary answers, in the form of full abstraction results based on a typed observational equivalence due to Atkey. Our results elucidate hitherto missing formal links between seemingly related yet different type systems for concurrency.

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Juan C. Jaramillo, Dan Frumin, and Jorge A. Pérez. Around Classical and Intuitionistic Linear Processes. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jaramillo_et_al:LIPIcs.CONCUR.2024.30,
  author =	{Jaramillo, Juan C. and Frumin, Dan and P\'{e}rez, Jorge A.},
  title =	{{Around Classical and Intuitionistic Linear Processes}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.30},
  URN =		{urn:nbn:de:0030-drops-208026},
  doi =		{10.4230/LIPIcs.CONCUR.2024.30},
  annote =	{Keywords: Process calculi, session types, linear logic}
}

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DOI: 10.4230/LIPIcs.FSCD.2019.5

Bicategories in Univalent Foundations

Authors: Benedikt Ahrens, Dan Frumin, Marco Maggesi, and Niels van der Weide

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Abstract

We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories. To construct examples of those, we develop the notion of "displayed bicategories", an analog of displayed 1-categories introduced by Ahrens and Lumsdaine. Displayed bicategories allow us to construct univalent bicategories in a modular fashion. To demonstrate the applicability of this notion, we prove several bicategories are univalent. Among these are the bicategory of univalent categories with families and the bicategory of pseudofunctors between univalent bicategories. Our work is formalized in the UniMath library of univalent mathematics.

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Benedikt Ahrens, Dan Frumin, Marco Maggesi, and Niels van der Weide. Bicategories in Univalent Foundations. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ahrens_et_al:LIPIcs.FSCD.2019.5,
  author =	{Ahrens, Benedikt and Frumin, Dan and Maggesi, Marco and van der Weide, Niels},
  title =	{{Bicategories in Univalent Foundations}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.5},
  URN =		{urn:nbn:de:0030-drops-105124},
  doi =		{10.4230/LIPIcs.FSCD.2019.5},
  annote =	{Keywords: bicategory theory, univalent mathematics, dependent type theory, Coq}
}

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Documents authored by Frumin, Dan

Around Classical and Intuitionistic Linear Processes

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Bicategories in Univalent Foundations

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