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.FSCD.2021.21
URN: urn:nbn:de:0030-drops-142598
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14259/
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Paulus, Joseph W. N. ; Nantes-Sobrinho, Daniele ; Pérez, Jorge A.

Non-Deterministic Functions as Non-Deterministic Processes

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LIPIcs-FSCD-2021-21.pdf (0.9 MB)

Abstract

We study encodings of the λ-calculus into the π-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider λ^↯_⊕, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider ?π, a π-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of λ^↯_⊕ into ?π and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in λ^↯_⊕ via typed processes in ?π. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interaction protocols.

BibTeX - Entry

@InProceedings{paulus_et_al:LIPIcs.FSCD.2021.21,
  author =	{Paulus, Joseph W. N. and Nantes-Sobrinho, Daniele and P\'{e}rez, Jorge A.},
  title =	{{Non-Deterministic Functions as Non-Deterministic Processes}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14259},
  URN =		{urn:nbn:de:0030-drops-142598},
  doi =		{10.4230/LIPIcs.FSCD.2021.21},
  annote =	{Keywords: Resource calculi, \pi-calculus, intersection types, session types, linear logic}
}

Keywords: Resource calculi, π-calculus, intersection types, session types, linear logic
Collection: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)
Issue Date: 2021
Date of publication: 06.07.2021

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