2 Search Results for "Paulus, Joseph W. N."

Document
DOI: 10.4230/LIPIcs.TYPES.2021.11
Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes

Authors: Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)

Abstract
Type-preserving translations are effective rigorous tools in the study of core programming calculi. In this paper, we develop a new typed translation that connects sequential and concurrent calculi; it is governed by type systems that control resource consumption. Our main contribution is the source language, a new resource λ-calculus with non-collapsing non-determinism and failures, dubbed uλ^{↯}_{⊕}. In uλ^{↯}_{⊕}, resources are split into linear and unrestricted; failures are explicit and arise from this distinction. We define a type system based on intersection types to control resources and fail-prone computation. The target language is 𝗌π, an existing session-typed π-calculus that results from a Curry-Howard correspondence between linear logic and session types. Our typed translation subsumes our prior work; interestingly, it treats unrestricted resources in uλ^{↯}_{⊕} as client-server session behaviours in 𝗌π.
Cite as

Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez. Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{paulus_et_al:LIPIcs.TYPES.2021.11,
  author =	{Paulus, Joseph W. N. and Nantes-Sobrinho, Daniele and P\'{e}rez, Jorge A.},
  title =	{{Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.11},
  URN =		{urn:nbn:de:0030-drops-167808},
  doi =		{10.4230/LIPIcs.TYPES.2021.11},
  annote =	{Keywords: Resource \lambda-calculus, intersection types, session types, process calculi}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.21
Non-Deterministic Functions as Non-Deterministic Processes

Authors: Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

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 𝗌π, 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 𝗌π and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in λ^↯_⊕ via typed processes in 𝗌π. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interaction protocols.
Cite as

Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez. Non-Deterministic Functions as Non-Deterministic Processes. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.21},
  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}
}
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