2 Search Results for "Neves, Renato"

Document
DOI: 10.4230/LIPIcs.CSL.2022.16
An Internal Language for Categories Enriched over Generalised Metric Spaces

Authors: Fredrik Dahlqvist and Renato Neves

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the idea of equivalence taking values in a quantale 𝒱, which covers the cases of (in)equations and (ultra)metric equations among others. Our main result is the introduction of a 𝒱-equational deductive system for linear λ-calculus together with a proof that it is sound and complete (in fact, an internal language) for a class of enriched autonomous categories. In the case of inequations, we get an internal language for autonomous categories enriched over partial orders. In the case of (ultra)metric equations, we get an internal language for autonomous categories enriched over (ultra)metric spaces. We use our results to obtain examples of inequational and metric equational systems for higher-order programs that contain real-time and probabilistic behaviour.
Cite as

Fredrik Dahlqvist and Renato Neves. An Internal Language for Categories Enriched over Generalised Metric Spaces. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dahlqvist_et_al:LIPIcs.CSL.2022.16,
  author =	{Dahlqvist, Fredrik and Neves, Renato},
  title =	{{An Internal Language for Categories Enriched over Generalised Metric Spaces}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.16},
  URN =		{urn:nbn:de:0030-drops-157362},
  doi =		{10.4230/LIPIcs.CSL.2022.16},
  annote =	{Keywords: \lambda-calculus, enriched category theory, quantale, equational theory}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2018.22
A Semantics for Hybrid Iteration

Authors: Sergey Goncharov, Julian Jakob, and Renato Neves

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract
The recently introduced notions of guarded traced (monoidal) category and guarded (pre-)iterative monad aim at unifying different instances of partial iteration whilst keeping in touch with the established theory of total iteration and preserving its merits. In this paper we use these notions and the corresponding stock of results to examine different types of iteration for hybrid computations. As a starting point we use an available notion of hybrid monad restricted to the category of sets, and modify it in order to obtain a suitable notion of guarded iteration with guardedness interpreted as progressiveness in time - we motivate this modification by our intention to capture Zeno behaviour in an arguably general and feasible way. We illustrate our results with a simple programming language for hybrid computations and interpret it over the developed semantic foundations.
Cite as

Sergey Goncharov, Julian Jakob, and Renato Neves. A Semantics for Hybrid Iteration. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{goncharov_et_al:LIPIcs.CONCUR.2018.22,
  author =	{Goncharov, Sergey and Jakob, Julian and Neves, Renato},
  title =	{{A Semantics for Hybrid Iteration}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.22},
  URN =		{urn:nbn:de:0030-drops-95604},
  doi =		{10.4230/LIPIcs.CONCUR.2018.22},
  annote =	{Keywords: Elgot iteration, guarded iteration, hybrid monad, Zeno behaviour}
}
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