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Documents authored by Jouannaud, Jean-Pierre

Document
DOI: 10.4230/LIPIcs.CSL.2015.423
Confluence of Layered Rewrite Systems

Authors: Jiaxiang Liu, Jean-Pierre Jouannaud, and Mizuhito Ogawa

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
We investigate a new, Turing-complete class of layered systems, whose linearized lefthand sides of rules can only be overlapped at the root position. Layered systems define a natural notion of rank for terms: the maximal number of redexes along a path from the root to a leaf. Overlappings are allowed in finite or infinite trees. Rules may be non-terminating, non-left-linear, or non-right- linear. Using a novel unification technique, cyclic unification, we show that rank non-increasing layered systems are confluent provided their cyclic critical pairs have cyclic-joinable decreasing diagrams.
Cite as

Jiaxiang Liu, Jean-Pierre Jouannaud, and Mizuhito Ogawa. Confluence of Layered Rewrite Systems. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 423-440, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{liu_et_al:LIPIcs.CSL.2015.423,
  author =	{Liu, Jiaxiang and Jouannaud, Jean-Pierre and Ogawa, Mizuhito},
  title =	{{Confluence of Layered Rewrite Systems}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{423--440},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.423},
  URN =		{urn:nbn:de:0030-drops-54293},
  doi =		{10.4230/LIPIcs.CSL.2015.423},
  annote =	{Keywords: Layers, confluence, decreasing diagrams, critical pairs, cyclic unification}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.257
Termination of Dependently Typed Rewrite Rules

Authors: Jean-Pierre Jouannaud and Jianqi Li

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
Our interest is in automated termination proofs of higher-order rewrite rules in presence of dependent types modulo a theory T on base types. We first describe an original transformation to a type discipline without type dependencies which preserves non-termination. Since the user must reason on expressions of the transformed language, we then introduce an extension of the computability path ordering CPO for comparing dependently typed expressions named DCPO. Using the previous result, we show that DCPO is a well-founded order, behaving well in practice.
Cite as

Jean-Pierre Jouannaud and Jianqi Li. Termination of Dependently Typed Rewrite Rules. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 257-272, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{jouannaud_et_al:LIPIcs.TLCA.2015.257,
  author =	{Jouannaud, Jean-Pierre and Li, Jianqi},
  title =	{{Termination of Dependently Typed Rewrite Rules}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{257--272},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.257},
  URN =		{urn:nbn:de:0030-drops-51684},
  doi =		{10.4230/LIPIcs.TLCA.2015.257},
  annote =	{Keywords: rewriting, dependent types, strong normalization, path orderings}
}
Document
DOI: 10.4230/LIPIcs.CSL.2012.350
Church-Rosser Properties of Normal Rewriting

Authors: Jean-Pierre Jouannaud and Jianqi Li

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

Abstract
We prove a general purpose abstract Church-Rosser result that captures most existing such results that rely on termination of computations. This is achieved by studying abstract normal rewriting in a way that allows to incorporate positions at the abstract level. New concrete Church-Rosser results are obtained, in particular for higher-order rewriting at higher types.
Cite as

Jean-Pierre Jouannaud and Jianqi Li. Church-Rosser Properties of Normal Rewriting. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 350-365, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{jouannaud_et_al:LIPIcs.CSL.2012.350,
  author =	{Jouannaud, Jean-Pierre and Li, Jianqi},
  title =	{{Church-Rosser Properties of Normal Rewriting}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{350--365},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.350},
  URN =		{urn:nbn:de:0030-drops-36839},
  doi =		{10.4230/LIPIcs.CSL.2012.350},
  annote =	{Keywords: abstract normal rewriting, Church-Rosser property}
}
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