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DOI: 10.4230/LIPIcs.RTA.2010.17
Higher-Order (Non-)Modularity

Authors: Claus Appel, Vincent van Oostrom, and Jakob Grue Simonsen

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)

Abstract
We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting systems modularity of confluence, normalization, and termination can be recovered by imposing suitable linearity constraints.
Cite as

Claus Appel, Vincent van Oostrom, and Jakob Grue Simonsen. Higher-Order (Non-)Modularity. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 17-32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{appel_et_al:LIPIcs.RTA.2010.17,
  author =	{Appel, Claus and van Oostrom, Vincent and Simonsen, Jakob Grue},
  title =	{{Higher-Order (Non-)Modularity}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{17--32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.17},
  URN =		{urn:nbn:de:0030-drops-26427},
  doi =		{10.4230/LIPIcs.RTA.2010.17},
  annote =	{Keywords: Higher-order rewriting, modularity, termination, normalization}
}
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