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DOI: 10.4230/LIPIcs.RTA.2011.299
URN: urn:nbn:de:0030-drops-31273
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3127/

Roux, Cody

Refinement Types as Higher-Order Dependency Pairs

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Abstract

Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher-order rewrite systems is still the subject of active research. We observe that a variant of refinement types allows us to express a form of higher-order dependency pair method: from the rewrite system labeled with typing information, we build a type-level approximated dependency graph, and describe a type level embedding preorder. We describe a syntactic termination criterion involving the graph and the preorder, which generalizes the simple projection criterion of Middeldorp and Hirokawa, and prove our main result: if the graph passes the criterion, then every well-typed term is strongly normalizing.

BibTeX - Entry

@InProceedings{roux:LIPIcs:2011:3127,
  author =	{Cody Roux},
  title =	{{Refinement Types as Higher-Order Dependency Pairs}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{299--312},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-30-9 },
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{10},
  editor =	{Manfred Schmidt-Schau{\ss}},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3127},
  URN =		{urn:nbn:de:0030-drops-31273},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.RTA.2011.299},
  annote =	{Keywords: Dependency Pairs, Higher-Order, Refinement Types}
}

Keywords: Dependency Pairs, Higher-Order, Refinement Types
Seminar: 22nd International Conference on Rewriting Techniques and Applications (RTA'11)
Issue date: 2011
Date of publication: 26.04.2011


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