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DOI: 10.4230/LIPIcs.RTA.2011.345
URN: urn:nbn:de:0030-drops-31343
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3134/

Stump, Aaron ; Kimmell, Garrin ; El Haj Omar, Roba

Type Preservation as a Confluence Problem

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Abstract

This paper begins with recent work by Kuan, MacQueen, and Findler, which shows how standard type systems, such as the simply typed lambda calculus, can be viewed as abstract reduction systems operating on terms. The central idea is to think of the process of typing a term as the computation of an abstract value for that term. The standard metatheoretic property of type preservation can then be seen as a confluence problem involving the concrete and abstract operational semantics, viewed as abstract reduction systems (ARSs). In this paper, we build on the work of Kuan et al. by showing show how modern ARS theory, in particular the theory of decreasing diagrams, can be used to establish type preservation via confluence. We illustrate this idea through several examples of solving such problems using decreasing diagrams. We also consider how automated tools for analysis of term-rewriting systems can be applied in testing type

BibTeX - Entry

@InProceedings{stump_et_al:LIPIcs:2011:3134,
  author =	{Aaron Stump and Garrin Kimmell and Roba El Haj Omar},
  title =	{{Type Preservation as a Confluence Problem}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{345--360},
  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/2011/3134},
  URN =		{urn:nbn:de:0030-drops-31343},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.RTA.2011.345},
  annote =	{Keywords: Term rewriting, Type Safety, Confluence}
}

Keywords: Term rewriting, Type Safety, Confluence
Seminar: 22nd International Conference on Rewriting Techniques and Applications (RTA'11)
Issue date: 2011
Date of publication: 26.04.2011


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