Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Bernadet, Alexis; Lengrand, Stéphane http://www.dagstuhl.de/lipics License
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URN: urn:nbn:de:0030-drops-32226
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Filter Models: Non-idempotent Intersection Types, Orthogonality and Polymorphism

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Abstract

This paper revisits models of typed lambda calculus based on filters of intersection types: By using non-idempotent intersections, we simplify a methodology that produces modular proofs of strong normalisation based on filter models. Building such a model for some type theory shows that typed terms can be typed with intersections only, and are therefore strongly normalising. Non-idempotent intersections provide a decreasing measure proving a key termination property, simpler than the reducibility techniques used with idempotent intersections. Such filter models are shown to be captured by orthogonality techniques: we formalise an abstract notion of orthogonality model inspired by classical realisability, and express a filter model as one of its instances, along with two term-models (one of which captures a now common technique for strong normalisation). Applying the above range of model constructions to Curry-style System F describes at different levels of detail how the infinite polymorphism of System F can systematically be reduced to the finite polymorphism of intersection types.

BibTeX - Entry

@InProceedings{bernadet_et_al:LIPIcs:2011:3222,
  author =	{Alexis Bernadet and St{\'e}phane Lengrand},
  title =	{{Filter Models: Non-idempotent Intersection Types, Orthogonality and Polymorphism}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{51--66},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Marc Bezem},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3222},
  URN =		{urn:nbn:de:0030-drops-32226},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2011.51},
  annote =	{Keywords: non-idempotent intersections, System F, realisability}
}

Keywords: non-idempotent intersections, System F, realisability
Seminar: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL
Issue date: 2011
Date of publication: 2011


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