License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2011.51
URN: urn:nbn:de:0030-drops-32226
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3222/
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Bernadet, Alexis ; Lengrand, Stéphane

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 =		{10.4230/LIPIcs.CSL.2011.51},
  annote =	{Keywords: non-idempotent intersections, System F, realisability}
}

Keywords: non-idempotent intersections, System F, realisability
Collection: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL
Issue Date: 2011
Date of publication: 31.08.2011

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