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DOI: 10.4230/LIPIcs.CSL.2011.51

Filter Models: Non-idempotent Intersection Types, Orthogonality and Polymorphism

Authors: Alexis Bernadet and Stéphane Lengrand

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

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.

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Alexis Bernadet and Stéphane Lengrand. Filter Models: Non-idempotent Intersection Types, Orthogonality and Polymorphism. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 51-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{bernadet_et_al:LIPIcs.CSL.2011.51,
  author =	{Bernadet, Alexis and Lengrand, St\'{e}phane},
  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 =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.51},
  URN =		{urn:nbn:de:0030-drops-32226},
  doi =		{10.4230/LIPIcs.CSL.2011.51},
  annote =	{Keywords: non-idempotent intersections, System F, realisability}
}

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Filter Models: Non-idempotent Intersection Types, Orthogonality and Polymorphism

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