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

Authors Alexis Bernadet, Stéphane Lengrand

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Alexis Bernadet
Stéphane Lengrand

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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)


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.
  • non-idempotent intersections
  • System F
  • realisability


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