Filter models: non-idempotent intersection types, orthogonality and polymorphism - long version

Alexis Bernadet (1) , Stéphane Lengrand (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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. 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.

Mots clés: non-idempotent intersections; I-filters models; System F; polymorphism; orthogonality models; realisability

Domaines: Logique en informatique [cs.LO]

Alexis Bernadet, Stéphane Lengrand. Filter models: non-idempotent intersection types, orthogonality and polymorphism - long version. 2011. ⟨hal-00600070v3⟩