Intersection Types for the lambda-mu Calculus
Abstract
We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of omega-algebraic lattices via Abramsky's domain-logic approach. This provides at the same time an interpretation of the type system and a proof of the completeness of the system with respect to the continuation models by means of a filter model construction. We then define a restriction of our system, such that a lambda-mu term is typeable if and only if it is strongly normalising. We also show that Parigot's typing of lambda-mu terms with classically valid propositional formulas can be translated into the restricted system, which then provides an alternative proof of strong normalisability for the typed lambda-mu calculus.
Keywords
Cite
@article{arxiv.1704.00272,
title = {Intersection Types for the lambda-mu Calculus},
author = {Steffen van Bakel and Franco Barbanera and Ugo de'Liguoro},
journal= {arXiv preprint arXiv:1704.00272},
year = {2019}
}