Intersection Types for the lambda-mu Calculus [article]

Steffen van Bakel, Franco Barbanera, Ugo de'Liguoro
2017 arXiv   pre-print
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
more » ... hen 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.
arXiv:1704.00272v2 fatcat:lwx7666epbhkxd7woj4ng3bj2m