INTERSECTION TYPES FOR THE λμ-CALCULUS

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 w-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.