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.

Source : oai:arXiv.org:1704.00272

DOI : 10.23638/LMCS-14(1:2)2018

Volume: Volume 14, Issue 1

Published on: January 10, 2018

Submitted on: January 10, 2018

Keywords: Computer Science - Logic in Computer Science,F.4,F.4.1

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