Characterisation of Strongly Normalising lambda-mu-Terms

TL;DR

This paper characterizes strongly normalising lambda-mu-terms using a specialized intersection and product type system, extending known lambda-term results to the lambda-mu-calculus and providing an alternative proof of strong normalisation.

Contribution

It introduces a novel type system that captures strong normalisation in lambda-mu-calculus, extending intersection type characterizations from lambda calculus.

Findings

Characterization of strongly normalising lambda-mu-terms via a new type system

Extension of intersection type characterisation from lambda calculus to lambda-mu-calculus

Alternative proof of strong normalisation for Parigot's propositional system

Abstract

We provide a characterisation of strongly normalising terms of the lambda-mu-calculus by means of a type system that uses intersection and product types. The presence of the latter and a restricted use of the type omega enable us to represent the particular notion of continuation used in the literature for the definition of semantics for the lambda-mu-calculus. This makes it possible to lift the well-known characterisation property for strongly-normalising lambda-terms - that uses intersection types - to the lambda-mu-calculus. From this result an alternative proof of strong normalisation for terms typeable in Parigot's propositional logical system follows, by means of an interpretation of that system into ours.