Reduction system for extensional lambda-mu calculus

Abstract

The Λμ-calculus is an extension of Parigot's λμ- calculus. For the untyped Λμ-calculus, Saurin proved some fundamental properties such as the standardization and the separation theorem. Nakazawa and Katsumata gave extensional models, called stream models, in which terms are represented as functions on streams. This paper introduces a conservative extension of the Λμ-calculus, called Λμ cons, from which the open term model is straightforwardly constructed as a stream model, and for which we can define a reduction system satisfying several fundamental properties such as confluence, subject reduction, and strong normalization. © 2014 Springer International Publishing Switzerland.