Sound and Complete Typing for lambda-mu

TL;DR

This paper introduces intersection and union type systems for lambda-mu calculus, demonstrating their soundness and completeness, which supports their use in defining semantics for the calculus.

Contribution

It presents a novel intersection-union type assignment system for lambda-mu calculus that is both sound and complete, ensuring robust semantic foundations.

Findings

Type assignment is complete (closed under subject-expansion)

Type assignment is sound (closed under subject-reduction)

Supports semantic definitions for lambda-mu calculus

Abstract

In this paper we define intersection and union type assignment for Parigot's calculus lambda-mu. We show that this notion is complete (i.e. closed under subject-expansion), and show also that it is sound (i.e. closed under subject-reduction). This implies that this notion of intersection-union type assignment is suitable to define a semantics.