Intersections and Unions of Session Types

Abstract

Prior work has extended the deep, logical connection between the linear sequent calculus and sessiontyped message-passing concurrent computation with equi-recursive types and a natural notion of subtyping. In this paper, we extend this further by intersection and union types in order to express multiple behavioral properties of processes in a single type. We prove session fidelity and absence of deadlock and illustrate the expressive power of our system with some simple examples. We observe that we can represent internal and external choice by intersection and union, respectively, which was previously suggested in [6,18] for a different language of session types motivated by operational rather than logical concerns.

Manifestly Phased Communication via Shared Session Types

“…The sharing semantics that we investigate in this paper was introduced in [BP17] by decomposing the exponential modality, which was previously known to provide a copying semantics through association with the exponential operator in linear logic. The type system arising from the correspondence with intuitionistic linear logic was later given a subtyping extension [AP16], which covered all linear connectives along with union and intersect types (still linear) that we omitted in our work. One stylistic difference between the two is that our subtyping is present directly in the type system, whereas the subtyping in [AP16] is implicitly present through a subsumption rule (and corresponding meta theory to prove its safety).…”

“…The type system arising from the correspondence with intuitionistic linear logic was later given a subtyping extension [AP16], which covered all linear connectives along with union and intersect types (still linear) that we omitted in our work. One stylistic difference between the two is that our subtyping is present directly in the type system, whereas the subtyping in [AP16] is implicitly present through a subsumption rule (and corresponding meta theory to prove its safety).…”

Empowering union and intersection types with integrated subtyping

“…Another way changing input contexts are used in subtyping is to track which subtyping goals are currently in progress. This is useful for regular subtyping systems [Bonchi and Pous 2013;Brandt and Henglein 1998;Gesbert et al 2015;Hosoya et al 2000;Kozen et al 1995], which are particularly common in domain-specific languages [Acay and Pfenning 2017;Ancona and Corradi 2016;Anderson et al 2014;Henglein and Nielsen 2011;Jeannin et al 2017] and are also used in C# [Hejlsberg et al 2005;Kennedy and Pierce 2007;Viroli 2000]. Whereas well-founded subtyping rules ensure recursive proof search terminates, regular subtyping rules ensure the recursion eventually repeats itself.…”

Foundations of Session Types

“…Union and external choice instead perfectly match in the simplified calculus of Padovani [25]. In the framework of the logical interpretation of session types [9], Acay and Pfenning [1] represent internal and external choices by intersection and union, respectively.…”