Nested Session Types

TL;DR

This paper extends session types with prenex polymorphism and nested recursive datatypes, providing a decidable type equality, an efficient algorithm, and practical implementation in the Rast language.

Contribution

It introduces the first formal metatheory for session types with prenex polymorphism and nested recursive datatypes, including a novel type equality algorithm and implementation.

Findings

Type equality is decidable via trace equivalence reduction.

The proposed algorithm is efficient and practically sufficient.

Extended Rast with nested session types demonstrates increased expressivity.

Abstract

Session types statically describe communication protocols between concurrent message-passing processes. Unfortunately, parametric polymorphism even in its restricted prenex form is not fully understood in the context of session types. In this paper, we present the metatheory of session types extended with prenex polymorphism and, as a result, nested recursive datatypes. Remarkably, we prove that type equality is decidable by exhibiting a reduction to trace equivalence of deterministic first-order grammars. Recognizing the high theoretical complexity of the latter, we also propose a novel type equality algorithm and prove its soundness. We observe that the algorithm is surprisingly efficient and, despite its incompleteness, sufficient for all our examples. We have implemented our ideas by extending the Rast programming language with nested session types. We conclude with several examples illustrating the expressivity of our enhanced type system.