Parallel Complexity Analysis with Temporal Session Types

TL;DR

This paper introduces temporal session types to analyze the timing and complexity of concurrent message-passing programs, enabling precise, compositional reasoning about communication latency, throughput, and parallel execution spans.

Contribution

It extends binary session types with temporal modalities, providing a novel framework for parametric complexity analysis of concurrent programs based on a Curry-Howard correspondence.

Findings

Temporal session types can express message rate, latency, and response times.

The analysis is sound, with proofs of progress and type preservation.

Examples demonstrate the approach's applicability to real concurrent systems.

Abstract

We study the problem of parametric parallel complexity analysis of concurrent, message-passing programs. To make the analysis local and compositional, it is based on a conservative extension of binary session types, which structure the type and direction of communication between processes and stand in a Curry-Howard correspondence with intuitionistic linear logic. The main innovation is to enrich session types with the temporal modalities next ($\bigcirc A$), always ($\Box A$), and eventually ($\Diamond A$), to additionally prescribe the timing of the exchanged messages in a way that is precise yet flexible. The resulting temporal session types uniformly express properties such as the message rate of a stream, the latency of a pipeline, the response time of a concurrent queue, or the span of a fork/join parallel program. The analysis is parametric in the cost model and the presentation focuses on communication cost as a concrete example. The soundness of the analysis is established by proofs of progress and type preservation using a timed multiset rewriting semantics. Representative examples illustrate the scope and usability of the approach.