Parallel complexity analysis with temporal session types

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 ( A), always (✷A), and eventually (✸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.

Asynchronous Timed Session Types

“…Our duality and subtyping are similar to those in [6], but apply to the asynchronous scenario. The work in [15] introduces a typed calculus based on temporal session types. The temporal modalities in [15] can be used as a discrete model of time.…”

“…The work in [15] introduces a typed calculus based on temporal session types. The temporal modalities in [15] can be used as a discrete model of time. Timed session types, thanks to clocks and resets, are able to model complex timed dependencies that temporal session types do not seem able to capture.…”

“…The calculi in [7,12,15] have been used in combination with session types. The calculus in [12] features a non-blocking receive primitive similar to our a 0 (b).…”

“…P . The calculus in [15], seems able to encode a non-blocking receive primitive like the one of [12] and a blocking receive primitive without timeout like our a ∞ (b). P .…”

“…Recent work, based on session types, focus on the relationship between time-sensitive protocols, modelled as timed extensions of session types, and their implementations abstracted as processes in some timed calculus. The relationship between protocols and processes is given in terms of static behavioural typing [12,15] or run-time monitoring [6,7,30] of processes against types. Existing work on timed session types [7,12,15,30] is based on simple abstractions for processes which do not capture time sensitive primitives such as blocking (as well as non-blocking) receive primitives with timeout and time consuming actions with variable, yet bound, duration.…”