On the boundary between decidability and undecidability of asynchronous session subtyping

Abstract

Session types are behavioural types for guaranteeing that concurrent programs are free from basic communication errors. Recent work has shown that asynchronous session subtyping is undecidable. However, since session types have become popular in mainstream programming languages in which asynchronous communication is the norm rather than the exception, it is crucial to detect significant decidable subtyping relations. Previous work considered extremely restrictive fragments in which limitations were imposed to the size of communication buffer (at most 1) or to the possibility to express multiple choices (disallowing them completely in one of the compared types). In this work, for the first time, we show decidability of a fragment that does not impose any limitation on communication buffers and allows both the compared types to include multiple choices for either input or output, thus yielding a fragment which is more significant from an applicability viewpoint. In general, we study the boundary between decidability and undecidability by considering several fragments of subtyping. Notably, we show that subtyping remains undecidable even if restricted to not using output covariance and input contravariance.

Asynchronous session subtyping as communicating automata refinement

“…We start with the formal syntax of binary session types, adopting a simplified notation (used, e.g. in [9,10]) without dedicated constructs for sending an output/receiving an input. We instead represent outputs and inputs directly inside choices.…”

“…Intuitively, this is due to the fact that it is no longer possible to express output divergent recursive types originating orphan messages. An important consequence is that since asynchronous subtyping of [22] is dual closed (see [10]), also the subtyping relation ≤ of Definition 14 enjoys such a property.…”

“…supertype. 1 Asynchronous session subtyping has been more recently investigated [8,10,22,34,35]: it is more permissive because it widens the synchronous subtyping relation by allowing the subtype to anticipate send actions, under the assumption that the subsequent communication protocol is not influenced by the anticipation. Anticipation is admitted because, in the presence of message queues, the effect of anticipating a send is simply that of enqueueing earlier, in the communication channel, the corresponding message.…”

Relating Session Types and Behavioural Contracts: The Asynchronous Case

“…We start with the formal syntax of binary session types, adopting a simplified notation (used, e.g., in [7,8]) without dedicated constructs for sending an output/receiving an input. We instead represent outputs and inputs directly inside choices.…”

“…The typical notion of subtyping for session types is the one by Gay and Hole [17] defined by considering synchronous communication: synchronous session subtyping only allows for a subtype to have fewer internal choices (sends), and more external choices (receives), than its supertype. Asynchronous session subtyping has been more recently investigated [25,24,15,8,6]: it is more permissive because it widens the synchronous subtyping relation by allowing the subtype to anticipate send actions, under the assumption that the subsequent communication protocol is not influenced by the anticipation. Anticipation is admitted because, in the presence of message queues, the effect of anticipating a send is simply that of enqueueing earlier, in the communication channel, the corresponding message.…”