Relating Session Types and Behavioural Contracts: The Asynchronous Case

We discuss the relationship between session types and behavioural contracts under the assumption that processes communicate asynchronously. We show the existence of a fully abstract interpretation of session types into a fragment of contracts, that maps session subtyping into binary compliance-preserving contract refinement. In this way, the recent undecidability result for asynchronous session subtyping can be used to obtain an original undecidability result for asynchronous contract refinement

Undecidability of asynchronous session subtyping

Session types are used to describe communication protocols in distributed systems and, as usual in type theories, session subtyping characterizes substitutability of the communicating processes. We investigate the (un)decidability of subtyping for session types in asynchronously communicating systems. We first devise a core undecidable subtyping relation that is obtained by imposing limitations on the structure of types. Then, as a consequence of this initial undecidability result, we show that (differently from what stated or conjectured in the literature) the three notions of asynchronous subtyping defined so far for session types are all undecidable. Namely, we consider the asynchronous session subtyping by Mostrous and Yoshida for binary sessions, the relation by Chen et al. for binary sessions under the assumption that every message emitted is eventually consumed, and the one by Mostrous et al. for multiparty session types. Finally, by showing that two fragments of the core subtyping relation are decidable, we evince that further restrictions on the structure of types make our core subtyping relation decidable.Comment: 36 page

Relating Session Types and Behavioural Contracts: the Asynchronous Case

International audienceWe discuss the relationship between session types and be-havioural contracts under the assumption that processes communicate asynchronously. We show the existence of a fully abstract interpretation of session types into a fragment of contracts, that maps session subtyping into binary compliance-preserving contract refinement. In this way, the recent undecidability result for asynchronous session subtyping can be used to obtain an original undecidability result for asynchronous contract refinement

Asynchronous session subtyping as communicating automata refinement

International audienceWe study the relationship between session types and behavioural contracts, representing Communicating Finite State Machines (CFSMs), under the assumption that processes communicate asynchronously. Session types represent a syntax-based approach for the description of communication protocols, while behavioural contracts, formally expressing CFSMs, follow an operational approach. We show the existence of a fully abstract interpretation of session types into a fragment of contracts that maps session subtyping into binary compliance-preserving CFSMs/behavioural contract refinement. In this way, on the one hand, we enrich the theory of session types with an operational characterization and, on the other hand, we use recent undecidability results for asynchronous session subtyping to obtain an original undecidability result for asynchronous CFSMs/behavioural contract refinement

On the boundary between decidability and undecidability of asynchronous session subtyping

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

On the preciseness of subtyping in session types: 10 years later

The PPDP Most Influential Paper 10-Year Award for our work [11] was a delightful surprise. We subsequently reviewed the subsequent literature to see how our results have been utilised. This short note aims to capture crucial references without missing too many

Fair Refinement for Asynchronous Session Types

International audienceSession types are widely used as abstractions of asynchronous message passing systems. Refinement for such abstractions is crucial as it allows improvements of a given component without compromising its compatibility with the rest of the system. In the context of session types, the most general notion of refinement is the asynchronous session subtyping, which allows to anticipate message emissions but only under certain conditions. In particular, asynchronous session subtyping rules out candidates subtypes that occur naturally in communication protocols where, e.g., two parties simultaneously send each other a finite but unspecified amount of messages before removing them from their respective buffers. To address this shortcoming, we study fair compliance over asynchronous session types and fair refinement as the relation that preserves it. This allows us to propose a novel variant of session subtyping that leverages the notion of controllability from service contract theory and that is a sound characterisation of fair refinement. In addition, we show that both fair refinement and our novel subtyping are undecidable. We also present a sound algorithm, and its implementation, which deals with examples that feature potentially unbounded buffering

A Session Subtyping Tool

International audienceSession types are becoming popular and have been integrated in several mainstream programming languages. Nevertheless, while many programming languages consider asynchronous fifo channel communication, the notion of subtyping used in session type implementations is the one defined by Gay and Hole for synchronous communication. This might be because there are several notions of asynchronous session subtyping, these notions are usually undecidable, and only recently sound (but not complete) algorithmic characterizations for these subtypings have been proposed. But the fact that the definition of asynchronous session subtyping and the theory behind related algorithms are not easily accessible to non-experts may also prevent further integration. The aim of this paper, and of the tool presented therein, is to make the growing body of knowledge about asynchronous session subtyping more accessible, thus promoting its integration in practical applications of session types

Session Types with Arithmetic Refinements

Session types statically prescribe bidirectional communication protocols for message-passing processes. However, simple session types cannot specify properties beyond the type of exchanged messages. In this paper we extend the type system by using index refinements from linear arithmetic capturing intrinsic attributes of data structures and algorithms. We show that, despite the decidability of Presburger arithmetic, type equality and therefore also subtyping and type checking are now undecidable, which stands in contrast to analogous dependent refinement type systems from functional languages. We also present a practical, but incomplete algorithm for type equality, which we have used in our implementation of Rast, a concurrent session-typed language with arithmetic index refinements as well as ergometric and temporal types. Moreover, if necessary, the programmer can propose additional type bisimulations that are smoothly integrated into the type equality algorithm

A sound algorithm for asynchronous session subtyping and its implementation

Session types, types for structuring communication between endpoints in concurrent systems, are recently being integrated into mainstream programming languages. In practice, a very important notion for dealing with such types is that of subtyping, since it allows for typing larger classes of systems, where a program has not precisely the expected behavior but a similar one. Unfortunately, recent work has shown that subtyping for session types in an asynchronous setting is undecidable. To cope with this negative result, the only approaches we are aware of either restrict the syntax of session types or limit communication (by considering forms of bounded asynchrony). Both approaches are too restrictive in practice, hence we proceed differently by presenting an algorithm for checking subtyping which is sound, but not complete (in some cases it terminates without returning a decisive verdict). The algorithm is based on a tree representation of the coinductive definition of asynchronous subtyping; this tree could be infinite, and the algorithm checks for the presence of finite witnesses of infinite successful subtrees. Furthermore, we provide a tool that implements our algorithm. We use this tool to test our algorithm on many examples that cannot be managed with the previous approaches, and to provide an empirical evaluation of the time and space cost of the algorithm