Multiparty Sessions based on Proof Nets

We interpret Linear Logic Proof Nets in a term language based on Solos calculus. The system includes a synchronisation mechanism, obtained by a conservative extension of the logic, that enables to define non-deterministic behaviours and multiparty sessions.Comment: In Proceedings PLACES 2014, arXiv:1406.331

Session Types in Concurrent Calculi: Higher-Order Processes and Objects

This dissertation investigates different formalisms, in the form of programming language calculi, that are aimed at providing a theoretical foundation for structured concurrent programming based on session types. The structure of a session type is essentially a process-algebraic style description of the behaviour of a single program identifier serving as a communication medium (and usually referred to as a channel): the types incorporate typed inputs, outputs, and choices which can be composed to form larger protocol descriptions. The effectiveness of session typing can be attributed to the linear treatment of channels and session types, and to the use of tractable methods such as syntactic duality to decide if the types of two connected channels are compatible. Linearity is ensured when accumulating the uses of a channel into a composite type that describes also the order of those actions. Duality provides a tractable and intuitive method for deciding when two connected channels can interact and exchange values in a statically determined type-safe way. We present our contributions to the theory of sessions, distilled into two families of programming calculi, the first based on higher-order processes and the second based on objects. Our work unifies, improves and extends, in manifold ways, the session primitives and typing systems for the Lambda-calculus, the Pi-calculus, the Object-calculus, and their combinations in multi-paradigm languages. Of particular interest are: the treatment of infinite interactions expressed with recursive sessions; the capacity to encapsulate channels in higher-order structures which can be exchanged and kept suspended, i.e., the use of code as data; the integration of protocol structure directly into the description of objects, providing a powerful and uniformly extensible set of implementation abstractions; finally, the introduction of asynchronous subtyping, which enables controlled reordering of actions on either side of a session. Our work on higher-order processes and on object calculi for session-based concurrent programming provides a theoretical foundation for programming language design integrating functional, process, and object-oriented features

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

Affine Sessions

Session types describe the structure of communications implemented by channels. In particular, they prescribe the sequence of communications, whether they are input or output actions, and the type of value exchanged. Crucial to any language with session types is the notion of linearity, which is essential to ensure that channels exhibit the behaviour prescribed by their type without interference in the presence of concurrency. In this work we relax the condition of linearity to that of affinity, by which channels exhibit at most the behaviour prescribed by their types. This more liberal setting allows us to incorporate an elegant error handling mechanism which simplifies and improves related works on exceptions. Moreover, our treatment does not affect the progress properties of the language: sessions never get stuck

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

Hybrid Session Verification through Endpoint API Generation

© Springer-Verlag Berlin Heidelberg 2016.This paper proposes a new hybrid session verification methodology for applying session types directly to mainstream languages, based on generating protocol-specific endpoint APIs from multiparty session types. The API generation promotes static type checking of the behavioural aspect of the source protocol by mapping the state space of an endpoint in the protocol to a family of channel types in the target language. This is supplemented by very light run-time checks in the generated API that enforce a linear usage discipline on instances of the channel types. The resulting hybrid verification guarantees the absence of protocol violation errors during the execution of the session. We implement our methodology for Java as an extension to the Scribble framework, and use it to specify and implement compliant clients and servers for real-world protocols such as HTTP and SMTP

The Paths to Choreography Extraction

Choreographies are global descriptions of interactions among concurrent components, most notably used in the settings of verification (e.g., Multiparty Session Types) and synthesis of correct-by-construction software (Choreographic Programming). They require a top-down approach: programmers first write choreographies, and then use them to verify or synthesize their programs. However, most existing software does not come with choreographies yet, which prevents their application. To attack this problem, we propose a novel methodology (called choreography extraction) that, given a set of programs or protocol specifications, automatically constructs a choreography that describes their behavior. The key to our extraction is identifying a set of paths in a graph that represents the symbolic execution of the programs of interest. Our method improves on previous work in several directions: we can now deal with programs that are equipped with a state and internal computation capabilities; time complexity is dramatically better; we capture programs that are correct but not necessarily synchronizable, i.e., they work because they exploit asynchronous communication

Reversing Single Sessions

Session-based communication has gained a widespread acceptance in practice as a means for developing safe communicating systems via structured interactions. In this paper, we investigate how these structured interactions are affected by reversibility, which provides a computational model allowing executed interactions to be undone. In particular, we provide a systematic study of the integration of different notions of reversibility in both binary and multiparty single sessions. The considered forms of reversibility are: one for completely reversing a given session with one backward step, and another for also restoring any intermediate state of the session with either one backward step or multiple ones. We analyse the costs of reversing a session in all these different settings. Our results show that extending binary single sessions to multiparty ones does not affect the reversibility machinery and its costs

On the relative expressiveness of higher-order session processes

By integrating constructs from the λ-calculus and the π-calculus, in higher-order process calculi exchanged values may contain processes. This paper studies the relative expressiveness of HOπ, the higher-order π-calculus in which communications are governed by session types. Our main discovery is that HO, a subcalculus of HOπ which lacks name-passing and recursion, can serve as a new core calculus for session-typed higher-order concurrency. By exploring a new bisimulation for HO, we show that HO can encode HOπ fully abstractly (up to typed contextual equivalence) more precisely and efficiently than the first-order session π-calculus (π). Overall, under session types, HOπ, HO, and π are equally expressive; however, HOπ and HO are more tightly related than HOπ and π

Soft Session Types

We show how systems of session types can enforce interactions to be bounded for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as intuitionistic linear logic formulas. Our main result is the existence, for every typable process, of a polynomial bound on the length of any reduction sequence starting from it and on the size of any of its reducts.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407