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

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

Session Types for Broadcasting

Up to now session types have been used under the assumptions of point to point communication, to ensure the linearity of session endpoints, and reliable communication, to ensure send/receive duality. In this paper we define a session type theory for broadcast communication semantics that by definition do not assume point to point and reliable communication. Our session framework lies on top of the parametric framework of broadcasting psi-calculi, giving insights on developing session types within a parametric framework. Our session type theory enjoys the properties of soundness and safety. We further believe that the solutions proposed will eventually provide a deeper understanding of how session types principles should be applied in the general case of communication semantics.Comment: In Proceedings PLACES 2014, arXiv:1406.331

Session Types as Generic Process Types

Behavioural type systems ensure more than the usual safety guarantees of static analysis. They are based on the idea of "types-as-processes", providing dedicated type algebras for particular properties, ranging from protocol compatibility to race-freedom, lock-freedom, or even responsiveness. Two successful, although rather different, approaches, are session types and process types. The former allows to specify and verify (distributed) communication protocols using specific type (proof) systems; the latter allows to infer from a system specification a process abstraction on which it is simpler to verify properties, using a generic type (proof) system. What is the relationship between these approaches? Can the generic one subsume the specific one? At what price? And can the former be used as a compiler for the latter? The work presented herein is a step towards answers to such questions. Concretely, we define a stepwise encoding of a pi-calculus with sessions and session types (the system of Gay and Hole) into a pi-calculus with process types (the Generic Type System of Igarashi and Kobayashi). We encode session type environments, polarities (which distinguish session channels end-points), and labelled sums. We show forward and reverse operational correspondences for the encodings, as well as typing correspondences. To faithfully encode session subtyping in process types subtyping, one needs to add to the target language record constructors and new subtyping rules. In conclusion, the programming convenience of session types as protocol abstractions can be combined with the simplicity and power of the pi-calculus, taking advantage in particular of the framework provided by the Generic Type System.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

Session types revisited

Session types are a formalism used to model structured communication-based programming. A binary session type describes communication by specifying the type and direction of data exchanged between two parties. When session types and session processes are added to the syntax of standard π-calculus they give rise to additional separate syntactic categories. As a consequence, when new type features are added, there is duplication of effort in the theory: the proofs of properties must be checked both on standard types and on session types. We show that session types are encodable into standard π- types, relying on linear and variant types. Besides being an expressivity result, the encoding (i) removes the above redundancies in the syntax, and (ii) the properties of session types are derived as straightforward corollaries, exploiting the corresponding properties of standard π-types. The robustness of the encoding is tested on a few extensions of session types, including subtyping, polymorphism and higher-order communications

Uniqueness Typing for Resource Management in Message-Passing Concurrency

We view channels as the main form of resources in a message-passing programming paradigm. These channels need to be carefully managed in settings where resources are scarce. To study this problem, we extend the pi-calculus with primitives for channel allocation and deallocation and allow channels to be reused to communicate values of different types. Inevitably, the added expressiveness increases the possibilities for runtime errors. We define a substructural type system which combines uniqueness typing and affine typing to reject these ill-behaved programs

Recursive Session Types Revisited

Session types model structured communication-based programming. In particular, binary session types for the pi-calculus describe communication between exactly two participants in a distributed scenario. Adding sessions to the pi-calculus means augmenting it with type and term constructs. In a previous paper, we tried to understand to which extent the session constructs are more complex and expressive than the standard pi-calculus constructs. Thus, we presented an encoding of binary session pi-calculus to the standard typed pi-calculus by adopting linear and variant types and the continuation-passing principle. In the present paper, we focus on recursive session types and we present an encoding into recursive linear pi-calculus. This encoding is a conservative extension of the former in that it preserves the results therein obtained. Most importantly, it adopts a new treatment of the duality relation, which in the presence of recursive types has been proven to be quite challenging.Comment: In Proceedings BEAT 2014, arXiv:1408.556

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