Type systems for distributed programs: session communication

Distributed systems are everywhere around us and guaranteeing their correctness is of paramount importance. It is natural to expect that these systems interact and communicate among them to achieve a common task. In this work, we develop techniques based on types and type systems for the verification of correctness, consistency and safety properties related to communication in complex distributed systems. We study advanced safety properties related to communication, like deadlock or lock freedom and progress. We study session types in the pi-calculus describing distributed systems and communication-centric computation. Most importantly, we de- fine an encoding of the session pi-calculus into the standard typed pi-calculus in order to understand the expressive power of these concurrent calculi. We show how to derive in the session pi-calculus basic properties, like type safety or complex ones, like progress, by exploiting this encoding

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

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

Trees from Functions as Processes

Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such trees. We apply these conditions to various encodings of the call-by-name {\lambda}-calculus, showing how the two kinds of tree can be obtained by varying the behavioural equivalence adopted in the {\pi}-calculus and/or the encoding

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

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

Precise subtyping for synchronous multiparty sessions

The notion of subtyping has gained an important role both in theoretical and applicative domains: in lambda and concurrent calculi as well as in programming languages. The soundness and the completeness, together referred to as the preciseness of subtyping, can be considered from two different points of view: operational and denotational. The former preciseness has been recently developed with respect to type safety, i.e. the safe replacement of a term of a smaller type when a term of a bigger type is expected. The latter preciseness is based on the denotation of a type which is a mathematical object that describes the meaning of the type in accordance with the denotations of other expressions from the language. The result of this paper is the operational and denotational preciseness of the subtyping for a synchronous multiparty session calculus. The novelty of this paper is the introduction of characteristic global types to prove the operational completeness

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

On the preciseness of subtyping in session types

Subtyping in concurrency has been extensively studied since early 1990s as one of the most interesting issues in type theory. The correctness of subtyping relations has been usually provided as the soundness for type safety. The converse direction, the completeness, has been largely ignored in spite of its usefulness to define the greatest subtyping relation ensuring type safety. This paper formalises preciseness (i.e. both soundness and completeness) of subtyping for mobile processes and studies it for the synchronous and the asynchronous session calculi. We first prove that the well-known session subtyping, the branching-selection subtyping, is sound and complete for the synchronous calculus. Next we show that in the asynchronous calculus, this subtyping is incomplete for type-safety: that is, there exist session types T and S such that T can safely be considered as a subtype of S, but T ≤ S is not derivable by the subtyping. We then propose an asynchronous sub-typing system which is sound and complete for the asynchronous calculus. The method gives a general guidance to design rigorous channel-based subtypings respecting desired safety properties