Context-Free Session Type Inference

Some interesting communication protocols can be precisely described only by context-free session types, an extension of conventional session types with a general form of sequential composition. The complex metatheory of context-free session types, however, hinders the definition of corresponding checking and inference algorithms. In this work we address and solve these problems introducing a new type system for context-free session types of which we provide two OCaml embeddings

Session Coalgebras: A Coalgebraic View on Regular and Context-Free Session Types

Compositional methods are central to the verification of software systems. For concurrent and communicating systems, compositional techniques based on behavioural type systems have received much attention. By abstracting communication protocols as types, these type systems can statically check that channels in a program interact following a certain protocol—whether messages are exchanged in the intended order. In this article, we put on our coalgebraic spectacles to investigate session types, a widely studied class of behavioural type systems. We provide a syntax-free description of session-based concurrency as states of coalgebras. As a result, we rediscover type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations. In turn, this coinductive presentation enables us to derive a decidable type system with subtyping for the π-calculus, in which the states of a coalgebra will serve as channel protocols. Going full circle, we exhibit a coalgebra structure on an existing session type system, and show that the relations and type system resulting from our coalgebraic perspective coincide with existing ones. We further apply to session coalgebras the coalgebraic approach to regular languages via the so-called rational fixed point, inspired by the trinity of automata, regular languages, and regular expressions with session coalgebras, rational fixed point, and session types, respectively. We establish a suitable restriction on session coalgebras that determines a similar trinity, and reveals the mismatch between usual session types and our syntax-free coalgebraic approach. Furthermore, we extend our coalgebraic approach to account for context-free session types, by equipping session coalgebras with a stack

Characteristic Bisimulation for Higher-Order Session Processes

Characterising contextual equivalence is a long-standing issue for higher-order (process) languages. In the setting of a higher-order pi-calculus with sessions, we develop characteristic bisimilarity, a typed bisimilarity which fully characterises contextual equivalence. To our knowledge, ours is the first characterisation of its kind. Using simple values inhabiting (session) types, our approach distinguishes from untyped methods for characterising contextual equivalence in higher-order processes: we show that observing as inputs only a precise finite set of higher-order values suffices to reason about higher-order session processes. We demonstrate how characteristic bisimilarity can be used to justify optimisations in session protocols with mobile code communication

Session Types in Abelian Logic

There was a PhD student who says "I found a pair of wooden shoes. I put a coin in the left and a key in the right. Next morning, I found those objects in the opposite shoes." We do not claim existence of such shoes, but propose a similar programming abstraction in the context of typed lambda calculi. The result, which we call the Amida calculus, extends Abramsky's linear lambda calculus LF and characterizes Abelian logic.Comment: In Proceedings PLACES 2013, arXiv:1312.221

A Graphical Approach to Progress for Structured Communication in Web Services

We investigate a graphical representation of session invocation interdependency in order to prove progress for the pi-calculus with sessions under the usual session typing discipline. We show that those processes whose associated dependency graph is acyclic can be brought to reduce. We call such processes transparent processes. Additionally, we prove that for well-typed processes where services contain no free names, such acyclicity is preserved by the reduction semantics. Our results encompass programs (processes containing neither free nor restricted session channels) and higher-order sessions (delegation). Furthermore, we give examples suggesting that transparent processes constitute a large enough class of processes with progress to have applications in modern session-based programming languages for web services.Comment: In Proceedings ICE 2010, arXiv:1010.530

A type checking algorithm for qualified session types

We present a type checking algorithm for establishing a session-based discipline in the pi calculus of Milner, Parrow and Walker. Our session types are qualified as linear or unrestricted. Linearly typed communication channels are guaranteed to occur in exactly one thread, possibly multiple times; afterwards they evolve as unrestricted channels. Session protocols are described by a type constructor that denotes the two ends of one and the same communication channel. We ensure the soundness of the algorithm by showing that processes consuming all linear resources are accepted by a type system preserving typings during the computation and that type checking is consistent w.r.t. structural congruence.Comment: In Proceedings WWV 2011, arXiv:1108.208

Using Session Types for Reasoning About Boundedness in the Pi-Calculus

The classes of depth-bounded and name-bounded processes are fragments of the pi-calculus for which some of the decision problems that are undecidable for the full calculus become decidable. P is depth-bounded at level k if every reduction sequence for P contains successor processes with at most k active nested restrictions. P is name-bounded at level k if every reduction sequence for P contains successor processes with at most k active bound names. Membership of these classes of processes is undecidable. In this paper we use binary session types to decise two type systems that give a sound characterization of the properties: If a process is well-typed in our first system, it is depth-bounded. If a process is well-typed in our second, more restrictive type system, it will also be name-bounded.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.0004