Session types are a typed approach to message-passing concurrency, where types describe sequences of intended exchanges over channels. Session type systems have been given strong logical foundations via Curry-Howard correspondences with linear logic, a resource-aware logic that naturally captures structured interactions. These logical foundations provide an elegant framework to specify and (statically) verify message-passing processes. In this paper, we rigorously compare different type systems for concurrency derived from the Curry-Howard correspondence between linear logic and session types. We address the main divide between these type systems: the classical and intuitionistic presentations of linear logic. Over the years, these presentations have given rise to separate research strands on logical foundations for concurrency; the differences between their derived type systems have only been addressed informally. To formally assess these differences, we develop πULL, a session type system that encompasses type systems derived from classical and intuitionistic interpretations of linear logic. Based on a fragment of Girard's Logic of Unity, πULL provides a basic reference framework: we compare existing session type systems by characterizing fragments of πULL that coincide with classical and intuitionistic formulations. We analyze the significance of our characterizations by considering the locality principle (enforced by intuitionistic interpretations but not by classical ones) and forms of process composition induced by the interpretations.

Protection of confidential data is an important security consideration of today's applications. Of particular concern is to guard against unintentional leakage to a (malicious) observer, who may interact with the program and draw inference from made observations. Information flow control (IFC) type systems address this concern by statically ruling out such leakage. This paper contributes an IFC type system for message-passing concurrent programs, the computational model of choice for many of today's applications such as cloud computing and IoT applications. Such applications typically either implicitly or explicitly codify protocols according to which message exchange must happen, and to statically ensure protocol safety, behavioral type systems such as session types can be used. This paper marries IFC with session typing and contributes over prior work in the following regards: (1) support of realistic cyclic process networks as opposed to the restriction to tree-shaped networks, (2) more permissive, yet entirely secure, IFC control, exploiting cyclic process networks, and (3) considering deadlocks as another form of side channel, and asserting deadlock-sensitive noninterference (DSNI) for well-typed programs. To prove DSNI, the paper develops a novel logical relation that accounts for cyclic process networks. The logical relation is rooted in linear logic, but drops the tree-topology restriction imposed by prior work.

We tackle the challenge of ensuring the deadlock-freedom property for message-passing processes that communicate asynchronously in cyclic process networks. Our contributions are twofold. First, we present Asynchronous Priority-based Classical Processes (APCP), a session-typed process framework that supports asynchronous communication, delegation, and recursion in cyclic process networks. Building upon the Curry-Howard correspondences between linear logic and session types, we establish essential meta-theoretical results for APCP, most notably deadlock freedom. Second, we present a new concurrent $\lambda$-calculus with asynchronous session types, dubbed LASTn. We illustrate LASTn by example and establish its meta-theoretical results; in particular, we show how to soundly transfer the deadlock-freedom guarantee from APCP. To this end, we develop a translation of terms in LASTn into processes in APCP that satisfies a strong formulation of operational correspondence.

The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing concurrency. Central to this approach is the resource consumption paradigm heralded by Linear Logic. In this paper, we investigate a new point in the design space of session type systems for message-passing concurrent programs. We identify O’Hearn and Pym’s Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language. This leads to a treatment of non-linear resources that is radically different from existing approaches based on Linear Logic. We introduce a new π-calculus with sessions, called πBI; its most salient feature is a construct called spawn, which expresses new forms of sharing that are induced by structural principles in BI. We illustrate the expressiveness of πBI and lay out its fundamental theory: type preservation, deadlock-freedom, and weak normalization results for well-typed processes; an operationally sound and complete typed encoding of an affine λ-calculus; and a non-interference result for access of resources.

Protocols provide the unifying glue in concurrent and distributed software today; verifying that message-passing programs conform to such governing protocols is important but difficult. Static approaches based on multiparty session types (MPST) use protocols as types to avoid protocol violations and deadlocks in programs. An elusive problem for MPST is to ensure both protocol conformance and deadlock-freedom for implementations with interleaved and delegated protocols. We propose a decentralized analysis of multiparty protocols, specified as global types and implemented as interacting processes in an asynchronous π-calculus. Our solution rests upon two novel notions: router processes and relative types. While router processes use the global type to enable the composition of participant implementations in arbitrary process networks, relative types extract from the global type the intended interactions and dependencies between pairs of participants. In our analysis, processes are typed using APCP, a type system that ensures protocol conformance and deadlock-freedom with respect to binary protocols, developed in prior work. Our decentralized, router-based analysis enables the sound and complete transference of protocol conformance and deadlock-freedom from APCP to multiparty protocols.