On duality relations for session types

Session types are a type formalism used to describe communication protocols over private session channels. Each participant in a binary session owns one endpoint of a session channel. A key notion is that of duality: the endpoints of a session channel should have dual session types in order to guarantee communication safety. Duality relations have been independently defined in different ways and different works, without considering their effect on the type system. In this paper we systematically study the existing duality relations and some new ones, and compare them in order to understand their expressiveness. The outcome is that those relations are split into two groups, one related to the na¨ıve inductive duality, and the other related to a notion of mutual compliance, which we borrow from the literature on contracts for web-services

Domain-Aware Session Types

We develop a generalization of existing Curry-Howard interpretations of (binary) session types by relying on an extension of linear logic with features from hybrid logic, in particular modal worlds that indicate domains. These worlds govern domain migration, subject to a parametric accessibility relation familiar from the Kripke semantics of modal logic. The result is an expressive new typed process framework for domain-aware, message-passing concurrency. Its logical foundations ensure that well-typed processes enjoy session fidelity, global progress, and termination. Typing also ensures that processes only communicate with accessible domains and so respect the accessibility relation. Remarkably, our domain-aware framework can specify scenarios in which domain information is available only at runtime; flexible accessibility relations can be cleanly defined and statically enforced. As a specific application, we introduce domain-aware multiparty session types, in which global protocols can express arbitrarily nested sub-protocols via domain migration. We develop a precise analysis of these multiparty protocols by reduction to our binary domain-aware framework: complex domain-aware protocols can be reasoned about at the right level of abstraction, ensuring also the principled transfer of key correctness properties from the binary to the multiparty setting

A linear decomposition of multiparty sessions for safe distributed programming

Multiparty Session Types (MPST) is a typing discipline for message-passing distributed processes that can ensure properties such as absence of communication errors and deadlocks, and protocol conformance. Can MPST provide a theoretical foundation for concurrent and distributed programming in "mainstream" languages? We address this problem by (1) developing the first encoding of a full-fledged multiparty session π-calculus into linear π-calculus, and(2) using the encoding as the foundation of a practical toolchain for safe multiparty programming in Scala. Our encoding is type-preserving and operationally sound and complete. Crucially, it keeps the distributed choreographic nature of MPST, illuminating that the safety properties of multiparty sessions can be precisely represented with a decomposition into binary linear channels. Previous works have only studied the relation between (limited) multiparty and binary sessions via centralised orchestration means. We exploit these results to implement an automated generation of Scala APIs for multiparty sessions, abstracting existing libraries for binary communication channels. This allows multiparty systems to be safely implemented over binary message transports, as commonly found in practice. Our implementation is the first to support distributed multiparty delegation: Our encoding yields it for free, via existing mechanisms for binary delegation

EXPRESSing Session Types

To celebrate the 30th edition of EXPRESS and the 20th edition of SOS we overview how session types can be expressed in a type theory for the standard $\pi$-calculus by means of a suitable encoding. The encoding allows one to reuse results about the $\pi$-calculus in the context of session-based communications, thus deepening the understanding of sessions and reducing redundancies in their theoretical foundations. Perhaps surprisingly, the encoding has practical implications as well, by enabling refined forms of deadlock analysis as well as allowing session type inference by means of a conventional type inference algorithm.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.0578

Coherence Generalises Duality: A Logical Explanation of Multiparty Session Types

Wadler introduced Classical Processes (CP), a calculus based on a propositions-as-types correspondence between propositions of classical linear logic and session types. Carbone et al. introduced Multiparty Classical Processes, a calculus that generalises CP to multiparty session types, by replacing the duality of classical linear logic (relating two types) with a more general notion of coherence (relating an arbitrary number of types). This paper introduces variants of CP and MCP, plus a new intermediate calculus of Globally-governed Classical Processes (GCP). We show a tight relation between these three calculi, giving semantics-preserving translations from GCP to CP and from MCP to GCP. The translation from GCP to CP interprets a coherence proof as an arbiter process that mediates communications in a session, while MCP adds annotations that permit processes to communicate directly without centralised control

Session types in practical programming

Programs are more distributed and concurrent today than ever before, and structural communications are at the core. Constructing and debugging such programs are hard due to the lack of formal specifications and verifications of concurrency. Recent advances in type systems allow us to specify the structures of communications as session types, thus enabling static type checking of the usages of communication channels against protocols. The soundness of session type systems implies communication fidelity and absence of deadlock. This work proposes to formalize multiparty dependent session types as an expressive and practical type discipline for enforcing communication protocols. The type system is formulated in the setting of multi-threaded λ-calculus with inspirations from multirole logic. It is sound, and it provides linearity and coherence guarantees entirely statically. The type system supports recursion and polymorphism. The formulation is particularly suitable for practical implementation, and this work provides such a runtime implementation