Kai Pischke | Searcharxiv

arXiv2026

Asynchronous Global Protocols, Precisely: Full Proofs

Asynchronous multiparty session types are a type-based framework which ensure the compatibility of components in a distributed system by checking compliance against a specified global protocol. We propose a top-down approach, starting with the global protocol which is then projected into a set of local specifications. Next, we use an asynchronous refinement relation, precise asynchronous multiparty subtyping, to enable local specifications to be optimised by permuting actions within individual asynchronous components. This supports local reasoning, as each component can be independently developed and refined in isolation, before being integrated into a larger system. We show that this methodology guarantees both type soundness and liveness of the collection of optimised components. In this article, we first propose new operational semantics of global protocols which capture sound optimisations in the context of asynchronous message-passing. Next we define an asynchronous association between global protocols and a set of optimised local types. Thirdly, we prove, for the first time, the correctness of the most expressive endpoint projection in the literature, coinductive full merging projection. We then show the main theorems of this article: soundness and completeness of the operational correspondence of the asynchronous association. As a consequence, the association acts as an invariant that can be used to transfer key theorems from the bottom-up system to the top-down system. In particular, we used this to prove type soundness, session-fidelity, deadlock-freedom and liveness of the collection of optimised endpoints.

cs.PL↗

arXiv2026

Top-down = Bottom-up: Sound and Complete Characterisations of Liveness by Multiparty Global Protocols

Multiparty session types (MPST) are a type discipline for concurrent and distributed systems, designed to ensure not only type safety and deadlock-freedom, but also liveness of typed communicating processes. Two main MPST methodologies, top-down and bottom-up, have been proposed and are integrated into a wide range of programming languages and tools. The top-down strategy starts by specifying the overall choreography of the protocol (called a global type), from which a set of local types that satisfy safety and liveness are generated by endpoint projection (EPP). Once each participant is type-checked against a generated local type, liveness of the set of typed processes is automatically ensured by construction. The bottom-up strategy directly checks whether local types inferred from processes satisfy liveness to enforce liveness of processes. Since the top-down strategy depends on global types and the EPP algorithms, it has often been considered that the top-down system offers strictly less typability than the bottom-up system. Our paper negates this belief. We prove that, using the precise subtyping for the subsumption rule, the top-down strategy offers exactly the same typability as the bottom-up system. More precisely, a multiparty session $M$ is typable and verified to be live by the bottom-up typing system if and only if $M$ is typable by the top-down typing system. The key to the proof is a principal global type inference algorithm which builds a principal global type from an arbitrary set of live local types. We have implemented the global type inference algorithm together with projection, process type checking and local type inference algorithms, and built a toolchain for both the top-down and bottom-up strategies. We evaluated our toolchain with representative examples from the literature, confirming that the top-down approach is more efficient than the bottom-up approach.

cs.PL↗