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

2026-07-23

AI Summary

This work resolves a longstanding misconception regarding the inequivalence of top-down and bottom-up approaches to liveness verification in multiparty session types, rigorously establishing for the first time that both paradigms possess identical typability power. By introducing a precise subtyping relation and a principal global type inference algorithm, the authors unify the theoretical foundations of these two methodologies and enable efficient endpoint projection (EPP) alongside local type inference. The resulting comprehensive toolchain is empirically validated on representative concurrent and distributed system benchmarks, demonstrating not only the formal equivalence between the top-down and bottom-up approaches but also the superior practical efficiency of the top-down method.

Abstract

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.

Problem

• multiparty session types
• liveness
• top-down
• bottom-up
• global types

Innovation

• multiparty session types
• liveness
• global type inference
• endpoint projection
• type system completeness