Formulas as Processes, Deadlock-Freedom as Choreographies (Extended Version)
arXiv:2501.08928 · doi:10.1007/978-3-031-91118-7_2
Abstract
We introduce a novel approach to studying properties of processes in the Ï-calculus based on a processes-as-formulas interpretation, by establishing a correspondence between specific sequent calculus derivations and computation trees in the reduction semantics of the recursion-free Ï-calculus. Our method provides a simple logical characterisation of deadlock-freedom for the recursion- and race-free fragment of the Ï-calculus, supporting key features such as cyclic dependencies and an independence of the name restriction and parallel operators. Based on this technique, we establish a strong completeness result for a nontrivial choreographic language: all deadlock-free and race-free finite Ï-calculus processes composed in parallel at the top level can be faithfully represented by a choreography. With these results, we show how the paradigm of computation-as-derivation extends the reach of logical methods for the study of concurrency, by bridging important gaps between logic, the expressiveness of the Ï-calculus, and the expressiveness of choreographic languages.
Extended version of the paper "Formulas as Processes, Deadlock-Freedom as Choreographies", accepted at ESOP2025