Abstract We present PolyChor $\lambda$ , a language for higher-order functional choreographic programming —an emerging paradigm for concurrent programming. In choreographic programming, programmers write the desired cooperative behaviour of a system of processes and then compile it into an implementation for each process, a translation called endpoint projection . Unlike its predecessor, Chor $\lambda$ , PolyChor $\lambda$ has both type and process polymorphism inspired by System F $_\omega$ . That is, PolyChor $\lambda$ is the first (higher-order) functional choreographic language which gives programmers the ability to write generic choreographies and determine the participants at runtime. This novel combination of features also allows PolyChor $\lambda$ processes to communicate distributed values , leading to a new and intuitive way to write delegation. While some of the functional features of PolyChor $\lambda$ give it a weaker correspondence between the semantics of choreographies and their endpoint-projected concurrent systems than some other choreographic languages, we still get the hallmark end result of choreographic programming: projected programmes are deadlock-free by design.

Choreographic programming is a paradigm for concurrent and distributed software, whereby descriptions of the intended communications (choreographies) are automatically compiled into distributed code with strong safety and liveness properties (e.g., deadlock-freedom). Recent efforts tried to combine the theories of choreographic programming and higher-order functional programming, in order to integrate the benefits of the former with the modularity of the latter. However, they do not offer a satisfactory theory of compilation compared to the literature, because of important syntactic and semantic shortcomings: compilation is not modular (editing a part might require recompiling everything) and the generated code can perform unexpected global synchronisations. In this paper, we find that these shortcomings are not mere coincidences. Rather, they stem from genuine new challenges posed by the integration of choreographies and functions: knowing which participants are involved in a choreography becomes nontrivial, and divergence in applications requires rethinking how to prove the semantic correctness of compilation. We present a novel theory of compilation for functional choreographies that overcomes these challenges, based on types and a careful design of the semantics of choreographies and distributed code. The result: a modular notion of compilation, which produces code that is deadlock-free and correct (it operationally corresponds to its source choreography).