Open compliance in multiparty sessions with partial typing

Multiparty sessions are a foundational model for distributed entities interacting through message passing. Communication is disciplined by global types: well-typed sessions are lock-free and their participants do follow the described protocols. A key issue is the composition of well-typed sessions, that we face via the participants-as-interfaces approach. We study session composition when a client session is connected to compliant server sessions, where compliance is naturally biased towards the client. We prove that a unique session can be constructed by transforming the interface participants of the client and the servers into gateways (that is, forwarders), if the sessions are well-typed and the compliance relation can be proved. The obtained session has a global type that can be derived from the global types of the composing sessions and the proof of compliance among the client and the servers. A novelty of our approach is that in the composition we only ensure Lock-freedom for the client session, disregarding this property for the server sessions, via a partial typing system. This choice strongly simplifies the construction of the gateways. We consider the present study as a further step toward a theory of Open MultiParty Session Types.