On the Fair Termination of Client-Server Sessions

Client-server sessions are based on a variation of the traditional interpretation of linear logic propositions as session types in which non-linear channels (those regulating the interaction between a pool of clients and a single server) are typed by coexponentials instead of the usual exponentials. Coexponentials enable the modeling of racing interactions, whereby clients compete to interact with a single server whose internal state (and thus the offered service) may change as the server processes requests sequentially. In this work we present a fair termination result for CSLL$^\infty$, a core calculus of client-server sessions. We design a type system such that every well-typed term corresponds to a valid derivation in $\mu$MALL$^\infty$, the infinitary proof theory of linear logic with least and greatest fixed points. We then establish a correspondence between reductions in the calculus and principal reductions in $\mu$MALL$^\infty$. Fair termination in CSLL$^\infty$ follows from cut elimination in $\mu$MALL$^\infty$.