Recursive Session Logical Relations (2208.13741v2)

Abstract: Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical relations. Logical relations only recently were adopted for session types--but exclusively for terminating languages. This paper scales logical relations to recursive session types. It develops a logical relation for progress-sensitive noninterference for linear session types, tackling the challenges non-termination and concurrency pose. The contributions include secrecy-polymorphic processes and the logical relation with metatheory. A distinguishing feature is the choice of "step index" of the logical relation, allowing for a natural proof of transitivity and soundness.