Bounded polymorphism in session types

Session types allow high-level specifications of structured patterns of communication, such as client-server protocols, to be expressed as types and verified by static typechecking. In collaboration with Malcolm Hole, we have previously introduced a notion of subtyping for session types, formulated for an extended pi calculus. Subtyping allows one part of a system, for example a server, to be refined without invalidating type-correctness of other parts, for example clients. We now introduce bounded polymorphism, based on the same notion of subtyping, in order to support more precise and flexible specifications of protocols; in particular, a choice of type in one message may affect the types of future messages. We formalize the syntax, operational semantics and typing rules of an extended pi calculus, and prove that typechecking guarantees absence of run-time communication errors. We study algorithms for checking instances of the subtype relation in two versions of our system, which we call Kernel S6 and Full S6, and establish that subtyping in Kernel S6 is decidable but subtyping in Full S6 is undecidable.