Polymorphic lambda calculus with context-free session types

Session types provide a typing discipline for structured communication on bidirectional channels. Context-free session types overcome the restriction to tail recursive protocols characteristic of conventional session types. This extension enables the serialization and deserialization of tree structures in a fully type-safe manner. We present the theory underlying the language FreeST 2, which features context-free session types in an extension of System F with linear types and a kinding system to distinguish message types, session types, and channel types. The system presents metatheoretical challenges which we address: contractivity in the presence of polymorphism, a non-trivial equational theory on types, and decidability of type equivalence. We also establish standard results on typing preservation, progress, and a characterization of erroneous processes.