Linear Logical Relations and Observational Equivalences for Session-Based Concurrency

We investigate strong normalization, confluence, and behavioral equality in the realm of session-based concurrency. These interrelated issues underpin advanced correctness analysis in models of structured communications. The starting point for our study is an interpretation of linear logic propositions as session types for communicating processes, proposed in prior work. Strong normalization and confluence are established by developing a theory of logical relations. Defined upon a linear type structure, our logical relations remain remarkably similar to those for functional languages. We also introduce a natural notion of observational equivalence for session-typed processes. Strong normalization and confluence come in handy in the associated coinductive reasoning: as applications, we prove that all proof conversions induced by the logic interpretation actually express observational equivalences, and explain how type isomorphismsresulting from linear logic equivalences are realized by coercions between interface types of session-based concurrent systems.