Biblio

Software services and governing communication protocols are increasingly domain-aware. Domains can have multiple interpretations, such as the principals on whose behalf processes act or the location at which parties reside. Domains impact protocol compliance and access control, two central issues to overall functionality and correctness in distributed systems. This paper proposes a session-typed process framework for domain-aware communication-centric systems based on a CurryHoward interpretation of linear logic, here augmented with nominals from hybrid logic indicating domains. These nominals are explicit in the process expressions and govern domain migration, subject to a parametric accessibility relation familiar from the Kripke semantics for modal logic. Flexible access relationships among domains can be elegantly defined and statically enforced. The framework can also account for scenarios in which domain information is discovered only at runtime. Due to the logical origins of our systems, well-typed processes enjoy session fidelity, global progress, and termination. Moreover, well-typed processes always respect the accessibility relation and satisfy a form of domain parametricity, two properties crucial to show that domain-related properties of concrete programs are satisfied. 

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.

We investigate a notion of behavioral genericity in the context of session type disciplines. To this end, we develop a logically motivated theory of parametric polymorphism, reminiscent of the Girard-Reynolds polymorphic λ-calculus, but casted in the setting of concurrent processes. In our theory, polymorphism accounts for the exchange of abstract communication protocols and dynamic instantiation of heterogeneous interfaces, as opposed to the exchange of data types and dynamic instantiation of individual message types. Our polymorphic session-typed process language satisfies strong forms of type preservation and global progress, is strongly normalizing, and enjoys a relational parametricity principle. Combined, our results confer strong correctness guarantees for communicating systems. In particular, parametricity is key to derive non-trivial results about internal protocol independence, a concurrent analogous of representation independence, and non-interference properties of modular, distributed systems.