Biblio

We develop a theory of inductive and coinductive session types in a computational interpretation of linear logic, enabling the representation of potentially infinite interactions in a compositionally sound way that preserves logical soundness, a major stepping stone towards a full dependent type theory for expressing and reasoning about session-based concurrent higher order distributed programs. The language consists of a λ-calculus with inductive types and a contextual monadic type encapsulating session-based concurrency, treating monadic values as first-class objects. We consider general fixpoint and cofixpoint constructs, subject to natural syntactic constraints, as a means of producing inductive and coinductive definitions of session-typed processes, that until now have only been considered using general recursion, which is incompatible with logical consistency and introduces compositional divergence. We establish a type safety result for our language, including protocol compliance and progress of concurrent computation, and also show, through a logical relations argument, that all well-typed programs are compositionally non-divergent. Our results entail the logical soundness of the framework, and enable compositional reasoning about useful infinite interactive behaviors, while ruling out unproductive infinite behavior.

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.

Throughout the years, several typing disciplines for the π-calculus have been proposed. Arguably, the most widespread of these typing disciplines consists of session types. Session types describe the input/output behavior of processes and traditionally provide strong guarantees about this behavior (i.e., deadlock freedom and fidelity). While these systems exploit a fundamental notion of linearity, the precise connection between linear logic and session types has not been well understood. This paper proposes a type system for the π-calculus that corresponds to a standard sequent calculus presentation of intuitionistic linear logic, interpreting linear propositions as session types and thus providing a purely logical account of all key features and properties of session types. We show the deep correspondence between linear logic and session types by exhibiting a tight operational correspondence between cut elimination steps and process reductions. We also discuss an alternative presentation of linear session types based on classical linear logic, and compare our development with other more traditional session type systems. 

In prior research we have developed a Curry-Howard interpretation of linear sequent calculus as session-typed processes. In this paper we uniformly integrate this computational interpretation in a functional language via a linear contextual monad that isolates session-based concurrency. Monadic values are open process expressions and are first class objects in the language, thus providing a logical foundation for higher-order session typed processes. We illustrate how the combined use of the monad and recursive types allows us to cleanly write a rich variety of concurrent programs, including higher-order programs that communicate processes. We show the standard metatheoretic result of type preservation, as well as a global progress theorem, which to the best of our knowledge, is new in the higher-order session typed setting.

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.