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. †

Abstract. 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.

Abstract. 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.

We develop an interpretation of linear type theory as dependent session types for a term passing extension of the π-calculus. The type system allows us to express rich constraints on sessions, such as interface contracts and proof-carrying certification, which go beyond existing session type systems, and are here justified on purely logical grounds. We can further refine our interpretation using proof irrelevance to eliminate communication overhead for proofs between trusted parties. Our technical results include type preservation and global progress, which in our setting naturally imply compliance to all properties declared in interface contracts expressed by dependent types.

The Go programming language has been heavily adopted in industry as a language that efficiently combines systems programming with concurrency. Go's concurrency primitives, inspired by process calculi such as CCS and CSP, feature channel-based communication and lightweight threads, providing a distinct means of structuring concurrent software. Despite its popularity, the Go programming ecosystem offers little to no support for guaranteeing the correctness of message-passing concurrent programs. This work proposes a practical verification framework for message passing concurrency in Go by developing a robust static analysis that infers an abstract model of a program's communication behaviour in the form of a behavioural type, a powerful process calculi typing discipline. We make use of our analysis to deploy a model and termination checking based verification of the inferred behavioural type that is suitable for a range of safety and liveness properties of Go programs, providing several improvements over existing approaches. We evaluate our framework and its implementation on publicly available real-world Go code. CCS CONCEPTS • Theory of computation → Verification by model checking; Type theory; Process calculi; • Software and its engineering → Model checking; Automated static analysis; Software verification; Concurrent programming languages;

Abstract. In prior work we proposed an interpretation of intuitionistic linear logic propositions as session types for concurrent processes. The type system obtained from the interpretation ensures fundamental properties of session-based typed disciplines-most notably, type preservation, session fidelity, and global progress. In this paper, we complement and strengthen these results by developing a theory of logical relations. Our development is based on, and is remarkably similar to, that for functional languages, extended to an (intuitionistic) linear type structure. A main result is that well-typed processes always terminate (strong normalization). We also introduce a notion of observational equivalence for sessiontyped processes. As applications, we prove that all proof conversions induced by the logic interpretation actually express observational equivalences, and explain how type isomorphisms resulting from linear logic equivalences are realized by coercions between interface types of session-based concurrent systems.

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Shared session types generalize the Curry-Howard correspondence between intuitionistic linear logic and the session-typed π-calculus with adjoint modalities that mediate between linear and shared session types, giving rise to a programming model where shared channels must be used according to a locking discipline of acquire-release. While this generalization greatly increases the range of programs that can be written, the gain in expressiveness comes at the cost of deadlock-freedom, a property which holds for many linear session type systems. In this paper, we develop a type system for logically-shared sessions in which types capture not only the interactive behavior of processes but also constrain the order of resources (i.e., shared processes) they may acquire. This typelevel information is then used to rule out cyclic dependencies among acquires and synchronization points, resulting in a system that ensures deadlock-free communication for well-typed processes in the presence of shared sessions, higher-order channel passing, and recursive processes. We illustrate our approach on a series of examples, showing that it rules out deadlocks in circular networks of both shared and linear recursive processes, while still being permissive enough to type concurrent implementations of shared imperative data structures as processes.