Session Types with Arithmetic Refinements

Session types statically prescribe bidirectional communication protocols for message-passing processes. However, simple session types cannot specify properties beyond the type of exchanged messages. In this paper we extend the type system by using index refinements from linear arithmetic capturing intrinsic attributes of data structures and algorithms. We show that, despite the decidability of Presburger arithmetic, type equality and therefore also subtyping and type checking are now undecidable, which stands in contrast to analogous dependent refinement type systems from functional languages. We also present a practical, but incomplete algorithm for type equality, which we have used in our implementation of Rast, a concurrent session-typed language with arithmetic index refinements as well as ergometric and temporal types. Moreover, if necessary, the programmer can propose additional type bisimulations that are smoothly integrated into the type equality algorithm

Rast: A Language for Resource-Aware Session Types

Traditional session types prescribe bidirectional communication protocols for concurrent computations, where well-typed programs are guaranteed to adhere to the protocols. However, simple session types cannot capture properties beyond the basic type of the exchanged messages. In response, recent work has extended session types with refinements from linear arithmetic, capturing intrinsic attributes of processes and data. These refinements then play a central role in describing sequential and parallel complexity bounds on session-typed programs. The Rast language provides an open-source implementation of session-typed concurrent programs extended with arithmetic refinements as well as ergometric and temporal types to capture work and span of program execution. To further support generic programming, Rast also enhances arithmetically refined session types with recently developed nested parametric polymorphism. Type checking relies on Cooper's algorithm for quantifier elimination in Presburger arithmetic with a few significant optimizations, and a heuristic extension to nonlinear constraints. Rast furthermore includes a reconstruction engine so that most program constructs pertaining the layers of refinements and resources are inserted automatically. We provide a variety of examples to demonstrate the expressivity of the language

On Session Typing, Probabilistic Polynomial Time, and Cryptographic Experiments

A system of session types is introduced as induced by a Curry Howard correspondence applied to bounded linear logic, suitably extended with probabilistic choice operators and ground types. The resulting system satisfies some expected properties, like subject reduction and progress, but also unexpected ones, like a polynomial bound on the time needed to reduce processes. This makes the system suitable for modelling experiments and proofs from the so-called computational model of cryptography

Rast: A Language for Resource-Aware Session Types

Traditional session types prescribe bidirectional communication protocols for concurrent computations, where well-typed programs are guaranteed to adhere to the protocols. However, simple session types cannot capture properties beyond the basic type of the exchanged messages. In response, recent work has extended session types with refinements from linear arithmetic, capturing intrinsic attributes of processes and data. These refinements then play a central role in describing sequential and parallel complexity bounds on session-typed programs. The Rast language provides an open-source implementation of session-typed concurrent programs extended with arithmetic refinements as well as ergometric and temporal types to capture work and span of program execution. To further support generic programming, Rast also enhances arithmetically refined session types with recently developed nested parametric polymorphism. Type checking relies on Cooper's algorithm for quantifier elimination in Presburger arithmetic with a few significant optimizations, and a heuristic extension to nonlinear constraints. Rast furthermore includes a reconstruction engine so that most program constructs pertaining the layers of refinements and resources are inserted automatically. We provide a variety of examples to demonstrate the expressivity of the language

Refinements for multiparty message-passing protocols: specification-agnostic theory and implementation

Multiparty message-passing protocols are notoriously difficult to design, due to interaction mismatches that lead to errors such as deadlocks. Existing protocol specification formats have been developed to prevent such errors (e.g. multiparty session types (MPST)). In order to further constrain protocols, specifications can be extended with refinements, i.e. logical predicates to control the behaviour of the protocol based on previous values exchanged. Unfortunately, existing refinement theories and implementations are tightly coupled with specification formats. This paper proposes a framework for multiparty message-passing protocols with refinements and its implementation in Rust. Our work decouples correctness of refinements from the underlying model of computation, which results in a specification-agnostic framework. Our contributions are threefold. First, we introduce a trace system which characterises valid refined traces, i.e. a sequence of sending and receiving actions correct with respect to refinements. Second, we give a correct model of computation named refined communicating system (RCS), which is an extension of communicating automata systems with refinements. We prove that RCS only produce valid refined traces. We show how to generate RCS from mainstream protocol specification formats, such as refined multiparty session types (RMPST) or refined choreography automata. Third, we illustrate the flexibility of the framework by developing both a static analysis technique and an improved model of computation for dynamic refinement evaluation. Finally, we provide a Rust toolchain for decentralised RMPST, evaluate our implementation with a set of benchmarks from the literature, and observe that refinement overhead is negligible

Relating Functional and Imperative Session Types

Imperative session types provide an imperative interface to session-typed communication. In such an interface, channel references are first-class objects with operations that change the typestate of the channel. Compared to functional session type APIs, the program structure is simpler at the surface, but typestate is required to model the current state of communication throughout. Following an early work that explored the imperative approach, a significant body of work on session types has neglected the imperative approach and opts for a functional approach that uses linear types to manage channel references soundly. We demonstrate that the functional approach subsumes the early work on imperative session types by exhibiting a typing and semantics preserving translation into a system of linear functional session types. We further show that the untyped backwards translation from the functional to the imperative calculus is semantics preserving. We restrict the type system of the functional calculus such that the backwards translation becomes type preserving. Thus, we precisely capture the difference in expressiveness of the two calculi and conclude that the lack of expressiveness in the imperative calculus is largely due to restrictions imposed by its type system.Comment: 39 pages, insubmissio

Session Kotlin: A hybrid session type embedding in Kotlin

Concurrency and distribution have become essential for building modern applications. However, developing and maintaining these apps is not an easy task. Communication errors are a common source of problems: unexpected messages cause runtime errors, and mutual dependencies lead to deadlocks. To address these issues, developers can define communication protocols that detail the structure and order of the transmitted messages, but maintaining protocol fidelity can be complex if carried out manually. Session types formalize this concept by materializing the communication protocol as a type that can be enforced by the language’s type system. In this thesis we present the first embedding of session types in Kotlin: we propose a Domain-Specific Language (DSL) for multiparty ses- sion types that lets developers write safe concurrent applications, with built-in validation and integrating code generation in the language’s framework.A concorrência e a distribuição têm-se tornado essenciais na construção de aplicações modernas. No entanto, desenvolver e manter estas aplicações não é tarefa fácil. Erros de comunicação são uma fonte comum de problemas: mensagens inesperadas causam erros durante a execução de código, e dependências mútuas levam a deadlocks. Para resolver estas questões, é tipico definir protocolos de comunicação que detalham a estrutura e a ordem das mensagens transmitidas, mas garantir o seu cumprimento pode ser complexo se feito manualmente. Os tipos de sessão formalizam este conceito ao materializar o protocolo de comunicação como um tipo que pode ser gerido pelo sistema de tipos da linguagem. Nesta tese apresentamos o primeiro embedding de tipos de sessão em Kotlin: propomos uma Linguagem de Domínio Específica para tipos de sessão com múltiplos participantes que permite aos programadores a escrita de aplicações concorrentes seguras, incorporando validação e integrando a geração de código no framework da linguagem