The asynchronous and unidirectional communication model supported by mailboxes is a key reason for the success of actor languages like Erlang and Elixir for implementing reliable and scalable distributed systems. Although actors eliminate many of the issues stemming from shared memory concurrency, they remain vulnerable to communication errors such as protocol violations and deadlocks. Behavioural types make it possible to detect communication errors early in the development process, but most work has addressed channel-based languages rather than actor languages. Mailbox types are a novel behavioural type system for actors first introduced for a process calculus, and capture the contents of a mailbox as a commutative regular expression. Due to aliasing and nested evaluation contexts, moving from a process calculus to a programming language is challenging. This paper presents Pat, the first programming language incorporating mailbox types, and describes an algorithmic type system. Pat is a higher-order functional language with sums, products, and lists, along with interfaces that allow finer-grained reasoning about mailbox contents. Typechecking in Pat detects four classes of behavioural error: protocol violation, unexpected message, forgotten reply and self-deadlock, as well as the usual data type errors. The Pat type system makes essential use of quasi-linear typing to tame some of the complexity introduced by aliasing. We make use of a co-contextual algorithmic type system, achieved through a novel use of backwards bidirectional typing, and we prove it sound and complete with respect to our declarative type system. We implement a type checker, and use it to demonstrate the expressiveness of Pat on a factory automation case study and a series of examples from the Savina actor benchmark suite. This establishes a foundation for applying mailbox typing to practical actor languages.

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