Typed Non-determinism in Concurrent Calculi: The Eager Way

Abstract

We consider the problem of designing typed concurrent calculi with non-deterministic choice in which types leverage linearity for controlling resources, thereby ensuring strong correctness properties for processes. This problem is constrained by the delicate tension between non-determinism and linearity. Prior work developed a session-typed π-calculus with standard non-deterministic choice; well-typed processes enjoy type preservation and deadlock-freedom. Central to this typed calculus is a lazy semantics that gradually discards branches in choices. This lazy semantics, however, is complex: various technical elements are needed to describe the non-deterministic behavior of typed processes. This paper develops an entirely new approach, based on an eager semantics, which more directly represents choices and commitment. We present a π-calculus in which non-deterministic choices are governed by this eager semantics and session types. We establish its key correctness properties, including deadlock-freedom, and demonstrate its expressivity by correctly translating a typed resource λ-calculus.

arXiv admin note: substantial text overlap with arXiv:2408.07915