A Functional View of Join

Join calculus, usually presented as a process calculus, is suitable as a foundation of both sequential and concurrent programming. We give a new operational semantics of join calculus, expressed as a reduction system with a single reduction rule similar to beta reduction in lambda calculus. We also introduce a new Hindley/Milner style type system for join calculus. Compared to previous work, the type system gives more accurate types of composite and mutually recursive definitions. The type system's soundness is established by showing that our reduction rule keeps typings invariant. We present an algorithm for type inference and show its soundness and completeness.