Continuation Semantics for Concurrency with Multiple Channels Communication

In this paper we investigate the formal design of concurrent languages based on the concept of continuation. We present a denotational approach of concurrent programs by using continuations for concurrency. We illustrate the approach by designing a continuation semantics for a language with nondeterministic choice, sequential and parallel composition, and a mechanism of communication and synchronization on multiple channels. For our language, we also present an operational semantics, and establish the formal relation between the denotational and operational semantics. We accomplish the semantic investigation in the mathematical framework of complete metric spaces.