A timed semantics of Orc

Orc is a kernel language for structured concurrent programming. Orc provides three powerful combinators that define the structure of a concurrent computation. These combinators support sequential and concurrent execution, and concurrent execution with blocking and termination. Orc is particularly well-suited for task orchestration, a form of concurrent programming with applications in workflow, business process management, and web service orchestration. Orc provides constructs to orchestrate the concurrent invocation of services while managing time-outs, priorities, and failures of services or communication. Our previous work on the semantics of Orc has focused on its asynchronous behavior. The inclusion of time or the effect of delay on a computation had not been modeled. In this paper, we define an operational semantics of Orc that allows reasoning about delays, which are introduced explicitly by time-based constructs or implicitly by network delays. We develop a number of identities among Orc expressions and define an equality relation that is a congruence. We also present a denotational semantics in which the meaning of an Orc program is a set of traces, and show that the two semantics are equivalent.