When web services are used to coalesce around the distributed applications, one prominent solution to manage and coordinate web services is the use of process management. Many researches have been done to deal with automatic discovery and composition issues of web services. However, the problem of how to run a process that is composed of distributed services is seldom considered. In this paper, based on our previous work, the Smart Process-based Application Model (SPM), we formalize Smart Process (SP) using algebra CCS, and discuss the benefits. In particular, we propose goal-based algorithms to run Smart Process.