  Web Service Composition creates new composite Web Services from the
collection of existing ones to be composed further and embodies the added
values and potential usages of Web Services. Web Service Composition includes
two aspects: Web Service orchestration denoting a workflow-like composition
pattern and Web Service choreography which represents an aggregate composition
pattern. There were only a few works which give orchestration and choreography
a relationship. In this paper, we introduce an architecture of Web Service
Composition runtime which establishes a natural relationship between
orchestration and choreography through a deep analysis of the two ones. Then we
use an actor-based approach to design a language called AB-WSCL to support such
an architecture. To give AB-WSCL a firmly theoretic foundation, we establish
the formal semantics of AB-WSCL based on concurrent rewriting theory for
actors. Conclusions that well defined relationships exist among the components
of AB-WSCL using a notation of Compositionality is drawn based on semantics
analysis. Our works can be bases of a modeling language, simulation tools,
verification tools of Web Service Composition at design time, and also a Web
Service Composition runtime with correctness analysis support itself.
