Web services have become more and more important in these years, and BPEL4WS (BPEL) is a de facto standard for the web service composition and orchestration. It contains several distinct features, including the scope-based compensation and fault handling mechanism. We have considered the operational semantics and denotational semantics for BPEL, where a set of algebraic laws can be achieved via these two models, respectively. In this paper, we consider the inverse work, deriving the operational semantics and denotational semantics from algebraic semantics for BPEL. In our model, we introduce four types of typical programs, by which every program can be expressed as the summation of these four types. Based on the algebraic semantics, the strategy for deriving the operational semantics is provided and a transition system is derived by strict proof. This can be considered as the soundness exploration for the operational semantics based on the algebraic semantics. Further, the equivalence between the derivation strategy and the derived transition system is explored, which can be considered as the completeness of the operational semantics. Finally, the derivation of the denotational semantics from algebraic semantics is explored, which can support to reason about more program properties easily.
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