Bigraphical Reactive Systems (BRSs) have been proposed as a formal meta-model for global ubiquitous computing that encompasses process calculi for mobility, notably the π-calculus and the Mobile Ambients calculus, as well as graphical models for concurrency such as Petri Nets. In this paper we demonstrate that BRSs also allow natural formalizations of programming languages used in practice. We do so by providing a direct and extensible formalization of a subset of WS-BPEL as a binding bigraphical reactive system using the BPL Tool developed in the Bigraphical Programming Languages (BPL) project. The tool allows for compositional definition, visualization and simulation of the execution of bigraphical reactive systems. The formalization exploits the close correspondence between bigraphs and XML to provide a formalized run-time format very close to standard WS-BPEL syntax.
The formalization is the starting point of an endeavor to provide a completely formalized and extensible business process engine within the Computer Supported Mobile Adaptive Business Processes (CosmoBiz) research project at the IT University of Copenhagen. Building upon the formalization of WS-BPEL we propose and formalize HomeBPEL, a higher-order WS-BPEL-like business process execution language where processes are first-class values that can be stored in variables, passed as messages, and activated as embedded sub-instances. A sub-instance is similar to a WS-BPEL scope, except that it can be dynamically frozen and stored as a process in a variable, and then subsequently be thawed when reactivated as a sub-instance. We motivate HomeBPEL by an example of pervasive health care where treatment guidelines are dynamically deployed as sub processes that may be delegated dynamically to other workflow engines and in particular stay available for disconnected operation on mobile devices.