Implementing Communicating Processes in the Event of Interface Difference

We present here an implementation relation which formalises the notion that a system built of communicating processes is an acceptable implementation of another base or specification system in the event that the two systems have different interfaces. Such a treatment has obvious applicability to the software development process, where an implementation component may be expressed at a different level of abstraction to the relevant specification component. We extend the results of our previous work and combine into a single scheme implementation relations previously presented. We also relax the restrictions previously placed upon specification processes. Using this new implementation relation, two basic kinds of results are obtained: realisability and compositionality. The former ensures that an implementation, when plugged into an appropriate environment, should yield a conventional implementation of the specification, and also that the implementation relation is acceptable when used in the event that specification and implementation systems have the same interfaces. The latter requires that a specification composed of several connected systems may be implemented by connecting their respective implementations.