Modal Interface Theories for Communication-Safe Component Assemblies

We propose an extension of the abstract rules for independent implementability of reactive components proposed in interface theories to take into account interface assemblies. As a concrete instantiation we extend existing interface theories for modal I/O-transition systems to support assemblies, (greybox) assembly refinement and assembly encapsulation. We introduce a new notion of communication-safety for N-ary assemblies which overcomes problems with previous definitions of interface compatibility. We show that communication-safety can be checked incrementally. We also show that communication-safety is preserved by assembly refinement, that blackbox refinement of component interfaces is compositional w.r.t. greybox refinement of assemblies and, conversely, that assembly encapsulation maps greybox to blackbox refinement. The methodology of our approach is illustrated by a small case study.