A general framework for architecture composability

Architectures depict design principles: paradigms that can be understood by all, allow thinking on a higher plane and avoiding low-level mistakes. They provide means for ensuring correctness by construction by enforcing global properties characterizing the coordination between components. An architecture can be considered as an operator A that, applied to a set of components (Formula presented.) , builds a composite component (Formula presented.) meeting a characteristic property (Formula presented.). Architecture composability is a basic and common problem faced by system designers. In this paper, we propose a formal and general framework for architecture composability based on an associative, commutative and idempotent architecture composition operator (Formula presented.). The main result is that if two architectures A₁ and A₂ enforce respectively safety properties (Formula presented.) and (Formula presented.) , the architecture (Formula presented.) enforces the property (Formula presented.) , that is both properties are preserved by architecture composition. We also establish preservation of liveness properties by architecture composition. The presented results are illustrated by a running example and a case study.