Abstract
Model composition is a crucial activity in Model Driven Engineering both to reuse validated and verified model elements and to handle separately the various aspects in a complex system and then weave them while preserving their properties. Many research activities target this compositional validation and verification (V & V) strategy: allow the independent assessment of components and minimize the residual V & V activities at assembly time. However, there is a continuous and increasing need for the definition of new composition operators that allow the reconciliation of existing models to build new systems according to various requirements. These ones are usually built from scratch and must be systematically verified to assess that they preserve the properties of the assembled elements. This verification is usually tedious but is mandatory to avoid verifying the composite system for each use of the operators. Our work addresses these issues, we first target the use of proof assistants for specifying and verifying compositional verification frameworks relying on formal verification techniques instead of testing and proofreading. Then, using a divide and conquer approach, we focus on the development of elementary composition operators that are easy to verify and can be used to further define complex composition operators. In our approach, proofs for the complex operators are then obtained by assembling the proofs of the basic operators. To illustrate our proposal, we use the Coq proof assistant to formalize the language-independent elementary composition operators Union and Substitution and the proof that the conformance of models with respect to metamodels is preserved during composition. We show that more sophisticated composition operators that share parts of the implementation and have several properties in common (especially: aspect oriented modeling composition approach, invasive software composition, and package merge) can then be built from the basic ones, and that the proof of conformance preservation can also be built from the proofs of basic operators.