Translating essential OCL invariants to nested graph constraints focusing on set operations

Abstract

Domain-specific modeling languages (DSMLs) are usually defined by meta-modeling where invariants are defined in the Object Constraint Language (OCL). This approach is purely declarative in the sense that instance construction is not incorporated but has to added. In contrast, graph grammars incorporate the stepwise construction of instances by applying transformation rules. Establishing a formal relation between meta-modeling and graph transformation opens up the possibility to integrate techniques of both fields. This integration can be advantageously used for optimizing DSML definition. Generally, a meta-model is translated to a type graph with a set of nested graph constraints. In this paper, we consider the translation of Essential OCL invariants to nested graph constraints. Building up on a translation of Core OCL invariants, we focus here on the translation of set operations. The main idea is to use the characteristic function of sets to translate set operations to corresponding Boolean operations. We show that a model satisfies an Essential OCL invariant iff its corresponding instance graph satisfies the corresponding nested graph constraint.