A Meta-model Semantics for Structural Constraints in UML

The UML standard has adopted a meta-modelling approach to defining the abstract syntax of UML. A meta-modelling approach is taken essentially to aid the construction of automated tools, but the semantics is defined by statements in English. A meta-model that incorporates precise semantics would support the construction of tools that could perform semantically-oriented tasks, such as consistency checking. One approach to defining the formal semantics of a language is denotational: essentially elaborating (in mathematics) the value or instance denoted by an expression of the language in a particular context. However, instances must also be expressed in some language: in UML, instances of the static model are expressed using object diagrams. Thus a meta-model can be constructed which incorporates (a) the modelling language itself, (b) the modelling language of instances, and (c) the mapping of one into the other. The current UML meta-model provides some support for (a) and (b), but not (c). (c) is the part that carries the semantics. This paper presents one such meta-model, for a fragment of UML suitable for describing and constraining object structures. The fragment includes parts of class diagrams and invariants in the style of OCL. An indication is given as to how the approach could be extended to models characterising dynamic behaviour.