On the Semantics of Object-oriented Data Structures and Path Expressions (Extended Version)

\UML/ØCL is perceived as the de-facto standard for specifying object-oriented models in general and data models in particular. Since recently, all data types of \UML/ØCL comprise two different exception elements: \inlineoclinvalid (“bottom” in semantics terminology) and \inlineoclnull (for “non-existing element”). This has far-reaching consequences on both the logical and algebraic properties of ØCL expressions as well as the path expressions over object-oriented data structures, \ie, class models. In this paper, we present a formal semantics for object-oriented data models in which all data types and, thus, all class attributes and path expressions, support \inlineoclinvalid and \inlineoclnull. Based on this formal semantics, we present a set of ØCL test cases that can be used for evaluating the support of \inlineoclnull and \inlineoclinvalid in ØCL tools.