To support new application areas for database systems such as mechanical engineering applications or office automation applications a powerful data model is required that supports the modelling of complex data, e.g. the object-oriented model. The object-oriented model supports subtyping, inheritance, operator overloading and overriding. These are features to assist the programmer in managing the complexity of the data being modelled. Another desirable feature of a powerful data model is the ability to use inverted functions in the query language, i.e. for an arbitrary function call fn(x)=y, retrieve the arguments x for a given result y. Optimization of database queries is important in a large database system since query optimization can reduce the execution cost dramatically. The optimization considered here is a cost-based global optimization where all operations are assigned a cost and a way of a priori estimating the number of objects in the result. To utilize available indexes t...

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