Object-Oriented Queries: Equivalence and Optimization.
Gail M. Shaw, Stanley B. Zdonik · 1989
data types can also define equality operations. Such operations are typespecific and will not be considered in this paper. Objects can be represented graphically, where nodes are objects or atomic values, arcs connect collection type objects to all objects that are members of the collection, and arcs connect non-collection type objects to the values of all properties of that object (similarly to [11] for example). Nodes representing atomic values are leaves and are labelled with the atomic value. Nodes representing non-atomic objects are labelled with an (artificial) object identifier as well as the object type. Types can be labelled symbolically, using ? for set types, !? for tuple types, and ffl for other abstract data types. In Figure 1 three set objects are represented graphically. Note that graphs b and c represent 3-equal set objects: C 2 and C 1 are 1-equal, making t 3 and t 5 2-equal (t 1 and t 4 are 1-equal, therefore 2-equal), thus S 2 and S 3 are 3-equal. Object S1 (graph a...