The Powerset Algebra as a Natural Tool to Handle Nested Database Relations

The nested relational algebra is often inadequate as a tool to handle nested relations, since several important queries, such as transitive closure, cannot expressed by it. On the other hand, the powerset algebra does allow the expression of transitive closure, but in a too expensive way. Therefore, we consider various other extensions to the nested algebra, such as least tixpoint and programming constructs, and show the query languages obtained in this way to be equivalent to (a slight extension of) the powerset algebra, thus both emphasizing the naturalness and strength of the latter as a tool to manipulate nested relations, and, at the same time, indicating better ways to implement the powerset algebra.