Highly expressive query languages for unordered data trees

We study highly expressive query languages for unordered data trees, using as formal vehicles Active XML and extensions of languages in the while family. All languages may be seen as adding some form of control on top of a set of basic pattern queries. The results highlight the impact and interplay of different factors: the expressive power of basic queries, the embedding of computation into data (as in Active XML), and the use of deterministic vs. nondeterministic control. All languages are Turing complete, but not necessarily query complete in the sense of Chandra and Harel. Indeed, we show that some combinations of features yield serious limitations, analogous to FOk definability in the relational context. On the other hand, the limitations come with benefits such as the existence of powerful normal forms. Other languages are "almost" complete, but fall short because of subtle limitations reminiscent of the copy elimination problem in object databases.