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On the basis of regular tree grammars, we present a formal framework for XML schema languages. This framework helps to describe, compare, and implement such schema languages in a rigorous manner. Our main results are as follows: (1) a simple framework to study three classes of tree languages (local, single-type, and regular); (2) classification and comparison of schema languages (DTD, W3C XML Schema, and RELAX NG) based on these classes; (3) efficient document validation algorithms for these classes; and (4) other grammatical concepts and advanced validation algorithms relevant to an XML model (e.g., binarization, derivative-based validation).

XDuce is a statically typed programming language for XML processing. Its basic data values are XML documents, and its types (so-called regular expression types ) directly correspond to document schemas. XDuce also provides a flexible form of regular expression pattern matching , integrating conditional branching, tag checking, and subtree extraction, as well as dynamic typechecking. We survey the principles of XDuce's design, develop examples illustrating its key features, describe its foundations in the theory of regular tree automata, and present a complete formal definition of its core, along with a proof of type safety.

We propose regular expression types as a foundation for statically typed XML processing languages. Regular expression types, like most schema languages for XML, introduce regular expression notations such as repetition (*), alternation (|), etc., to describe XML documents. The novelty of our type system is a semantic presentation of subtyping, as inclusion between the sets of documents denoted by two types. We give several examples illustrating the usefulness of this form of subtyping in XML processing.The decision problem for the subtype relation reduces to the inclusion problem between tree automata, which is known to be EXPTIME-complete. To avoid this high complexity in typical cases, we develop a practical algorithm that, unlike classical algorithms based on determinization of tree automata, checks the inclusion relation by a top-down traversal of the original type expressions. The main advantage of this algorithm is that it can exploit the property that type expressions being compared often share portions of their representations. Our algorithm is a variant of Aiken and Murphy's set-inclusion constraint solver, to which are added several new implementation techniques, correctness proofs, and preliminary performance measurements on some small programs in the domain of typed XML processing.