Departmental Papers (CIS)

Date of this Version

January 2005

Document Type

Journal Article


Copyright ACM, 2005. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Programming Languages and Systems, Volume 27, Issue 1, January 2005, pages 46-90.
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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.


programming languages, language constructs and features, data types and structures, languages, theory, type systems, XML, subtyping



Date Posted: 16 March 2005

This document has been peer reviewed.