Boolean operations and inclusion test for attribute-element constraints

The history of schema languages for XML is (roughly) an increase of expressiveness. While early schema languages mainly focused on the element structure, Clark first paid an equal attention to attributes by allowing both element and attribute constraints in a single constraint expression (we call his mechanism "attribute-element constraints"). In this paper, we investigate intersection and difference operations and inclusion test for attribute-element constraints, in view of their importance in static typechecking for XML processing programs. The contributions here are (1) proofs of closure under intersection and difference as well as decidability of inclusion test and (2) algorithm formulations incorporating a "divide-and-conquer" strategy for avoiding an exponential blowup for typical inputs.

[1]  Mark Nottingham,et al.  The Atom Syndication Format , 2005, RFC.

[2]  Makoto Murata,et al.  Transformation of Documents and Schemas by Patterns and Contextual Conditions , 1996, PODP.

[3]  Gérard Berry,et al.  From Regular Expressions to Deterministic Automata , 1986, Theor. Comput. Sci..

[4]  Silvano Dal-Zilio,et al.  XML Schema, Tree Logic and Sheaves Automata , 2003, RTA.

[5]  C. M. Sperberg-McQueen,et al.  Extensible Markup Language (XML) , 1997, World Wide Web J..

[6]  Dan Suciu,et al.  Typechecking for XML transformers , 2000, J. Comput. Syst. Sci..

[7]  Haruo Hosoya.  Validation and boolean operations for attribute-element constraints , 2002 .

[8]  C. M. Sperberg-McQueen,et al.  Extensible markup language , 1997 .

[9]  Benjamin C. Pierce,et al.  Regular expression types for XML , 2005, ACM Trans. Program. Lang. Syst..

[10]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[11]  Benjamin C. Pierce,et al.  Regular expression pattern matching for XML , 2003, POPL '01.

[12]  Akihiko Tozawa.  Towards static type checking for XSLT , 2001, DocEng '01.

[13]  Giuseppe Castagna,et al.  Semantic subtyping , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[14]  Derick Wood,et al.  Regular tree and regular hedge languages over unranked alphabets , 2001 .

[15]  Nils Klarlund,et al.  DSD: A schema language for XML , 2000, FMSP '00.

[16]  Janusz A. Brzozowski,et al.  Derivatives of Regular Expressions , 1964, JACM.

[17]  Benjamin C. Pierce,et al.  XDuce: A Typed XML Processing Language (Preliminary Report) , 2000, WebDB.

[18]  Benjamin C. Pierce,et al.  A record calculus based on symmetric concatenation , 1991, POPL '91.