Thèmes COM et SYM -Systèmes communicants et Systèmes symboliqueś Equipes-Projets Wam et Sardes Rapport de recherche n°6590 -Juillet 2008 -41 pagesAbstract: We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically type-check XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of a formula. The logic corresponds to the alternation free modal µ-calculus without greatest fixpoint, restricted to finite trees, and where formulas are cycle-free. Our proof method is based on two auxiliary results. First, XML regular tree types and XPath expressions have a linear translation to cycle-free formulas. Second, the least and greatest fixpoints are equivalent for finite trees, hence the logic is closed under negation.Building on these results, we describe a practical, effective system for solving the satisfiability of a formula. The system has been experimented with some decision problems such as XPath emptiness, containment, overlap, and coverage, with or without type constraints. The benefit of the approach is that our system can be effectively used in static analyzers for programming languages manipulating both XPath expressions and XML type annotations (as input and output types).Key-words: Mu-calculus, satisfiability, trees, XPath, queries, XML, types, regular tree grammars An extended abstract of this work was presented at the ACM Conference on Programming Language Design and Implementation (PLDI), 2007 [21]. Extensions included in this article notably comprise proof sketches, crucial implementation techniques for building a satisfiability-testing algorithm which performs well in practice, a detailed description of the algorithm, and formal descriptions and explanations about an important property of the logic: cycle-freeness for formulas.

During the life cycle of an XML application, both schemas and queries may change from one version to another. Schema evolutions may affect query results and potentially the validity of produced data. Nowadays, a challenge is to assess and accommodate the impact of these changes in evolving XML applications. Such questions arise naturally in XML static analyzers. These analyzers often rely on decision procedures such as inclusion between XML schemas, query containment and satisfiability. However, existing decision procedures cannot be used directly in this context. The reason is that they are unable to distinguish information related to the evolution from information corresponding to bugs. This paper proposes a predicate language within a logical framework that can be used to make this distinction.We present a system for monitoring the effect of schema evolutions on the set of admissible documents and on the results of queries. The system is very powerful in analyzing various scenarios where the result of a query may not be anymore what was expected. Specifically, the system is based on a set of predicates which allow a fine-grained analysis for a wide range of forward and backward compatibility issues. Moreover, the system can produce counterexamples and witness documents which are useful for debugging purposes. The current implementation has been tested with realistic use cases, where it allows identifying queries that must be reformulated in order to produce the expected results across successive schema versions.