XPath Typing Using a Modal Logic with Converse for Finite Trees

Pierre Genevès 1 Nabil Layaïda 1 Alan Schmitt 2
1 WAM - Web, adaptation and multimedia
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
2 SARDES - System architecture for reflective distributed computing environments
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically typecheck 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 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. With these proofs, we describe a practically 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).
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Communication dans un congrès
Proceedings of the ACM SIGPLAN Workshop on Programming Language Techniques for XML colocated with POPL 2007, 2007, Nice, France. pp.1, 2007
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Pierre Genevès, Nabil Layaïda, Alan Schmitt. XPath Typing Using a Modal Logic with Converse for Finite Trees. Proceedings of the ACM SIGPLAN Workshop on Programming Language Techniques for XML colocated with POPL 2007, 2007, Nice, France. pp.1, 2007. 〈hal-00189131〉

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