Logics for XML

TL;DR

This thesis develops a fixpoint temporal logic based system for static analysis of XML processing languages, enabling efficient reasoning about XPath and XML schemas with practical applications in static analyzers.

Contribution

Introduces a decidable, expressive logic derived from the mu-calculus for XML analysis, with algorithms and implementation for static type-checking and containment problems.

Findings

Logic is decidable in exponential time.

System effectively handles XPath and XML schema analysis.

Practical experiments show efficiency in realistic scenarios.

Abstract

This thesis describes the theoretical and practical foundations of a system for the static analysis of XML processing languages. The system relies on a fixpoint temporal logic with converse, derived from the mu-calculus, where models are finite trees. This calculus is expressive enough to capture regular tree types along with multi-directional navigation in trees, while having a single exponential time complexity. Specifically the decidability of the logic is proved in time 2^O(n) where n is the size of the input formula. Major XML concepts are linearly translated into the logic: XPath navigation and node selection semantics, and regular tree languages (which include DTDs and XML Schemas). Based on these embeddings, several problems of major importance in XML applications are reduced to satisfiability of the logic. These problems include XPath containment, emptiness, equivalence, overlap, coverage, in the presence or absence of regular tree type constraints, and the static type-checking of an annotated query. The focus is then given to a sound and complete algorithm for deciding the logic, along with a detailed complexity analysis, and crucial implementation techniques for building an effective solver. Practical experiments using a full implementation of the system are presented. The system appears to be efficient in practice for several realistic scenarios. The main application of this work is a new class of static analyzers for programming languages using both XPath expressions and XML type annotations (input and output). Such analyzers allow to ensure at compile-time valuable properties such as type-safety and optimizations, for safer and more efficient XML processing.