Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions where node car
dinality constraints occur along a path in a tree. We present a logic capable of expressing deep counting along paths which may include arbitrary recursive forward and backward navigation. The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes. While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a decidable tree logic whose main features can be decided in exponential time. Our logic being closed under negation, it may be used to decide typical problems on XPath queries such as satisfiability, type checking with relation to regular types, containment, or equivalence.
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node cardinali
ty constraints occur along a path in a tree. We present a logic capable of expressing deep counting along paths which may include arbitrary recursive forward and backward navigation. The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes. While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a tree logic decidable in exponential time.
This document describes how to use the XML static analyzer in practice. It provides informal documentation for using the XML reasoning solver implementation. The solver allows automated verification of properties that are expressed as logical formula
s over trees. A logical formula may for instance express structural constraints or navigation properties (like e.g. path existence and node selection) in finite trees. Logical formulas can be expressed using the syntax of XPath expressions, DTD, XML Schemas, and Relax NG definitions.
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 theses changes in rapidly evolving XML applications. This article proposes a logical framework and tool for verifying forward/backward compatibility issues involving schemas and queries. First, it allows analyzing relations between schemas. Second, it allows XML designers to identify queries that must be reformulated in order to produce the expected results across successive sche
