Commutativity Analysis in XML Update Languages

A common approach to XML updates is to extend XQuery with update operations. This approach results in very expressive languages which are convenient for users but are difficult to reason about. Deciding whether two expressions can commute has numerous applications from view maintenance to rewriting-based optimizations. Unfortunately, commutativity is undecidable in most recent XML update languages. In this paper, we propose a conservative analysis for an expressive XML update language that can be used to determine whether two expressions commute. The approach relies on a form of path analysis that computes upper bounds for the nodes that are accessed or modified in a given update expression. Our main result is a commutativity theorem that can be used to identify commuting expressions.