XPath Formal Semantics and Beyond: a Coq based approach

XPath was introduced as the standard language for addressing parts of XML documents, and has been widely adopted by practioners and theoreticaly studied. We aim at building a logical framework for formal study and analysis of XPath and have to face the combinatorial complexity of formal proofs caused by XPath expressive power. We chose the Coq proof assistant and its powerful inductive constructions to rigorously investigate XPath peculiarities. We focus in this paper on a basic modeling of XPath syntax and semantics, and make two contributions. First, we propose a new formal semantics, which is an interpretation of paths as first order logic propositions that turned out to greatly simplify our formal proofs. Second, we formally prove that this new interpretation is equivalent to previously known XPath denotational semantics [20, 18], opening perspectives for more ambitious mathematical characterizations. We illustrate our Coq based model through several examples and we develop a formal proof of a simple yet significant XPath property that compare quite favorably to a former informal proof proposed in [18].