Evaluation of XPath Fragments Using Lambda Calculi

XML Path Language (XPath) is the most important standard for navigation within XML documents nowadays. In this paper we present the state of our current research that is focused on using a functional framework based on simply typed lambda calculi and a general type system XML-λ for description of semantics of a query language. With such formalism we are able to describe the semantics of all language constructs and evaluate XPath queries using the XML-λ virtual machine. 1 Motivation and Problem Statement The World Wide Web Consortium designed the XML language [2] for an exchange of data on the Web and elsewhere. Then, there arose many subsequent proposals of query languages. One of the most important of them is the XML Path Language – XPath [4]. It is a language for addressing parts of an XML document, designed to be used by both XSLT and XPointer. Later on, its extended version (denoted as 2.0) became a crucial part of the XQuery 1.0 standard [1]. As all experimenters who try to develop an efficient implementation of the standard we have faced this problem during our work on a prototype of a native XML database management system ExDB [10] within our research group. While the XPath engine is usually heavily used it is worth to put extra effort into its optimal design. With respect to the fact that we deal for a long time with a functional data model for XML and its properties our current research is focused on using such model for evaluating XPath queries. Proposed paper suggest a way how to transform XPath queries into their functional version and then evaluate it using a functional virtual machine. Actually, it is only an outline of the research (ergo ”Work in Progress”) but so far the result is promising. Our long-term goal is to extend the scope of this work to XPath 2.0 and further to XQuery 1.0 – here we plan to formalize so called Core XQuery 1.0 [9] that is formed mainly by the FLWOR (For–Let–Where– OrderBy–Return) expression and XPath node selection. Results of this research are also expected to be published as a consistent work in the doctoral thesis of the first author. 2 Related Work The essential document – XML Path Language Version 1.0 [4] – defines the syntax of the language and its informal semantics. The most important part is the description of the data model used (XML Infoset [5]) and denotation of all location paths (i.e. axis, node tests and predicates). The standard also defines few basic functions for manipulation with XML documents. Successive works propose various extended data models and discuss the efficiency and complexity of XPath evaluation algorithms. From the point of XPath’s semantics, Wadler discussed the denotational semantics, for example here [13] or [14], seen from an XSLT point of view. Gottlob et al. [7, 8] propose their own denotational semantics and discuss mostly the time and space complexity of XPath evaluation algorithms using their proposals. 3 Prerequisite Specifications We expect that the reader is familiar with XML, XPath and other W3C’s specifications. XML-λ is not so known and therefore, for convenience, we repeat basic facts in following sections.