A formal semantics of patterns in XSLT

Programming language theorists have developed a number of techniques to formally capture the meaning of programming languages. As our epigram insists, these theories are best applied not when a language is too old for help, but when it is aborning and subject to guidance. XSLT is a language for transforming XML documents into other XML documents [XSLT]. A key element of XSLT is the sub-language of patterns, which is used for matching and selection. The pattern language of XSLT has recently evolved into XPath [XPath], a language of selection paths and expressions that performs core functions of both XSLT and XPointer [XPointer]. This note presents a formal semantics of the pattern language from the 16 December 1998 draft of XSLT [XSL-Dec98]. The semantics is clear and concise, summarizing in one page of formulas what required about ten pages of prose to describe. With the aid of the semantics one can rigorously state and prove properties of the language; these properties helped to guide future development of the XSLT design; thus fullfilling Reynolds’s prescription. The semantics was developed using standard techniques from the programming language community, and this article provides a tutorial introduction to these techniques. While little here will be new to the language theorist, some of what is here may be of use to the markup technologist. A formal semantics brings to light issues that can be hard to spot in an english language description. For instance, matching is a central concept in XSLT. Here is how it was described in [XSL-Dec98].