Converting into pattern-based schemas: a formal approach

A traditional distinction among markup languages is how descriptive or prescriptive they are. We identify six levels along the descriptive/prescriptive spectrum. Schemas at a specific level of descriptiveness that we call "Descriptive No Order" (DNO) specify a list of allowable elements, their number and requiredness, but do not impose any order upon them. We have defined a pattern-based model based on a set of named patterns, each of which is an object and its composition rule (content model), enough to write descriptive schemas for arbitrary documents. We show that any schema can be converted into a pattern-based one without loss of information at the DNO level (invariant conversion). We present a formal analysis of invariant conversions of arbitrary schemas as a demonstration of the correctness and completeness of our pattern model. Although all examples are given in DTD syntax, the results should apply equally to XSD, Relax NG, or other schema languages.