On the basis of regular tree grammars, we present a formal framework for XML schema languages. This framework helps to describe, compare, and implement such schema languages in a rigorous manner. Our main results are as follows: (1) a simple framework to study three classes of tree languages (local, single-type, and regular); (2) classification and comparison of schema languages (DTD, W3C XML Schema, and RELAX NG) based on these classes; (3) efficient document validation algorithms for these classes; and (4) other grammatical concepts and advanced validation algorithms relevant to an XML model (e.g., binarization, derivative-based validation).

We present the functional language CDuce, discuss some design issues, and show its adequacy for working with XML documents. Distinctive features of CDuce are a powerful pattern matching, first class functions, overloaded functions, a very rich type system (arrows, sequences, pairs, records, intersections, unions, differences), precise type inference for patterns and error localization, and a natural interpretation of types as sets of values. We also outline some important implementation issues; in particular, a dispatch algorithm that demonstrates how static type information can be used to obtain very efficient compilation schemas.

this paper we describe a statically typed XML processing language called XDuce (o#cially pronounced "transduce"). XDuce is a functional language whose primitive data structures represent XML documents and whose types---called regular expression types---correspond to document schemas. The motivating principle behind its design is that a simple, clean, and powerful type system for XML processing can be based directly on the theory of regular tree automata

We propose regular expression pattern matching as a core feature of programming languages for manipulating XML. We extend conventional pattern-matching facilities (as in ML) with regular expression operators such as repetition (*), alternation (|), etc., that can match arbitrarily long sequences of subtrees, allowing a compact pattern to extract data from the middle of a complex sequence. We then show how to check standard notions of exhaustiveness and redundancy for these patterns. Regular expression patterns are intended to be used in languages with type systems based on regular expression types. To avoid excessive type annotations, we develop a type inference scheme that propagates type constraints to pattern variables from the type of input values. The type inference algorithm translates types and patterns into regular tree automata, and then works in terms of standard closure operations (union, intersection, and difference) on tree automata. The main technical challenge is dealing with the interaction of repetition and alternation patterns with the first-match policy, which gives rise to subtleties concerning both the termination and precision of the analysis. We address these issues by introducing a data structure representing these closure operations

U.C. San Diego

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Abstract We show how higher kinded generic programming can be represented faithfully within a dependently typed programming system. This development has been implemented using the Oleg system. The present work can be seen as evidence for our thesis that extensions of type systems can be done by programming within a dependently typed language, using data as codes for types. 1.

We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically type-check XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of a formula. The logic corresponds to the alternation free modal µ-calculus without greatest fixpoint, restricted to finite trees, and where formulas are cycle-free. Our proof method is based on two auxiliary results. First, XML regular tree types and XPath expressions have a linear translation to cycle-free formulas. Second, the least and greatest fixpoints are equivalent for finite trees, hence the logic is closed under negation. Building on these results, we describe a practical, effective system for solving the satisfiability of a formula. The system has been experimented with some decision problems such as XPath emptiness, containment, overlap, and coverage, with or without type constraints. The benefit of the approach is that our system can be effectively used in static analyzers for programming languages

. This document proposes an algebra for XML Query. The algebra has been submitted to the W3C XML Query Working Group. A novel feature of the algebra is the use of regular-expression types, similar in power to DTDs or XML Schemas, and closely related to Hasoya and Pierce's work on Xduce. The iteration construct is based on the notion of a monad, and involves novel typing rules not encountered elsewhere. 1 Introduction This document proposes an algebra for XML Query. This work builds on long standing traditions in the database community. In particular, we have been inspired by systems such as SQL, OQL, and nested relational algebra (NRA). We have also been inspired by systems such as Quilt, UnQL, XDuce, XML-QL, XPath, XQL, XSLT, and YATL. We give citations for all these systems below. In the database world, it is common to translate a query language into an algebra; this happens in SQL, OQL, and NRA, among others. The purpose of the algebra is twofold. First, the algebra is used to give...

A mathematical framework using formal language theory to describe and compare XML schema languages is presented. Our framework uses the work in two related areas -- regular tree languages [CDG + 97] and ambiguity in regular expressions [BEGO71, BKW98]. Using these work as well as the content in two classical references [HU79, AU79], we present the following results: (1) a normal form representation for regular tree grammars, (2) a framework of marked regular expressions and model groups, and their ambiguities, (3) five subclasses of regular tree grammars and their corresponding languages to describe XML content models: regular tree languages, TD(1) (top-down input scan with 1-vertical lookahead), single-type constraint languages, TDLL(1) (top-down and left-right input scan with 1-vertical and 1-horizontal lookaheads) , and local tree languages, (4) the closure properties of the five language classes under boolean set operations, (5) a classification and comparison of a few ...