XML transformations are very sensitive to types: XML types describe the tags and attributes of XML elements as well as the number, kind, and order of their sub-elements. Therefore, operations, even simple ones, that modify these features may affect the types of documents. Operations on XML documents are performed by iterators that, to be useful, need to be typed by a kind of polymorphism that goes beyond what currently exists. For this reason these iterators are not programmed but, rather, hard-coded in the language. However, this approach soon reaches its limits, as the hard-coded iterators cannot cover fairly standard usage scenarios. As a solution to this problem we propose a generic language to define iterators for XML data to be grafted on some host programming language. We show that our language mostly offers the required degree of polymorphism, study its formal properties, and show its expressiveness and practical impact by providing several usage examples and encodings.

Abstract. We describe DMSL, a domain specific language for defining schema mappings. Schema mappings are assertions in carefully crafted logics that express constraints between data represented in different formats, including XML and relational schema. DMSL is suitable for representing programs over mappings, which, for instance, occur in dataflow graphs of mappings. DMSL programs of mapping type are statically guaranteed by a qualified type system to denote satisfiable constraints; the principal polymorphic schemas of source and target solution data instances are automatically inferred. DMSL implements a variety of operations over mappings (e.g., composition) by interfacing with IBM’s Clio Mapping Engine. 1

One lesson learned painfully over the past twenty years is the perilous interaction of Curry-style typing with evaluation order and side-effects. This led eventually to the value restriction on polymorphism in ML, as well as, more recently, to similar artifacts in type systems for ML with intersection and union refinement types. For example, some of the traditional subtyping laws for unions and intersections are unsound in the presence of effects, while union-elimination requires an evaluation context restriction in addition to the value restriction on intersection-introduction. Our aim is to show that rather than being ad hoc artifacts, phenomena such as the value and evaluation context restrictions arise naturally in type systems for effectful languages, out of principles of duality. Beginning with a review of recent work on the Curry-Howard interpretation of focusing proofs as pattern-matching programs,

We present an extension of XDuce, a programming language dedicated to the processing of XML documents, with polymorphism and abstract types, two crucial features for programming in the large. We show that this extension makes it possible to deal with first class functions and eases the interoperability with other languages. A key mechanism of XDuce is its powerful pattern matching construction and we mainly focus on this construction and its interaction with abstract types. Additionally, we present a novel type inference algorithm for XDuce patterns, which works directly on the syntax of patterns.

We consider a type algebra equipped with recursive, product, function, intersection, union, and complement types together with type variables and implicit universal quantification over them. We consider the subtyping relation recently defined by Castagna and Xu over such type expressions and show how this relation can be decided in EXPTIME, answering an open question. The novelty, originality and strength of our solution reside in introducing a logical modeling for the semantic subtyping framework. We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system. This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful in the context of XML.

We examine schema mappings from a type-theoretic perspective and aim to facilitate and formalize the reuse of mappings. Starting with the mapping language of Clio, we present a type-checking algorithm such that typeable mappings are necessarily satisfiable. We add type variables to the schema language and present a theory of polymorphism, including a sound and complete type inference algorithm and a semantic notion of a principal type of a mapping. Principal types, which intuitively correspond to the minimum amount of schema structure required by the mappings, have an important application for mapping reuse. Concretely, we show that mappings can be reused, with the same semantics, on any schemas as long as these schemas are expansions (i.e., subtypes) of the principal types.

Abstract. Working with XML data often yields to practical situations in which the programmer would need to assign parametric polymorphic types to higher-order functions. However, up to date, there is no satisfactory way to do it. The indirect purpose of this article is to define a system to remedy this lack. Its actual goal is to study parametric polymorphism for a type system with recursive, product, union, intersection, negation, and function types (the first three constructions are sufficient to encode XML types). We first recall why the definition of such a system was considered hard— when not impossible—and then present the main ideas at the basis of our solution. In particular, we introduce the notion of “convexity” on which our solution is built up and discuss its connections with parametricity as defined by Reynolds to whose study our work sheds new light. Categories and Subject Descriptors D.3.3 [Programming Languages]:

We consider a type algebra equipped with recursive, product, function, intersection, union, and complement types together with type variables and implicit universal quantification over them. We consider the subtyping relation recently defined by Castagna and Xu over such type expressions and show how this relation can be decided in EXPTIME, answering an open question. The novelty, originality and strength of our solution reside in introducing a logical modeling for the semantic subtyping framework. We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system. This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful in the context of XML.

In general, typechecking refers to the problem where, given a program P, an input type σ, and an output type τ, one must decide whether P is type-safe, that is, whether it produces only outputs of type τ when run on inputs of type σ. In the XML context, typechecking problems mainly arise in two forms: •XML-to-XML transformations, where P transforms XML documents conforming to a given type into XML documents conforming to another given type; and •XML publishing, where P transforms relational databases into XML views of these databases and it is necessary to check that all generated views conform to a specified type. A type for XML documents is typically a regular tree language, usually expressed as a schema written in a schema language such as DTD, XML Schema, or a Relax NG (see XML Types). In the XML publishing case, the input type σ is a relational database schema, possibly with integrity constraints. Typechecking problems may or may not be decidable, depending on (1) the class of programs considered, (2) the class of input types (relational schemas, DTDs, XML Schemas, Relax NG schema, or perhaps other subclasses of the regular tree languages), and (3) the class of output types. In cases where it is decidable, typechecking can be done exactly. In cases where it is undecidable, one must revert to approximate or incomplete typecheckers that may return false negatives—i.e., may reject a program even if it is type-safe. Even when exact typechecking