Parametric polymorphism for XML

Abstract

Despite the extensiveness of recent investigations on static typing for XML, parametric polymorphism has rarely been treated. This well-established typing discipline can also be useful in XML processing in particular for programs involving "parametric schemas," i.e., schemas parameterized over other schemas (e.g., SOAP). The difficulty in treating polymorphism for XML lies in how to extend the "semantic" approach used in the mainstream (monomorphic) XML type systems. A naive extension would be "semantic" quantification over all substitutions for type variables. However, this approach reduces to an NEXPTIME-complete problem for which no practical algorithm is known. In this paper, we propose a different method that smoothly extends the semantic approach yet is algorithmically easier. In this, we devise a novel and simple marking technique, where we interpret a polymorphic type as a set of values with annotations of which subparts are parameterized. We exploit this interpretation in every ingredient of our polymorphic type system such as subtyping, inference of type arguments, and so on. As a result, we achieve a sensible system that directly represents a usual expected behavior of polymorphic type systems-"values of variable types are never reconstructed"-in a reminiscence of Reynold's parametricity theory. Also, we obtain a set of practical algorithms for typechecking by local modifications to existing ones for a monomorphic system.

A Type-Safe Embedding of XDuce into ML

“…In fact, this result is not surprising given that similar observations can be made when extending XDuce with polymorphism [15]. We conjecture that we maintain coherence if we require that polymorphic functions are unambiguous following the approach in [15].…”

“…We foresee several possible solutions to the problem by either demanding explicit annotations or restricting the form of polymorphism. We plan to pursue this topic in the future following the work of Hosoya and Frisch and Castagna [15].…”

“…Note that the semantic preservation result and thus coherence may not hold for arbitrary matching policies. E.g., the latest description of XDuce [14,15] assumes a indeterministic (matching) semantics. Further coherence problems arise once we integrate additional language features such as ML-style polymorphism (see upcoming Example 5.1).…”

“…We conjecture that we maintain coherence if we require that polymorphic functions are unambiguous following the approach in [15].…”

Verification of tree-processing programs via higher-order mode checking

“…Thus, our method can be used as an alternative for a verification purpose. Meanwhile their type systems support advanced programming features such as parametric polymorphism (Hosoya et al 2009) and regular expression pattern matching (Hosoya et al 2000). Extensions of our method with these features are left for future work.…”