Typed iterators for XML

Abstract

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 languages. 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. This language can either be used as a compilation target (e.g., for XPATH) or it can be grafted on any statically typed host programming language (as long as this has product types) to endow it with XML processing capabilities. 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.

Set-theoretic foundation of parametric polymorphism and subtyping

“…3 We dubbed this property convexity after convex formulas: a formula is convex if whenever it entails a disjunction of formulas, then it entails one of them. The ⇒ direction of (8) (the other direction is trivial) states the convexity of assignments with respect to emptiness: 4 This holds true even for languages with bounded quantification which, as it is well known, defines the subtyping relation for type variables. Bounded quantification does not require any modification to our system, since it can be encoded by intersections: a type variable α bounded by a type t can be encoded by a fresh (unbounded) variable β by replacing β∧t for every occurrence of α.…”

“…Clearly, the containment on the right hand side of (4) is a necessary condition for subtyping. Unfortunately, considering it also as necessary and, thus, using (4) to define subtyping yields a subtyping relation that suffers too many problems to be useful. The first obstacle is that, as conjectured by Hosoya in [15], if the subtyping relation defined by (4) is decidable (which is an open problem), then deciding it is at least as hard as the satisfiability problem for set constraint systems with negative constraints, which is NEXPTIME-complete and for which, so far, no practical algorithm is known.…”

“…4 Type variables are special because their intersection with any ground type may be non-empty, whatever this type is. 3 We dubbed this property convexity after convex formulas: a formula is convex if whenever it entails a disjunction of formulas, then it entails one of them.…”

“…Finally, we signal the work on polymorphic iterators for XML presented in [4]. It introduces a very simple strongly normalizing calculus fashioned to define tree iterators.…”

Static and dynamic semantics of NoSQL languages

“…In this work we show that the two visions can coexist: we type data by semantic subtyping [16], a type system conceived for semistructured data, and describe computations by our filters which are untyped combinators that, thanks to a technique of weak typing introduced in [9], can polymorphically type the results of data query and processing with a high degree of precision. The conception of filters is driven by the schema of the data rather than the execution model and we use them (i) to capture and give a uniform semantics to a wide range of semi structured data processing capabilities, (ii) to give a type system that encompasses the types defined for such languages, if any, notably Pig, Jaql and AQL (but also XML query and processing languages: see Section 5.3), (iii) to infer the precise result types of queries written in these languages as they are (so without the addition of any explicit type annotation/definition or new construct), and (iv) to show how minimal extensions/modifications of the current syntax of these languages can bring dramatic improvements in the precision of the inferred types.…”