Thèmes COM et SYM -Systèmes communicants et Systèmes symboliqueś Equipes-Projets Wam et Sardes Rapport de recherche n°6590 -Juillet 2008 -41 pagesAbstract: 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 manipulating both XPath expressions and XML type annotations (as input and output types).Key-words: Mu-calculus, satisfiability, trees, XPath, queries, XML, types, regular tree grammars An extended abstract of this work was presented at the ACM Conference on Programming Language Design and Implementation (PLDI), 2007 [21]. Extensions included in this article notably comprise proof sketches, crucial implementation techniques for building a satisfiability-testing algorithm which performs well in practice, a detailed description of the algorithm, and formal descriptions and explanations about an important property of the logic: cycle-freeness for formulas.

JavaScript is the most widely used web language for client-side applications. Whilst the development of JavaScript was initially just led by implementation, there is now increasing momentum behind the ECMA standardisation process. The time is ripe for a formal, mechanised specification of JavaScript, to clarify ambiguities in the ECMA standards, to serve as a trusted reference for high-level language compilation and JavaScript implementations, and to provide a platform for high-assurance proofs of language properties. We present JSCert, a formalisation of the current ECMA standard in the Coq proof assistant, and JSRef, a reference interpreter for JavaScript extracted from Coq to OCaml. We give a Coq proof that JSRef is correct with respect to JSCert and assess JSRef using test262, the ECMA conformance test suite. Our methodology ensures that JSCert is a comparatively accurate formulation of the English standard, which will only improve as time goes on. We have demonstrated that modern techniques of mechanised specification can handle the complexity of JavaScript.

We propose a novel approach to the well-known view update problem for the case of tree-structured data: a domain-specific programming language in which all expressions denote bi-directional transformations on trees. In one direction, these transformations---dubbed lenses ---map a "concrete" tree into a simplified "abstract view"; in the other, they map a modified abstract view, together with the original concrete tree, to a correspondingly modified concrete tree. Our design emphasizes both robustness and ease of use, guaranteeing strong well-behavedness and totality properties for well-typed lenses.We identify a natural space of well-behaved bi-directional transformations over arbitrary structures, study definedness and continuity in this setting, and state a precise connection with the classical theory of "update translation under a constant complement" from databases. We then instantiate this semantic framework in the form of a collection of lens combinators that can be assembled to describe transformations on trees. These combinators include familiar constructs from functional programming (composition, mapping, projection, conditionals, recursion) together with some novel primitives for manipulating trees (splitting, pruning, copying, merging, etc.). We illustrate the expressiveness of these combinators by developing a number of bi-directional list-processing transformations as derived forms.

This paper presents a new distributed process calculus, called the M-calculus, that can be understood as a higher-order version of the Distributed Join calculus with programmable localities. The calculus retains the implementable character of the Distributed Join calculus while overcoming several important limitations: insufficient control over communication and mobility, absence of dynamic binding, and limited locality semantics. The calculus is equipped with a polymorphic type system that guarantees the unicity of locality names, even in presence of higher-order communications -- a crucial property for the determinacy of message routing in the calculus.