This note is about functions ƒ : Aω → Bω whose graph is recognized by a Büchi finite automaton on the product alphabet A x B. These functions are Baire class 2 in the Baire hierarchy of Borel functionsand it is decidable whether such function are continuous or not.In 1920 W. Sierpinski showed that a function $f : \mathbb{ R}\rightarrow \mathbb{R} $ is Baire class 1 if and only if both theovergraph and the undergraph of f are Fσ . We show thatsuch characterization is also true for functions on infinite wordsif we replace the real ordering by the lexicographical orderingon Bω . From this we deduce that it is decidable whethersuch function are of Baire class 1 or not. We extend this resultto real functions definable by automata in Pisot base.

Program slicing has been mainly studied in the context of imperative languages, where it has been applied to a wide variety of software engineering tasks, like program understanding, maintenance, debugging, testing, code reuse, etc. This work introduces the first forward slicing technique for declarative multi-paradigm programs which integrate features from functional and logic programming. Basically, given a program and a slicing criterion (a function call in our setting), the computed forward slice contains those parts of the original program which are reachable from the slicing criterion. Our approach to program slicing is based on an extension of (online) partial evaluation. Therefore, it provides a simple way to develop program slicing tools from existing partial evaluators and helps to clarify the relation between both methodologies. A slicing tool for the multi-paradigm language Curry, which demonstrates the usefulness of our approach, has been implemented in Curry itself.

Meseguer's rewriting logic and the rewriting logic CRWL are two well-known approaches to rewriting as logical deduction that, despite some clear similarities, were designed with different objectives. Here we study the relationships between them, both at a syntactic and at a semantic level. Even though it is not possible to establish an entailment system map between them, both can be naturally simulated in each other. Semantically, there is no embedding between the corresponding institutions. Along the way, the notions of entailment and satisfaction in Meseguer's rewriting logic are generalized.

The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the introduction of redundant arguments in the functions defined in the program. Redundancy of a parameter means that replacing it by any expression does not change the result. In this work, we provide methods for the analysis and elimination of redundant arguments in term rewriting systems as a model for the programs that can be written in more sophisticated languages. On the basis of the uselessness of redundant arguments, we also propose an erasure procedure which may avoid wasteful computations while still preserving the semantics (under ascertained conditions). A prototype implementation of these methods has been undertaken, which demonstrates the practicality of our approach.

In recent years much research and implementation effort has been devoted both to multiparadigm languages and constraint programming languages. Following up on a series of 11 workshops (WFLP) on multiparadigm languages and constraint programming, and as a result of an open call for submissions, the journal on Theory and Practice of Logic Programming is now publishing the results of the selection of the papers submitted to this special issue.

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described.