In this paper, we present an extended relational calculus for expressing queries in functional-logic deductive databases. This calculus is based on first-order logic and handles relation predicates, equalities and inequalities over partially defined terms, and approximation equations. For the calculus formulas, we have studied syntactic conditions in order to ensure the domain independence property. Finally, we have studied its equivalence w.r.t. the original query language, which is based on equality and inequality constraints.

In this paper, we study the integration of functional logic programming and databases by presenting a data model, and a query and data de nition language. The query and data de nition language is based on the use of a set of algebra operators over an extended relational algebra. The algebra expressions built from the extended algebra are used for expressing queries and rules. In addition, algebra expressions can be used for de ning functions, typical in a functional logic program.

Abstract. In this paper we present the main features of a deductive database language named IN DALOG based on the integration of functional and logic paradigms. As most deductive database systems, IN DA-LOG allows the handling of negation, higher-order functions, grouping operators, support for aggregation, handling of non-ground facts, and support for indexing structures on both extensional and intensional relations of a database. Moreover, we present the semantic foundations of this language. 1

Abstract Functional logic programming is a paradigm which integrates functional and logic programming. It is based on the use of rewriting rules for defining programs, and rewriting for goal solving. In this context, goals, usually, consist of equality (and, sometimes, inequality) constraints, which are solved in order to obtain answers, represented by means of substitutions. On the other hand, database programming languages involve a data model, a data definition language and, finally, a query language against the data defined according to the data model. To use functional logic programming as a database programming language, (1) we will propose a data model involving the main features adopted from functional logic programming (for instance, handling of partial and infinite data), (2) we will use conditional rewriting rules as data definition language, and finally, (3) we will deal with equality and inequality constraints as query language. Moreover, as most database systems, (4) we will propose an extended relational calculus and algebra, which can be used as alternative query languages in this framework. Finally, (5) we will prove that three alternative query languages are equivalent.

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Abstract. This paper adds the handling of negative information to a functional-logic deductive database language. By adopting as semantics for negation the so-called CRWLF, wherein the negation is intended as ’finite failure ’ of reduction, we will define Herbrand algebras and models for this semantics and a fix point operator to be used in a new goaldirected bottom-up evaluation mechanism based on magic transformations. This bottom-up evaluation will simulate the top-down one of the original program; in fact, it will carry out a goal-directed lazy evaluation. 1