A Safe Calculus and Algebra for Querying Functional Logic Deductive Databases

In this paper, we present an extended relational calculus and algebra for a functional logic deductive database language. The extended relational calculus is based on the relational first-order logic, by adding constraints in the form of equalities and disequalities over complex (partially defined and possibly infinite) values and interpreted functions. In addition, we propose the notion of safety over calculus formulas in order to guarantee the property of domain independence. In the case of the extended relational algebra, we provide a generalization of the selection and projection operators in order to restructure complex values by means of constructors and destructors, interpreted functions and function inverses, as well as, to consider equality and disequality constraints. Finally, we will state that the two query formalisms (calculus and algebra) are equivalent.