Comparison of Functional and Predicative Query Paradigms

In the last decade many extensions of the relational model were proposed, and basic properties of the relational model were investigated in their contexts. In particular, the equivalence of calculus and algebra, and the relative expressive power of other related languages were explored. This paper investigates this subject in a general framework, independently of any specific data type constructors that may exist in specific models, with the goal of making explicit the conditions that enable translation between query languages. The framework is based on a combination the well-founded approach of deductive programs and the initial algebra approach of algebraic specifications. The latter does not support negation (i.e., disequations); hence our combination contributes to the theory of algebraic specifications. Given the framework, we present the predicative and functional approaches to database description and querying. The first leads to the calculus and deductive approaches, the second to several algebras and, also, to generalizations that allow restricted definition by equations. We extend the notions of domain independence to our framework. We then present various sufficient conditions for the calculus and (some) algebra to be equivalent. We also compare the expressive power of algebras and more general languages to several deductive languages, under stratified and well-founded semantics. Finally, we define safety conditions and prove similar results for safe versions of the languages.