Implementing a Fixpoint Semantics for a Constraint Deductive Database based on Hereditary Harrop Formulas

Abstract

This work is aimed to show a concrete implementation of a deductive database system based on the scheme HH-(C) (Hereditary Harrop Formulas with Negation and Constraints) following a fixpoint semantics proposed in a previous work. We have developed a Prolog implementation for this scheme that is constraint system independent. therefore allowing to use it as a base for any instance of the formal scheme. We have developed several specific constraint systems: Real numbers, integers, Boolean and user-defined enumerated types. We have added types to the database so that relations become typed (as tables in relational databases) and each constraint is mapped to its corresponding constraint system. The predicates that compute the fixpoint giving the meaning to a database are described. In particular, we show the implementation of a forcing relation (for derivation steps) and highlight how the inherent difficulties have been overcome in a system allowing hypothetical queries, which make the database dynamically grow.