A hidden Herbrand theorem: combining the object and logic paradigms

The bene ts of the object, logic (or relational), functional, and constraint paradigms can be obtained from our previous combination of the object and functional paradigms in hidden algebra, by combining it with existential queries over the states and attributes of objects, and then lifting to hidden Horn clause logic with equality, using an extension of a result due to Diaconescu. We call this novel programming paradigm active constraint object programming, suggest some applications for it, and show that it is computationally feasible by reducing it to familiar problems over term algebras (i.e., Herbrand universes). Our main result is a version of Herbrand's Theorem, lifted from hidden algebra by the extended result of Diaconescu. This paper also contains new results on the existence of initial and nal models, and on the consistency of hidden theories.