A Category-Based Equational Logic Semantics to Constraint Programming

This paper exploits the point of view of constraint programming as computation in a logical system, namely constraint logic. We define the basic ingredients of constraint logic, such as constraint models and generalised polynomials. We show that constraint logic is an institution, and we internalise the study of constraint logic to the framework of category-based equational logic. By showing that constraint logic is a special case of category-based equational logic, we integrate the constraint logic programming paradigm into equational logic programming. Results include a Herbrand theorem for constraint logic programming characterising Herbrand models as initial models in constraint logic.