A Theoretical Framework for the Higher-Order Cooperation of Numeric Constraint Domains

This paper presents a theoretical framework for the integration of the cooperative constraint solving of numeric constraint domains into higher-order functional and logic programming on λ-abstractions, using an instance of a generic Constraint Functional Logic Programming (CFLP) scheme over a so-called higher-order coordination domain. We provide this framework as a powerful computational model for the higher-order cooperation of algebraic constraint domains over real numbers and integers, which has been useful in practical applications involving the hybrid combination of its components, so that more declarative and efficient solutions can be promoted. Our proposal of computational model has been proved sound and complete with respect to the declarative semantics provided by the CFLP scheme, and enriched with new mechanisms for modeling the intended cooperation among the numeric domains and a novel higher-order constraint domain equipped with a sound and complete constraint solver for solving higher-order equations. We argue the applicability of our approach describing a prototype implementation on top of the constraint functional logic system TOY.