A Fully Sound Goal Solving Calculus for the Cooperation of Solvers in the CFLP Scheme

The CFLP scheme for Constraint Functional Logic Programming has instances CFLP (D) corresponding to different constraint domains D. In this paper, we propose an amalgamated sum construction for building coordination domains C, suitable to represent the cooperation among several constraint domains D1, . . . ,Dn via a mediatorial domain M. Moreover, we present a cooperative goal solving calculus for CFLP (C), based on lazy narrowing, invocation of solvers for the different domains Di involved in the coordination domain C, and projection operations for converting Di constraints into Dj constraints with the aid of mediatorial constraints (so-called bridges) supplied by M. Under natural correctness assumptions for the projection operations, the cooperative goal solving calculus can be proved fully sound w.r.t. the declarative semantics of CFLP (C). As a relevant concrete instance of our proposal, we consider the cooperation between Herbrand, real arithmetic and finite domain constraints.