Declarative Constraint Programming with Definitional Trees

Abstract

The new generic scheme CFLP($\mathcal{D}$) has been recently proposed in [14] as a logical and semantic framework for lazy Constraint Functional Logic Programming over a parametrically given constraint domain $\mathcal{D}$. Further, [15] presented a Constrained Lazy Narrowing Calculus $CLNC(\mathcal{D})$ as a convenient computation mechanism for solving goals for CFLP($\mathcal{D}$)-programs, which was proved sound and strongly complete with respect to CFLP($\mathcal{D}$)’s semantics. Now, in order to provide a formal foundation for an efficient implementation of goal solving methods in existing systems such as Curry [8] and $\mathcal{TOY}$ [13,6], this paper enriches the CFLP($\mathcal{D}$) framework by presenting an optimization of the CLNC($\mathcal{D}$) calculus by means of definitional trees to efficiently control the computation. We prove that this new Constrained Demanded Narrowing Calculus CDNC($\mathcal({D}$) preserves the soundness and completeness properties of CLNC($\mathcal{D}$) and maintains the good properties shown for needed and demand-driven narrowing strategies [4,11,17].