Playing with $\cal{TOY}$ : Constraints and Domain Cooperation

Abstract

Abstract. This paper describes T OY, an implementation of a Constraint Functional Logic Programming scheme CF LP (C), where C is a coordination domain involving the cooperation among several constraint domains D1, ..., Dn via a mediatorial domain M . This implementation follows a cooperative goal solving calculus for CF LP (C) based on lazy narrowing, invocation of solvers for each domain Di, and projection operations for converting Di constraints into Dj constraints with the aid of mediatorial constraints supplied by M . Mediatorial constraints allow solving programs that require constraints of different domains, and projection may improve performance, allowing certain solvers to profit from (the projected forms) of constraints originally intended for other solvers. As a relevant concrete instance of our CF LP (C), we implemented the cooperation among Herbrand, real arithmetic and finite domain constraints, and the mediatorial constraints relate numeric variables belonging to the last two domains. These mediatorial constraints are the bridge #== :: int -> real -> bool (that evaluates to true if their arguments are equivalent -i.e., the real value is considered to represent the integer one-and false otherwise), and the antibridge #/== :: int -> real -> bool (with a countermeaning).

On the cooperation of the constraint domains ℋ, ℛ, and ℱ in CFLP

“…In this section, we study the performance of the systems TOY (Arenas et al 2007;Estévez-Martín et al 2006, 2007c, 2008b and META-S (Frank et al 2003a(Frank et al , 2003b(Frank et al , 2005, i.e., the closest related approach we are aware of when solving various problems requiring domain cooperation. After presenting a set of benchmarks in the first subsections, the following three subsections deal with an analysis of the benchmarks in each of the two systems and a comparison between both.…”

“…The current implementation has evolved from older versions that supported the domains H and R, but not yet FD and its cooperation with H and R. We describe the architectural components of the current TOY system and briefly discuss the implementation of the main cooperation mechanisms provided by CCLNC(C), namely bridges and projections. The reader is referred to Arenas et al (2007) and Estévez-Martín et al (2006, 2007c, 2008b for more details. Instead of using an abstract machine for running byte-code or intermediate code, TOY programs are compiled to and executed in Prolog, as in other related systems Fig.…”

“…A second objective of the paper is to describe the implementation of a CFLP system which supports the cooperation of solvers via bridges and projections for the Herbrand domain H and the two numeric domains R and FD, following the computational model provided by the CCLNC(C) goal-solving calculus. The implementation follows the techniques summarized in our previous papers (Estévez-Martín et al 2007a, 2007c, 2008b. It has been developed on top of the TOY system (Arenas et al 2007), which is in turn implemented on top of SICStus Prolog (2007).…”

“…In fact, Estévez-Martín et al (2007a) was a very preliminary work which focused on presenting bridges and providing evidence for their usefulness. Building upon these ideas, Estévez-Martín et al (2007b) introduced coordination domains and a cooperative goal-solving calculus over an arbitrary coordination domain, proving local soundness and completeness results, while Estévez-Martín et al (2008a) further elaborated the cooperative goal-solving calculus, providing stronger soundness and completeness results and experimental data on an implementation tailored to the cooperation of the domains H, FD, and R. Significant novelties in this paper include: technical improvements in the formalization of domains; a new notion of solver taking care of critical variables and well-typed solutions; a new notion of domain-specific constraint to clarify the behavior of coordination domains; various elaborations in the cooperative goal-solving transformations needed to deal with critical variables and domain-specific constraints; a more detailed presentation of the implementation results previously reported in Estévez-Martín et al (2007a, 2007c, 2008b; and quite extensive comparisons to other related approaches.…”