Mode-directed fixed point computation

Abstract

Goal-directed fixed point computation strategies have been widely adopted in the tabled logic programming paradigm. However, there are many situations in which a fixed point contains a large number or even infinite number of solutions. In these cases, a fixed point computation engine may not be efficient enough or feasible at all. We present a mode-declaration scheme which provides the capabilities to reduce a fixed point from a big solution set to a preferred small one, or from an infeasible infinite set to a finite one. We show the correctness of the mode-declaration scheme. One motivating application of our mode-declaration scheme is for dynamic programming, which is typically used for solving optimization problems. There is no need to define the value of an optimal solution recursively, instead, defining a general solution suffices. The optimal value as well as its corresponding concrete solution can be derived implicitly and automatically using a mode-directed fixed point computation engine. This mode-directed fixed point computation engine has been successfully implemented in a commercial Prolog system. © Springer-Verlag Berlin Heidelberg 2005.