Declarative solutions to partitioned-grid problems

The problem of partitioning grid-based applications for parallel computing can be solved easily and intuitively in a logic programming language such as Prolog, using only the single assignment property of the logic variable, and not the backtracking. We show that such a logic program can be transformed in a systematic way into a circular functional program, which runs 10 times faster than the original logic program. The transformation proceeds in a number of steps. The first step is novel, and we give a correctness proof. Our reasoning also uses a novel combination of concepts from both the logical and functional paradigms.