Prolog with Arrays and Bounded Quanti

It is proposed to add bounded quantiications to Prolog. The main reason is one of natural expression, many algorithms are expressed more elegantly in a declarative way using bounded quantiications than using existing means, i.e., recursion. In particular this is true for numerical algorithms, an area where Prolog has been virtually unsuccessful so far. Moreover, bounded quantiication has been found to be at least as eecient as recursion, when applicable. We outline an implementation of some bounded quantiications through an extension of Warren's abstract Prolog machine and give performance gures relative to re-cursion. Finally, we have shown elsewhere that bounded quantiication has a high potential for parallel implementation and we conclude in this paper that one can often run the same program eeciently on a sequential computer as well and on several kinds of parallel computers. 2 1 Introduction Barklund and Millroth 6] and Voronkov 25, 26] have proposed bounded quantiications as a computational device for repetition by iteration in logic programs. In this paper we argue for a useful extension of the Prolog programming language with bounded quantiications. Although we propose sequential operational semantics for these constructs here, we have shown elsewhere that many Prolog programs with bounded quantiications can also be run eeciently on parallel computers. We have run programs on both SIMD computers (Connection Machine Model CM-2 by Thinking Machines Corp.) 2] and shared-memory MIMD computers (SUN 630MP and Sequent Symmetry) 3]. Much of the beauty of bounded quantiications lies in the fact that they have a clear declarative semantics, while at the same time they behave well operationally on this wide range of sequential and parallel computers. The rest of the paper is structured as follows. Section 2 introduces syntax and informal semantics for bounded quantiications in Prolog. In Section 3 an extension of Prolog with arrays is proposed and motivated. Section 4 discusses sequential operational semantics for bounded quantiications. The implementation of Warren's abstract Prolog machine in which our experiments have been carried out is brieey described in Section 5. In Section 6 a set of instructions extending Warren's machine is proposed; compilation of bounded universal quantiications to the extended machine instruction set is deened in Section 7. Section 8 contains seven examples of Prolog programs with bounded quantiications and their resulting code, in some cases with corresponding recursive programs for comparison, ended with a list of measured run times. In Section 9 some further …