A -calculus Speciication of Prolog

A clear and modular speciication of Prolog using the-calculus is presented in this paper. Prolog goals are represented as-calculus processes, and Prolog predicate deenitions are translated into-calculus agent deenitions. Prolog's depth-rst left-right control strategy as well as the cut control operator are modeled by the synchronized communication among processes, which is similar in spirit to continuation-passing style implementation of Prolog. Prolog terms are represented by persistent processes, while logical variables are modeled by complex processes with channels that, at various times, can be written, read, and reset. Both uniications with and without backtracking are speciied by-calculus agent deenitions. A smooth merging of the speciication for control and the speciication for uniication gives a full speciication for much of Prolog. Some related and further works are also discussed. 1 Introduction Prolog is a simple, powerful and eecient programming language, but its depth-rst left-right control as well as the control operator cut (!) and its lack of the occurs check destroys the declarative reading of Prolog programs. For example, a left recursive clause will cause an innnite computation while a right recursive clause with same logic reading will terminate the computation. Hence, logic does not provide a simple and formal semantics for Prolog. In Ros92a] Ross provided an interesting speciication of Prolog control by mapping it into processes in the concurrent speciication language CCS Mil89]. In this paper, we develop and extend this approach signiicantly by using the-calculus, a richer concurrent speciication language. We are not only able to specify Prolog's control primitives but also its correct interaction with Prolog's uniication, including the lack of the occur-check and the construction of circular terms. The-calculus MPW92a, MPW92b, Mil91] is a calculus for modeling concurrent systems with evolving communication structure. It has been proven very powerful in modeling functional programming languagessMil90b] and object-oriented programming languagessWal90]. In this paper, we will introduce a clear and modular speciication for Prolog using the-calculus. The speciication is modular in the sense that the Prolog control part and uniication are speciied separately, but can be merged together smoothly to form a full speciication for Prolog. In fact, part of the motivation behind this paper was to understand how successfully the-calculus could be used to specify the operational semantics of a non-trivial programming language, in this case Prolog. As we hope it will be clear from this paper, the-calculus, along with a sorting discipline proposed for it, does indeed provide …