A Declarative Approach for First-Order Built-in’s of Prolog

We provide here a fram ework for studying Prolog program s w ith various bu ilt-in ’s th a t include arithm etic operations, and such metalogical relations like var and ground. To this end we propose a new, declarative sem antics and prove com pleteness of the Prolog com pu­ ta tion mechanism w .r.t. th is sem antics. We also show th a t this sem antics is fully abstrac t in an appropria te sense. Finally, we provide a m ethod for proving term ination of Prolog program s w ith bu ilt-in ’s which uses this sem antics. The m ethod is shown to be m odular and is illustra ted by proving term ination of a num ber of program s including the unify program of Sterling and Shapiro [17]. 1991 Mathematics Subject Classification: 68Q40, 68T15, 1991 CR Categories: F.3.2., F.4.1, H.3.3, 1.2.3.