Abstract: The data structure of Warren Abstract: Machine (WAM)is discussed. Interpretive implementation of the instruction repertoire of WAM and a new strategy to deal with arithmetic expressions efficiently are given. It is the back-end module of an optimizing Prolog compiler system which we developed, based on WAM. The system execution speed is 7~8 times as fast as the Prolog interpreter we developed previously, and 3~4 times the speed of SWI-Prolog compiler system.