CHIP in plain logic

The programming language Prolog allows succinct representation of a wide variety of scheduling problems. To speed up execution, a new version called CHIP (Constraint Handling In Prolog) was introduced that maintains the programming advantages of Prolog. CHIP achieves its speed by keeping track of the sets of possible values for each variable. In this way, a search can be abandoned as soon as any such set becomes empty. This mechanism is made part of the unification algorithm. CHIP maintains the conventional orientation of logic towards single values. Thus, an awkward theoretical structure results from interfacing with set orientation in unification. This problem is solved by using a set-orientation for the entire logic