Elimination of Negation in Term Algebras

runtime form of constructive negation does not have this advantage, but applies to many more programs. The simple form of the runtime method 1], given a negative goal :A, executes A; if A has a nite SLD-tree with answer substitutions (as substitution formulas) s 1 collection of substitutions in cases as described by Theorem 5, but in general cannot be presented this way. For example, the goal :append(x; y; z:nil) must return as an answer :9v (x = nil ^ y = v:nil ^ z = v:nil) ^ :9v (x = v:nil ^ y = nil ^ z = v:nil). Thus, again, Theorem 5 forces upon us an execution mechanism capable of handling inequalities. The general runtime method faces the same problems. Since the use of constraints has many advantages 11] and substitutions are too weak to represent the appropriate negative information, most approaches to constructive negation are based on constraints 28, 19, 43, 1, 41], rather than substitutions. The algorithm uncover is useful for reducing :s 1 ^ : : : ^ :s m , and the formulas produced by the Sato-Tamaki transformation, to a \simplest" form, with only inequalities that, as the theorem shows, are unavoidable.