Comments on "Logic-Programming with Equations"

The purpose of this note is to analyse the differences between some results contained in [ll and analogous results in [2,31. The three papers deal with the issue of how the basic execution mechanism of logic programming (i.e., SLD resolution) can be exploited to handle some kinds of equational theories: a set E of equations, which may be interpreted as a rewriting system (by orienting the equations), can be transformed into a set of Horn clauses to which ordinary SLD resolution can be applied to compute normal forms (instead of rewriting) and to solve equations (instead of narrowing [6]) w.r.t. the theory E. This technique, which we call Jutrening, consists in transforming functional nestings into atom conjunctions in the bodies of the Horn clauses that are created. See [2,3] for the definitions of the flattening algorithms for generic term rewriting systems, and see [1,5,7,8] for systems with constructors (i.e., rewriting systems involving the distinction between defined-function symbols and data-constructor symbols). The only difference between the two versions is that in the latter case applications of constructors are not flattened. Following the notation of [2,3], we will indicate by Raat the set of Horn clauses obtained by compiling the rewriting system R by means of the appropriate version