Unification Modulo an Equality Theory for Equational Logic Programming

Equational logic programming is an extended programming paradigm of equational programming. Central to the notion of equational logic programming is the problem of solving equations, which is also called unification in equational theories. In this paper, we investigate the problem of solving equations in O’Donnell’s equational language. We define an equality theory for this language which adequately captures the intended notion of equational programming in the original language. We present a novel technique of transforming narrowing derivations and show the effect of such a transformation on the generality of solutions. As the main result of this paper we show semantically and operationally that complete and minimal sets of solutions under this equality theory always exist and can be generated by a special class of narrowing derivations.