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This work was supported by ESPRIT Basic Research Action P3020 \Integration", by CICYT under grant TIC 91-0425 and by \Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of C.N.R." under grant n.9100880.PF69 Departamento de Sistemas Inform aticos y Computaci on, Universidad Polit ecnica de Valencia, Camino de Vera s/n, Apdo. 22012, 46020 Valencia, Spain. Dipartimento di Informatica, Universit a di Pisa, Corso Italia 40, 56125 Pisa, Italy In this paper we are concerned with an instance of the CLP scheme specialized in solving equations with respect to a Horn equational theory . The intended structure is given by the nest partition induced by on the Herbrand Universe over a nite one sorted alphabet. This work deals with the description of an incremental constraint solver as the kernel of an operational semantics for the language CLP( ). The primary issues are: how to verify the solvability of constraints in the structure by using some sound and complete semantic uni cation procedure such as narrowing, how to simplify constraints in a computation sequence, how to achieve incrementality in the computation process and how to pro t from nitely failed derivations as a heuristic for optimizing the algorithms.