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The new generic scheme CF LP (D) has been recently proposed in [24] as a logical and semantic framework for lazy constraint functional logic programming over a parametrically given constraint domain D. In this paper we extend such framework with a suitable operational semantics, which relies on a new constrained lazy narrowing calculus for goal solving parameterized by a constraint solver over the given domain D. This new calculus is sound and strongly complete w.r.t. the declarative semantics of CF LP (D) programs, which was formalized in [24] by means of a Constraint Rewriting Logic CRW L(D).

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