A Finite Representation of the Narrowing Space

Narrowing basically extends rewriting by allowing free variables in terms and by replacing matching with unification. As a consequence, the search space of narrowing becomes usually infinite, as in logic programming. In this paper, we introduce the use of some operators that allow one to always produce a finite graph that still represents all the narrowing derivations. Furthermore, we introduce a novel, compact equational representation of the (possibly infinite) answers computed by narrowing for a given initial term. Both the finite graphs and the equational representation of the computed answers might be useful in a number of areas, like program comprehension, static analysis, program transformation, etc.