Proc. of the 11th International Workshop on Functional and (Constraint) Logic Programming (WFLP 2002).
Needed narrowing is a complete and optimal operational principle for modern declarative languages which integrate the best features of (lazy) functional and logic programming. This paper investigates the formal relation between needed narrowing and another (not so lazy) demand-driven narrowing strategy which is the basis for popular implementations of non-strict functional logic languages. We demonstrate that needed narrowing and demand-driven lazy narrowing are computationally equivalent over the class of uniform programs, i.e., both strategies compute the same answers and values over this class of programs. We also introduce a complete refinement of demand-driven lazy narrowing, called uniform lazy narrowing, which is still equivalent to needed narrowing over the aforementioned class. Since actual implementations of functional logic languages are based on the transformation of the original program into a uniform one, which is then executed using the (demand-driven) lazy narrowing strategy, our results can be thought of as a formal basis for the correctness of these implementations.
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