Narrowing the Narrowing Space

We introduce a framework for managing as a whole the space of a narrowing computation. The aim of our framework is to find a finite representation of an infinite narrowing space. This, in turn, allows us to replace an infinite enumeration of computed answers with an equivalent finite representation. We provide a semidecidable condition for this result. Our framework is intended to be used by implementations of functional logic programming languages. Our approach borrows from the memoization technique used in the implementation of functional languages. Since narrowing adds non-determinism and unifiers to functional evaluation, we develop a new approach based on graphs to memoize the outcome of a goal.