Ensuring Global Termination of Partial Deduction while Allowing Flexible Polyvariance

The control of polyvariance is a key issue in partial deduction of logic programs. Certainly, only finitely many specialised versions of any procedure should be generated, while, on the other hand, overly severe limitations should not be imposed. In this paper, well-founded orderings serve as a starting point for tackling this so-called “global control” problem. Polyvariance is determined by the set of distinct “partially deduced” atoms generated during partial deduction. Avoiding ad-hoc techniques, we formulate a quite general framework where this set is represented as a tree structure. Associating weights with nodes, we define a well-founded order among such structures, thus obtaining a foundation for certified global termination of partial deduction. We present a terminating and correct template algorithm, concrete instances of which can be used in actual implementations, and report on the results of some experiments. Finally, we argue that the proposed framework can enhance the understanding of and support further advances towards (fully automatic) optimal program specialisation.