A Conceptual Embedding of Folding into Partial Deduction: Towards a Maximal Integration

The relation between partial deduction and the unfold/fold approach has been a matter of intense discussion. In this paper we consolidate the advantages of the two approaches and provide an extended partial deduction framework in which most of the tupling and deforestation transformations of the fold/unfold approach, as well the current partial deduction transformations, can be achieved. Moreover, most of the advantages of partial deduction, e.g. lower complexity and a more detailed understanding of control issues, are preserved. We build on well-defined concepts in partial deduction and present a conceptual embedding of folding into partial deduction, called conjunctive partial deduction. Two minimal extensions to partial deduction are proposed: using conjunctions of atoms instead of atoms as the principle specialisation entity and also renaming conjunctions of atoms instead of individual atoms. Correctness results for the extended framework (with respect to computed answer semantics and finite failure semantics) are given. Experiments with a prototype implementation are presented, showing that, somewhat to our surprise, conjunctive partial deduction not only handles the removal of unnecessary variables, but also leads to substantial improvements in specialisation for standard partial deduction examples.