On Program Transformation with Tupling Technique.

In this paper, we construct a theory for an automatic program transformation with tupling technique. We introduce a purely applicative programming language and formalize a problem to find a tuple for transformation of a recursive program written in the language. We discuss the transformation scheme with the tuple given as the solution to the problem and show that the execution efficiency will be improved by the new scheme. Under a certain constraint, we describe the method to find a tuple for a given program.