Cheap Tupling Transformation

Tupling is a well-known transformation tactic to obtain new recursive functions without redundant recursive calls and/or multiple traversals of common data, which is achieved by grouping some recursive functions into a tuple. Although being studied for a long time based on fold/unfold transformation, it su ers from the high cost of keeping track of function calls and has to use clever control to avoid in nite unfolding, which prevent it from being used in a practical compiler of functional languages. In this paper, we propose a cheap tupling based on the theory of constructive algorithmics. We give several simple but e ective calculational rules, which not only can be successfully applied to improve a lot of interesting recursive functions but also can be implemented e ciently.