Program Fusion with Paramorphisms

The design of programs as the composition of smaller ones is a wide spread approach to programming. In functional programming, this approach raises the necessity of creating a good amount of intermediate data structures with the only aim of passing data from one function to another. Using program fusion techniques, it is possible to eliminate many of those intermediate data structures by an appropriate combination of the codes of the involved functions. In the standard case, no mention to the eliminated data structure remains in the code obtained from fusion. However, there are situations in which parts of that data structure becomes an internal value manipulated by the fused program. This happens, for example, when primitive recursive functions (so-called paramorphisms) are involved. We show, for example, that the result of fusing a primitive recursive function p with another function f may give as result a function that contains calls to f. Moreover, we show that in some cases the result of fusion may be less efficient than the original composition. We also investigate a general recursive version of paramorphism. This study is strongly motivated by the development of a fusion tool for Haskell programs called HFUSION.