Transformation of Divide & Conquer to Nested Parallel Loops

We propose a sequence of equational transformations and specializations which turns a divide-and-conquer skeleton in Haskell into a parallel loop nest in C. Our initial skeleton is often viewed as general divide-and-conquer. The specializations impose a balanced call tree, a xed degree of the problem division, and elementwise operations. Our goal is to select parallel implementations of divide-and-conquer via a space-time mapping, which can be determined at compile time. The correctness of our transformations is proved by equational reasoning in Haskell; recursion and iteration are handled by induction. Finally, we demonstrate the practicality of the skeleton by expressing Strassen's matrix multiplication in it.