A Modular Derivation Strategy via Fusion and Tupling

We show how programming pearls can be systematically derived via fusion, followed by tupling transformations. By focusing on the elimination of intermediate data structures (fusion) followed by the elimination of redundant calls (tupling), we can systematically realise both space and time e cient algorithms from naive speci cations. We illustrate our approach using a well-known maximum segment sum (MSS) problem, and a lesser-known maximum segment product (MSP) problem. While the two problems share similar speci cations, their optimised codes are signi cantly di erent. This divergence in their transformed codes do not pose any di culty for our approach. In fact, by relying on modular transformation techniques, we are able to systematically reuse both code and transformation in our derivation.