A short cut to optimal sequences

We propose a method of developing efficient programs for finding the optimal sequence, such as the maximum valued one among those that are acceptable. We introduce a method of deriving efficient algorithms from naive enumerate-and-choose-style ones. Our method is based on shortcut fusion, which is a program transformation for eliminating intermediate data structures passed between functions, and a set of auxiliary transformations. As an implementation of our method, we introduce a library for finding optimal sequences. The library consists of proposed transformations, together with functions useful to describe desirable sequences, so that naive enumerate-and-choose-style programs will be automatically improved.