Explanations For Dynamic Programming

We present an approach for explaining dynamic programming that is based on computing with a granular representation of values that are typically aggregated during program execution. We demonstrate how to derive more detailed and meaningful explanations of program behavior from such a representation than would otherwise be possible. To illustrate the practicality of this approach we also present a Haskell library for dynamic programming that allows programmers to specify programs by recurrence relationships from which implementations are derived that can run with granular representation and produce explanations. The explanations essentially answer questions of why one result was obtained instead of another. While usually the alternatives have to be provided by a user, we will show that with our approach such alternatives can be in some cases anticipated and that corresponding explanations can be generated automatically.