Mathematics of Program Construction

Algebraic dynamic programming is a new method for developing and reasoning about dynamic programming algorithms. In this approach, so-called yield grammars and evaluation algebras constitute abstract specifications of dynamic programming algorithms. We describe how this theory is put to practice by providing a specification language that can both be embedded in a lazy functional language, and translated into an imperative language. Parts of the analysis required for the latter translation also gives rise to source-to-source transformations that improve the asymptotic efficiency of the functional implementation. The multi-paradigm system resulting from this approach provides increased programming productivity and effective validation.