Abstract
Dynamic programming algorithms are traditionally expressed by a set of table recurrences -- a low level of abstraction which renders the design of novel dynamic programming algorithms difficult and makes debugging cumbersome.Bellman's GAP is a declarative language supporting dynamic programming over sequence data. It implements algebraic dynamic programming and allows specifying algorithms by combining so-called yield grammars with evaluation algebras. Products on algebras allow to create novel types of analysis from already given ones, without modifying tested components. Bellman's GAP extends the previous concepts of algebraic dynamic programming in several respects, such as an interleaved product operation and the analysis of multi-track input.Extensive analysis of the yield grammar is required for generating efficient imperative code from the algebraic specification. This article gives an overview of the analyses required and presents three of them in detail. Measurements with real-world applications demonstrate the quality of the code produced.
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