We have discussed three basic problems that we feel limit the development of computational science---the connectivity, code generation and explanation problems. In earlier sections, we have given sample manifestations of these problems and have described how we foresee their amelioration. In brief, we believe that a combination of a mathematical software bus, a broad array of mathematical interchange formats and a variety of glue libraries will address the connectivity problem. We feel that the best approach to the code generation problem is through the use of program transformation techniques, which we and our colleagues have already successfully applied to a number of problems. A fundamental issue in any sort of collaboration, is a shared understanding of the meaning of mathematical expressions. This issue arises as a component of the connectivity problem. It is a technology that is needed to make libraries of transformations manageable and viable. This explanation problem will be addressed by the use of formal methods techniques.
The group of proposers is singularly well suited to address these problems with their experience in numerical, geometric and symbolic computing, programming languages, compilation and formal methods. In the body of the proposal we have indicated some of the technical details that need to be resolved in our research plan and our planned approach. Below we indicate the milestones we plan to meet on our path and through which we will measure our progress.