The investigators on this proposal come from a wide range disciplines within Computer Science: numerical analysis, computational geometry, symbolic computing, compilation, and applied logic. While each of our research interests are different, we have always found a common language for explaining our interests to each other---the language of computational mathematics. As we have started to look at larger scale computations and problems, we have found a need to combine the ideas and techniques we each developed. This process has led us to the observation that the software tools we have created cannot communicate and collaborate as readily as we can. As a matter of fact, in general, these tools cannot interoperate at all, except at the most primitive level, without significant design and coding effort.
Through discussions over the past two years, we have developed a coordinated plan to resolve what we believe are the basic problems of software collaboration. The resolution we advocate can be summarized as: Raise the semantic level of communications between programs from the level of text to the level of mathematics.
In Section 1.1 we briefly discuss the basic problems and relate them to our experiences. A summary of the research plan we intend to pursue to resolve these problems is given in Section 1.2 . Each of the three basic problems and the research program that addresses each of those problems is presented in Sections 2, 3 and 4. Additional detail on the database opportunity and the research required to undertake this project is given in Section 5 .