An interdisciplinary study on categorical computer mathematics

该项目的目的是从跨学科的角度对分类计算机数学进行调查。所有参加这个研究项目的研究人员都研究了范畴理论、Dedekind范畴、最终余代数、二维行刑队同步、证明和类型理论、均匀延迟电路的完备性、符号逻辑和计算逻辑、真实的函数的归纳推理、带有捕捉和抛出规则的直觉主义和经典自然演绎系统、通过实例测试证明以及蛋白质线程的近似，与范畴论的数学有关。作为研究项目的结果，我们在日本广泛地发展了计算机数学，即我们给出了许多有用的应用数学的新理论，证明了逻辑学、范畴论、自动机论和人工智能中的新定理，并最终提出了当代应用数学的新趋势。此外，首席研究员还在龙谷大学组织了日本应用数学联合会议，1996年12月、1997年12月和1998年12月塞塔市。(This联席会议的历史相当悠久，大约有三十年之久。该研究项目的详细摘要载于九州大学信息学系1999年3月印发的研究项目报告（小册子）。研究负责人代表项目研究者感谢给予的资金支持。

This project was organized for investigations on categorical computer mathematics from inter-disciplinary viewpoints. All the investigators joining with this research project studied theoryﾟCof categories, Dedekind categories, final coalgebras, two-dimensional firing squad synchro-nization, proof and type theories, completeness for uniformly delayed circuits, symbolic and computational logics, inductive inference of real functions, intuitionistic and classical natural deduction systems with catch and throw rules, testing proofs by examples, and an approximation of protein threading, concerned with mathematics of category theory. As the results of the research projects we extensively developed computer mathematics in Japan, that is, we gave a lot of new theories of useful applied mathematics, proved new theorems in logic, category theory, automata theory, and artificial intelligence, and finally suggested new trends of contemporary applied mathematics.Also the head investigator organized the Japanese joint conferences of applied mathematics at Ryukoku University, Seta City in December 1996, December 1997 and December 1998. (This joint conference has rather long history about thirty years long.) The detailed summary of this research project is described in the report of the research project (booklet), printed in Department of Informatics, Kyushu University, March 1999. The head investigator, on behalf of investigators of the project, is grateful for giving the financial support.