Implementation of Constructive Programming Based on Classical Logic

对于基于经典逻辑的构建编程的目标，本研究扩展了功能编程语言PA D2ct D2， which has catch/throw Mechanism as exception processing， and make the following result.首席调查员Sato studed the notion of binding variables， which is the portant notion for predicate logic and functional programming language。由于这项研究的结果，他提出了一个不需要重新计算绑定变量的计算。本结果是在1999年在意大利L'Aquia举行的第四次关于Lambda Calculi和应用的国际会议上提出的，由Kameyama研究的基于功能编程语言的经典逻辑和分类的类型Calculi进行的异常处理和部分连续性的研究。他解决了这种Calculi的问题和终结。本结果已发表在《理论计算机科学》中，研究者Takeuti研究了参数化多态性和数学索引之间的关系。数学索引是一种重要的方法，可以在构造性编程系统中推导出理论。他展示了数学定义的参数系统产生了各种形式的参数。这一结果发表在“Fundamenta Informaticae”上。

For the purpose of developing constructive programming based on classical logic, this research extended the functional programming language PAィイD2ctィエD2, which has catch/throw mechanism as exception processing, and made the following results.The head investigator Sato studied the notion of binding variables, which is the important notion for predicate logic and functional programming language. As the result of this study, he proposed a calculus which do not have renaming of bind variables. This result was presented in the 4th international conference on Typed Lambda Calculi and Application in 1999, at L'Aquia, Italy.The investigator Kameyama studied exception processing and partial contiunation in functional programming languages based on classical logic, and classified typical calculi with exception processing and partial continuation. He solved the problems of confluency and termination of such calculi. This results are to be published in 'Theoretical Computer Science'.The investigator Takeuti studied the relation between parametric polymorphism and mathematical induction. Mathematical induction is an important method to prove theorems in systems of constructive programming. He showed that system of parametricity derives various forms of mathematical induction. This result was published in 'Fundamenta Informaticae'.