Geometric Programming System

（1）几何编程语言的设计和实现，我们设计和实现了一种名为GPL的代数约束编程语言。使用全局变量-功能覆盖-阵列（Indefinite Size - Constraint Inheritance-Automatic Type Conversion）· We showed that various geometric objects such as images， points， lines， polygons and so on can be compactly described in GPL， and that facilities of function overloading， constraint inheritance，而且类型转换对于处理这些几何对象来说是非常有用的描述运算符。作为一个未来的问题，我们应该开发一个GPL的编译器。（2）通过综合逻辑和代数推理开发几何推理系统--我们开发了一种基于逻辑推理的新的几何推理方法，其中集成了基于第一顺序预测计算和代数推理使用格罗夫纳基方法的逻辑推理。我们开发了一种几何定理，并展示了新的推理方法比普通的方法更有力量。

(1)Design and Implementation of Geometric Programming Language ・ We designed and implemented an algebraic constraint programming language named GPL. Major characteristics of GPL are - Functional Programming Language with Global Variables - Function Overloading - Array of Indefinite Size - Constraint Inheritance - Automatic Type Conversion ・ We showed that various geometric objects such as images, points, lines, polygons and so on can be compactly described in GPL, and that facilities of function overloading, constraint inheritance, and type conversion are very useful to describe operators to process those geometric objects. ・ As a future problem, we should develop a compiler of GPL.(2)Development of Geometric Reasoning System by Integrated Logical and Algebraic Reasoning ・ We devised a new geometric reasoning method which integrates both logical reasoning based on the first order predicate calculus and algebraic reasoning using Grobner basis method. ・ We developed a geometric theorem prover and showed that the new reasoning method is more powerful than ordinary ones.