构造型几何定理及其机器证明系统

Hilbert 机械化定理表明,Pascal 几何中构造型交点定理可以机器证明。1982年,吴文俊教授给出了机械化定理的构造性证法。本文指出,通过添加若干新的构造类型,有更广泛的一类平面几何定理,其机器证明可以按照同样的构造性证法实现,我们称这类定理为构造型几何定理。作者适当调整吴文俊算法的步骤,在 HP1000小型计算机上建立了构造型几何定理的机器证明系统,效率大大提高,从而成功地证明了许多不平凡的几何定理,并且独立发现了相当深入的结果。

A MECHANICAL PROVING SYSTEM FOR CONSTRUCTIBLE THEOREMS IN ELEMENTARY GEOMETRY

In this paper,we point out that Hilbert's Mechanization Theorem may be extended to allconstructible theorems which can be mechanically proved in the same way by adjoining somenew constructive types.Using the Theorem-Prover built by the authors in rearranging thesteps of Wu's algorithm,many non-trivial theorems have been proved and some new resultshave also been discovered independently.