Gauge积分在HOL4中的形式化

Formalization of Gauge Integration Theory in HOL4

积分是许多数学理论的基础,如实数分析、信号与系统中微分方程的求解等等。Gauge积分是黎曼积分在闭区间上的推广,应用更加方便。将Gauge积分的运算性质在HOL4(Higher-Order Logic 4)中形式化,包括积分的线性运算性质、积分不等式、分部积分、积分分裂定理、子区间的可积性、对特殊函数的积分的形式化及积分极限定理、柯西可积准则,并根据相关性质对反相积分器进行了验证。

Integral is one of the most important foundations in many subjects, such as real analysis, the differential equa tions in signals and systems and so on. Gauge integral is a generalization of the Riemann integral in which some situa- tions are more useful than the Lebesgue integral. This paper formalized the operational properties which contain the fin- earity, ordering properties, integration by parts, the special functions and limit theorem, eauehy-type （HOIA）, and then used them to verify an inverting integral split theorem,integrability on a subinterval, integrability of integrability criterion of gauge integral in higher-order-logic 4 integrator.