The Gauge Integral Theory in HOL4. (2nd May 2013) - Shi, Zhiping; Gu, Weiqing; Li, Xiaojuan; Guan, Yong; Ye, Shiwei; Zhang, Jie; Wei, Hongxing
Abstract : The integral is one of the most important foundations for modeling dynamical systems. The gauge integral is a generalization of the Riemann integral and the Lebesgue integral and applies to a much wider class of functions. In this paper, we formalize the operational properties which contain the linearity, monotonicity, integration by parts, the Cauchy-type integrability criterion, and other important theorems of the gauge integral in higher-order logic 4 (HOL4) and then use them to verify an inverting integrator. The formalized theorem library has been accepted by the HOL4 authority and will appear in HOL4 Kananaskis-9.