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The Gauge Integral Theory in HOL4

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  • Zhiping Shi
  • Weiqing Gu
  • Xiaojuan Li
  • Yong Guan
  • Shiwei Ye
  • Jie Zhang
  • Hongxing Wei

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.

Suggested Citation

  • Zhiping Shi & Weiqing Gu & Xiaojuan Li & Yong Guan & Shiwei Ye & Jie Zhang & Hongxing Wei, 2013. "The Gauge Integral Theory in HOL4," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    • Handle: RePEc:hin:jnljam:160875
    DOI: 10.1155/2013/160875
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