The Gauge Integral Theory in HOL4
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 line...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/160875 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |