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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 160875, 7 pages
The Gauge Integral Theory in HOL4
1Beijing Engineering Research Center of High Reliable Embedded System, Capital Normal University, Beijing 100048, China
2State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
3College of Information Science and Engineering, Graduate University of Chinese Academy of Sciences, Beijing 100049, China
4College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China
5School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Received 6 February 2013; Accepted 27 February 2013
Academic Editor: Xiaoyu Song
Copyright © 2013 Zhiping Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- C. Kern and M. R. Greenstreet:, “Formal verification in hardware design: a survey,” ACM Transactions on Design Automation of Electronic Systems, vol. 4, no. 2, pp. 123–193, 1999.
- Stefan Richter, “Formalizing integration theory with an application to probabilistic algorithms,” in Proceedings of the 17th International Conference on Theorem Proving in Higher Order Logics (TPHOLs '04), K. Slind, A. Bunker, and G. Gepalakrishnan, Eds., vol. 3223 of Lecture Notes in Computer Science, pp. 271–286, Springer, Park City, Utah, USA, September 2004.
- J. D. Fleuriot, “On the mechanization of real analysis in Isabelle/HOL,” in Theorem Proving in Higher Order Logics, pp. 145–161, 2000.
- L. Cruz-Filipe, Constructive real analysis: a type-theoretical formalization and applications [Ph.D. thesis], University of Nijmegen, 2004.
- R. W. Butler, “Formalization of the integral calculus in the PVS theorem prover,” Journal of Formalized Reasoning, vol. 2, no. 1, pp. 1–26, 2009.
- T. Mhamdi, O. Hasan, and S. Tahar, “On the formalization of the Lebesgue integration theory in HOL,” in Interacitve Theorem Proving, vol. 6172 of Lecture Notes in Computer Science, pp. 387–402, Springer, 2010.
- J. Harrison, Theorem Proving with the Real Numbers, Springer, Heidelberg, Germany, 1998.
- C. Swartz, Introduction to Gauge Integrals, World Scientific, Singapore, 2001.
- R. A. Gordon, The Integrals of Lebesgue, Denjoy, Perron, and Henstock, vol. 4 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1994.