Abstract
Symplectic geometry is a versatile geometric theory widely used in many disciplines such as analytical mechanics, geometric topology and Lie group. However, when symplectic geometry is applied in practice, the satisfaction of its preconditions is often not formally verified. Therefore, it is necessary to make verifications on symplectic geometry and its applications. The purpose of the present work is to conduct such verifications by establishing a formal theorem library in HOL-Light. For this purpose, seven basic concepts are formalized at first. Then, the properties of symplectic vector spaces and symplectic matrices are formally verified. To validate the correctness of the formalized symplectic geometry and to demonstrate its applications, formal analysis is finally made on the symplectic features of matrix optics. The present work not only lays a necessary foundation for formal verifications in this field but also extends the library of theories of the HOL-Light system. Based on this foundation, some more sophisticated symplectic geometry theories and their engineering applications can be further formalized and verified.
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Acknowledgment
This work was supported by the National Natural Science Foundation of China (61472468, 61572331, 61602325, 61702348), the National Key Technology Research and Development Program (2015BAF13B01), National Key R&D Plan (2017YFC0806700, 2017YFB130253), the Project of the Beijing Municipal Science & Technology Commission (LJ201607) and Capital Normal University Major (key) Nurturing Project.
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Wang, G., Guan, Y., Shi, Z., Zhang, Q., Li, X., Li, Y. (2018). Formalization of Symplectic Geometry in HOL-Light. In: Sun, J., Sun, M. (eds) Formal Methods and Software Engineering. ICFEM 2018. Lecture Notes in Computer Science(), vol 11232. Springer, Cham. https://doi.org/10.1007/978-3-030-02450-5_16
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DOI: https://doi.org/10.1007/978-3-030-02450-5_16
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