Formalization of Matrix Theory in HOL4-Reference-Cited by-同舟云学术

Formalization of Matrix Theory in HOL4

Published:2014-01-01 Issue: Volume:6 Page:195276
ISSN:1687-8140
Container-title:Advances in Mechanical Engineering
language:en
Short-container-title:Advances in Mechanical Engineering

Author:

Shi Zhiping¹²³,Zhang Yan¹,Liu Zhenke¹,Kang Xinan¹,Guan Yong¹,Zhang Jie⁴,Song Xiaoyu⁵

Affiliation:

1. Beijing Key Laboratory of Electronic System Reliability Technology, Capital Normal University, Beijing 100048, China

2. State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences, 100190, China

3. Guangxi Key Laboratory of Trusted Software, Guilin University of Electronic Technology, 541004, China

4. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China

5. Electrical and Computer Engineering, Portland State University, Portland, OR 97201, USA

Abstract

Matrix theory plays an important role in modeling linear systems in engineering and science. To model and analyze the intricate behavior of complex systems, it is imperative to formalize matrix theory in a metalogic setting. This paper presents the higher-order logic (HOL) formalization of the vector space and matrix theory in the HOL4 theorem proving system. Formalized theories include formal definitions of real vectors and matrices, algebraic properties, and determinants, which are verified in HOL4. Two case studies, modeling and verifying composite two-port networks and state transfer equations, are presented to demonstrate the applicability and effectiveness of our work.

Funder

International Cooperation Program on Science and Technology

Publisher

SAGE Publications

Subject

Mechanical Engineering

Link

http://journals.sagepub.com/doi/pdf/10.1155/2014/195276

Reference14 articles.

1. Formal verification in hardware design

2. Mathematics mechanization and applications after thirty years

3. Proof System for Applied Pi Calculus

4. A novel formalization of symbolic trajectory evaluation semantics in Isabelle/HOL

5. A Family of Dynamic Description Logics for Representing and Reasoning About Actions

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Towards Verified Rounding Error Analysis for Stationary Iterative Methods;2022 IEEE/ACM Sixth International Workshop on Software Correctness for HPC Applications (Correctness);2022-11

2. Formal verification of Matrix based MATLAB models using interactive theorem proving;PeerJ Computer Science;2021-03-22

3. Formalization of Camera Pose Estimation Algorithm based on Rodrigues Formula;Formal Aspects of Computing;2020-11

4. Formalization of continuous Fourier transform in verifying applications for dependable cyber-physical systems;Journal of Systems Architecture;2020-06

5. Formal analysis of the kinematic Jacobian in screw theory;Formal Aspects of Computing;2018-11