Computer Science ›› 2016, Vol. 43 ›› Issue (11): 24-29.doi: 10.11896/j.issn.1002-137X.2016.11.005

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Higher-order Logic Formalization of Function Matrix and its Calculus

YANG Xiu-mei, GUAN Yong, SHI Zhi-ping, WU Ai-xuan, ZHANG Qian-ying and ZHANG Jie   

  • Online:2018-12-01 Published:2018-12-01

Abstract: Function matrix is widely employed in the modeling and analysis of dynamic system.Paper-pencil calculations,numerical calculations and symbolic algebra methods,which are used in traditional analysis of function matrix,cannot guarantee to provide accurate or correct results.Higher-order logic theorem proving,as a kind of highly reliable formal verification method,can overcome the above shortcomings.This paper formalized the related theories of function vector and function matrix in the higher-order logic theorem prover HOL4.Formal contents include the formal definitions and proving of function vector and function matrix,and their properties of continuity,differential and integral.The formal verification of the differential equation of rotation matrix in the robotic kinematics was given to illustrate the application of the formalization.

Key words: Function matrix,Calculus,Formal verification,Higher-order logic theorem proving

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