• 中国计算机学会会刊
  • 中国科技核心期刊
  • 中文核心期刊

计算机工程与科学 ›› 2023, Vol. 45 ›› Issue (07): 1178-1187.

• 高性能计算 • 上一篇    下一篇

格林定理的形式化及其初步应用

刘永梅1,2,王国辉1,关永2,张景芝2,施智平1,2,董璐1   

  1. (1.首都师范大学信息工程学院,北京 100048;
    2.电子系统可靠性与数理交叉学科国际科技合作基地,北京 100048)
  • 收稿日期:2022-03-01 修回日期:2022-07-27 接受日期:2023-07-25 出版日期:2023-07-25 发布日期:2023-07-11
  • 基金资助:
    国家重点研发计划(2019YFB1309900);国家自然科学基金(62002246,62272322,62272323);科技创新服务能力建设-基本科研业务费(科研费)项目(00621530290000)

Formal verification of Greens theorem and its applications

LIU Yong-mei1,2,WANG Guo-hui1,GUAN Yong2,ZHANG Jing-zhi2,SHI Zhi-ping1,2,DONG Lu1    

  1. (1.Information  Engineering College,Capital Normal University,Beijing 100048;
    2.International Science and Technology Cooperation Base of Electronic System Reliability 
    and Mathematical Interdisciplinary,Capital Normal University,Beijing 100048,China)
  • Received:2022-03-01 Revised:2022-07-27 Accepted:2023-07-25 Online:2023-07-25 Published:2023-07-11

摘要: 格林定理广泛应用于物理学、流体力学和化学等领域。通常使用传统的计算机仿真和数值计算方法构建基于格林定理的系统模型。然而,由于工具软件可能存在的系统缺陷导致模型出现偏差,从而使任务失败。为解决上述问题,采用基于高阶逻辑的形式化方法,在定理证明器HOL Light中实现了格林定理相关内容的高阶逻辑建模与验证。首先,对梯度、散度等基本概念和性质进行了形式化描述;其次,对格林定理及其性质进行了形式化建模与验证;最后,基于格林定理的形式化模型完成了地下水控制模型的高阶逻辑推导,进而确保系统模型的安全性。

关键词: 形式化验证, 定理证明, 格林定理, HOL Light

Abstract: Greens theorem is widely used in physics, hydrodynamics, chemistry and other fields. Traditional computer simulation and numerical calculation methods are usually used to build the system model based on Greens theorem. However, the possible system defects in the tool software lead to the deviation of the model, which makes the task fail. In order to solve the above problems, this paper adopts the formalization method based on higher-order logic to realize the higher-order logic modeling and verification of Greens theorem related content in the theorem prover HOL Light. Firstly, the basic concepts and properties of gradient and divergence are formally described. Secondly, formal modeling and verification of Greens theorem and its properties are carried out. Finally, the high-level logical derivation of groundwater control model is completed based on the formal model of Greens theorem, so as to ensure the safety of the system model.

Key words: formal verification, theorem proving, Greens theorem, HOL Light