基于划分递归和Morgan精化规则的非线性程序构造与验证方法

Changjing Wang, Zhongxiong Cao, Chul-Hi Yu, Changchang Wang, Qing Huang, Z. Zuo
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引用次数: 0

摘要

传统的程序精化策略不能精化为可执行的程序,存在验证可靠性低、自动化程度低等问题。针对上述问题,本文提出了一种基于划分递归和Morgan细化规则的非线性程序构造与验证方法。首先,我们使用递归定义技术来描述初始规范。然后使用循环不变量推导和Morgan的细化规则将规范转换为GCL(保护命令语言)程序。此外,在GCL程序中使用VCG (Verification Condition Generator)自动生成验证条件。伊莎贝尔定理证明者然后验证GCL程序的正确性。最后,GCL代码通过转换系统自动生成一个c++可执行程序。通过二叉树预序遍历程序的构造与验证,验证了该方法的有效性。该方法解决了构造过程的循环不变量难以获得和细化过程不够详细的问题。同时,提高了验证过程的自动化程度,减少了手工验证的工作量。
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Nonlinear Program Construction and Verification Method Based on Partition Recursion and Morgan's Refinement Rules
The traditional program refinement strategy cannot be refined to an executable program, and there are issues such as low verification reliability and automation. To solve the above problems, this paper proposes a nonlinear program construction and verification method based on partition recursion and Morgan's refinement rules. First, we use recursive definition technique to characterize the initial specification. The specification is then transformed into GCL(Guarded Command Language) programs using loop invariant derivation and Morgan's refinement rules. Furthermore, VCG (Verification Condition Generator) is used in the GCL program to generate the verification condition automatically. The Isabelle theorem prover then validates the GCL program's correctness. Finally, the GCL code generates a C++ executable program automatically via the conversion system. The effectiveness of this method is demonstrated using binary tree preorder traversal program construction and verification as an example. This method addresses the problem that the construction process's loop invariant is difficult to obtain and the refinement process is insufficiently detailed. At the same time, the method improves verification process automation and reduces the manual verification workload.
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来源期刊
Wuhan University Journal of Natural Sciences
Wuhan University Journal of Natural Sciences Multidisciplinary-Multidisciplinary
CiteScore
0.40
自引率
0.00%
发文量
2485
期刊介绍: Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.
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