采用形式化方法证明软件的正确性，是保障软件可靠性的有效方法.而对循环语句的分析与验证，是形式化证明中的关键，对循环语句的处理一直是程序分析与验证中的一个难点问题.提出使用循环语句修改的内存和这些内存中存放的新值来描述循环语句的执行效果，并将该执行效果定义为循环摘要.同时，提出一种自动生成循环摘要的方法，可以为操作常用数据结构的循环自动生成循环摘要，包含嵌套循环.此外，基于循环摘要，可以自动生成循环语句的规约，包括循环不变式、循环的前置条件以及循环的后置条件.已经实现了自动生成循环摘要以及循环规约的方法，并将它们集成到验证工具Accumulator中.实验结果表明，该方法可以有效地生成循环摘要，并生成多种类型的规约，从而辅助软件程序的形式化证明，提高验证的自动化程度和效率，减轻验证人员的负担.

Formal verification is an effective method to guarantee software reliability by proving the correctness of a program. Analyzing and verifying loops which are important and frequently-used statements is not only vital for formal verification, but also a hot topic in the research area of software development. This paper proposes using memories modified by a loop and new values stored in these memories after executing the loop to describe the execution effect of the loop. Such execution effect is defined as loop summary. In addition, this paper proposes an approach to automatically synthesize loop summaries for loops manipulating commonly-used data structures, including nested loops. Based on loop summaries, specifications can be generated automatically, including loop invariants, preconditions and post-conditions of loops. The proposed approach is implemented and integrated into the code-verification tool Accumulator. The approach is also evaluated with a variety of programs, and the results show that it is able to generate loop summaries and different kinds of specifications, therefore helping to ease the verification task by reducing the burden for programmers and improving the automatic level and efficiency.

国家自然科学基金（61632015，61561146394）；国家重点研发计划（2016YFB1000802）