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From Matching Logic To Parallel Imperative Language Verification
arXiv - CS - Formal Languages and Automata Theory Pub Date : 2021-02-08 , DOI: arxiv-2102.04011
ShangBei Wang

Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational semantics and can't seriously validate the program. Matching logic is proposed to make program verification based on operational semantics. In this paper, following Grigore Ro{\c{s}}u 's work, we consider matching logic for parallel imperative language(PIMP). According to our investigation, this paper is the first study on matching logic for PIMP. In our matching logic, we redefine "interference-free" to character parallel rule and prove the soundness of matching logic to the operational semantics of PIMP. We also link PIMP's operational semantics and PIMP's verification formally by constructing a matching logic verifier for PIMP which executes rewriting logic semantics symbolically on configuration patterns and is sound and complete to matching logic for PIMP. That is our matching logic verifier for PIMP is sound to the operational semantics of PIMP. Finally, we also verify the matching logic verifier through an example which is a standard problem in parallel programming.

中文翻译:

从匹配逻辑到并行命令式语言验证

程序验证是为了开发程序的证明系统,并根据程序的可信操作语义证明证明系统的健全性。但是,许多实用的程序验证程序都不基于操作语义,因此无法认真验证程序。提出了匹配逻辑以基于操作语义进行程序验证。在本文中,根据Grigore Ro {\ c {s}} u的工作,我们考虑了并行命令式语言(PIMP)的匹配逻辑。根据我们的调查,本文是针对PIMP匹配逻辑的首次研究。在我们的匹配逻辑中,我们将“无干扰”重新定义为字符并行规则,并证明匹配逻辑对于PIMP的操作语义的正确性。我们还将PIMP的操作语义与PIMP 通过构造用于PIMP的匹配逻辑验证器来正式进行验证,该验证器在配置模式上象征性地执行重写逻辑语义,并且对于PIMP的匹配逻辑是健全而完整的。那就是我们针对PIMP的匹配逻辑验证程序对PIMP的操作语义是合理的。最后,我们还通过一个示例验证了匹配逻辑验证器,该示例是并行编程中的一个标准问题。
更新日期:2021-02-09
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