We consider Hoare-style verification for the graph programming language GP 2. In previous work, graph properties were specified by so-called E-conditions which extend nested graph conditions. However, this type of assertions is not easy to comprehend by programmers that are used to formal specifications in standard first-order logic. In this paper, we present an approach to verify GP 2 programs with a standard first-order logic. We show how to construct a strongest liberal postcondition with respect to a rule schema and a precondition. We then extend this construction to obtain strongest liberal postconditions for arbitrary loop-free programs. Compared with previous work, this allows to reason about a vastly generalised class of graph programs. In particular, many programs with nested loops can be verified with the new calculus.

中文翻译：

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用一阶逻辑验证图程序（扩展版）

我们考虑了图编程语言 GP 2 的 Hoare 式验证。在之前的工作中，图属性由扩展嵌套图条件的所谓 E 条件指定。然而，对于习惯于标准一阶逻辑中的形式规范的程序员来说，这种类型的断言并不容易理解。在本文中，我们提出了一种使用标准一阶逻辑验证 GP 2 程序的方法。我们展示了如何根据规则模式和先决条件构建最强的自由后置条件。然后我们扩展这个构造以获得任意无循环程序的最强自由后置条件。与之前的工作相比，这允许对一类广泛泛化的图程序进行推理。特别是，许多带有嵌套循环的程序都可以用新的微积分进行验证。