We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by encoding properties at arbitrary timepoints and loop iterations. We guide and automate inductive loop reasoning in trace logic by using generic trace lemmas capturing inductive loop invariants. Our work is implemented in the RAPID framework, by extending and integrating superposition-based first-order reasoning within RAPID. We successfully used RAPID to prove correctness of many programs whose functional behavior are best summarized in the first-order theories of linear integer arithmetic, arrays and inductive data types.

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用于归纳循环推理的跟踪逻辑

我们提出了跟踪逻辑，这是多排序一阶逻辑的一个实例，可以自动对包含循环的程序进行部分正确性验证。跟踪逻辑概括了程序位置的语义，并通过在任意时间点和循环迭代对属性进行编码来捕获循环语义。我们通过使用通用跟踪引理捕获归纳循环不变量来指导和自动化跟踪逻辑中的归纳循环推理。我们的工作是在 RAPID 框架中实现的，通过在 RAPID 中扩展和集成基于叠加的一阶推理。我们成功地使用 RAPID 来证明许多程序的正确性，这些程序的功能行为在线性整数运算、数组和归纳数据类型的一阶理论中得到了最好的总结。