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A Precise Pictorial Language for Array Invariants

机译:数组不变量的精确图示语言

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Pictorial languages, while intuitive and descriptive, are rarely used as the primary reasoning language in program verification due to lack of precision. In this paper, we introduce a precise pictorial language for specifying array invariants that preserves visual perspicuity. The language extends Reynold's partition diagrams with the notion of a coloring, allowing assertions over portions of an array to be expressed by color-coding. The semantics of a coloring is given by a legend, mapping a colored partition of an array into a universally quantified predicate over the array. The pictorial syntax is an extension toinvariant diagrams, transition graphs where preconditions, postconditions and invariants, rather than the program code, determine the main program structure. We demonstrate the approach with three examples, verified using the Why3 theorem prover frontend.
机译:图形语言虽然直观且具有描述性,但由于缺乏精确性,因此很少被用作程序验证中的主要推理语言。在本文中,我们介绍了一种精确的图形语言,用于指定保留数组视觉不变性的数组不变量。该语言以着色的概念扩展了雷诺的分区图,从而允许通过颜色编码来表达数组各部分上的断言。着色的语义由图例给出,将图例的有色分区映射到数组上通用量化的谓词中。图形语法是对不变图,过渡图的扩展,其中前提条件,后置条件和不变条件(而不是程序代码)决定主程序结构。我们用三个示例演示了该方法,并使用Why3定理证明者前端进行了验证。

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