超越代数数据类型上的程序不变量的基本表示

Y. Kostyukov, D. Mordvinov, Grigory Fedyukovich
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引用次数: 13

摘要

一阶逻辑是表达计算性质的一种自然方式。它传统上用于各种程序逻辑中,用于表示正确性属性和证书。尽管这样的表示对于某些理论是表达性的,但它们不能表达代数数据类型(adt)的许多有趣的性质。在本文中,我们探讨了三种不同的方法来表示adt操作程序的程序不变量:树自动机和一阶公式有或没有大小约束。我们比较了这些表示的表达能力,并利用抽运引理证明了这两种一阶表示的负可定义性。本文提出了一种通过简化为有限模型查找器来自动推断adt操作程序的程序不变量的方法。被称为RInGen的实现已经与最先进的不变合成器进行了评估,并在实验中证明具有竞争力。特别是,由自动机表示的程序不变量能够表达更复杂的计算性质,并且它们的自动构造通常更便宜。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Beyond the elementary representations of program invariants over algebraic data types
First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some theories, they fail to express many interesting properties of algebraic data types (ADTs). In this paper, we explore three different approaches to represent program invariants of ADT-manipulating programs: tree automata, and first-order formulas with or without size constraints. We compare the expressive power of these representations and prove the negative definability of both first-order representations using the pumping lemmas. We present an approach to automatically infer program invariants of ADT-manipulating programs by a reduction to a finite model finder. The implementation called RInGen has been evaluated against state-of-the-art invariant synthesizers and has been experimentally shown to be competitive. In particular, program invariants represented by automata are capable of expressing more complex properties of computation and their automatic construction is often less expensive.
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