通过有效的命题公式对堆路径进行模块化推理

Shachar Itzhaky, A. Banerjee, N. Immerman, O. Lahav, Aleksandar Nanevski, Shmuel Sagiv
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引用次数: 30

摘要

具有传递闭包的一阶逻辑和分离逻辑使堆操作程序能够进行优雅的交互式验证。然而,不可判定的结果和检查有效性的高渐近复杂性阻碍了这些程序的完全自动验证,即使在这些逻辑中循环不变量和过程契约被指定为公式时也是如此。本文利用高效的完整决策过程解决了堆操作程序可达性特性的过程模块化验证问题:即,每当程序不满足其规范时,SAT求解器必须生成反例。通过(a)要求每个过程修改一组固定的堆分区并创建有限数量的堆共享,以及(b)限制程序契约和循环不变量仅使用堆中的确定性路径,我们表明堆可达性更新可以用一种简单的方式描述。这些限制迫使程序规范和验证条件位于具有传递闭包的一阶逻辑片段中,该片段可简化为有效的命题逻辑,从而促进健全,完整和有效的验证。我们在Z3上实现了一个工具,并报告了初步实验,这些实验建立了几个操作链接数据结构的程序的正确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modular reasoning about heap paths via effectively propositional formulas
First order logic with transitive closure, and separation logic enable elegant interactive verification of heap-manipulating programs. However, undecidabilty results and high asymptotic complexity of checking validity preclude complete automatic verification of such programs, even when loop invariants and procedure contracts are specified as formulas in these logics. This paper tackles the problem of procedure-modular verification of reachability properties of heap-manipulating programs using efficient decision procedures that are complete: that is, a SAT solver must generate a counterexample whenever a program does not satisfy its specification. By (a) requiring each procedure modifies a fixed set of heap partitions and creates a bounded amount of heap sharing, and (b) restricting program contracts and loop invariants to use only deterministic paths in the heap, we show that heap reachability updates can be described in a simple manner. The restrictions force program specifications and verification conditions to lie within a fragment of first-order logic with transitive closure that is reducible to effectively propositional logic, and hence facilitate sound, complete and efficient verification. We implemented a tool atop Z3 and report on preliminary experiments that establish the correctness of several programs that manipulate linked data structures.
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