The use of formal method techniques can contribute to the production of more reliable and dependable systems. However, a common bottleneck for industrial adoption of such techniques is the needs for interactive proofs. We use a popular formal method, called Event-B , as our working domain, and set invariant preservation (INV) proofs as targets, because INV proofs can account for a significant proportion of the proofs requiring human interactions. We apply an inductive theorem proving technique, called rippling, for Event-B INV proofs. Rippling automates proofs using meta-level guidance. The guidance is in particular useful to develop proof patches to recover failed proof attempts. We are interested in the case when a missing lemma is required. We combine a scheme-based theory-exploration system, called IsaScheme [ MRMDB10 ], with rippling to develop a proof patch via lemma discovery. We also develop two new proof patches to unfold operator definitions and to suggest case-splits, respectively. The combined use of rippling with these three proof patches as a proof method significantly improves the proof automation for our evaluation set.

中文翻译：

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通过涟漪和证明修补自动化 Event-B 不变证明

形式化方法技术的使用有助于产生更可靠和可靠的系统。然而，工业采用此类技术的一个常见瓶颈是对交互式证明的需求。我们使用一种流行的形式化方法，称为事件-B，作为我们的工作域，并将不变保存（INV）证明设置为目标，因为 INV 证明可以占需要人工交互的证明的很大一部分。我们对 Event-B INV 证明应用了一种称为 rippleing 的归纳定理证明技术。Rippling 使用元级指导自动进行证明。该指南对于开发证明补丁以恢复失败的证明尝试特别有用。我们对需要缺少引理的情况感兴趣。我们结合了一个基于方案的理论探索系统，称为方案[MRMDB10]，用涟漪通过引理发现开发一个证明补丁。我们还开发了两个新的证明补丁来分别展开运算符定义和建议案例拆分。将涟漪与这三个证明补丁结合使用作为证明方法显着提高了我们评估集的证明自动化。