Automating Event-B invariant proofs by rippling and proof patching

This work is supported by EPSRC grants EP/H024204/1, EP/E005713/1, EP/M018407/1 and EP/J001058/1.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.Publisher PDFPeer reviewe

Комплексный подход системы C-lightVer к автоматизированной локализации ошибок в C-программах

The C-lightVer system for the deductive verification of C programs is being developed at the IIS SB RAS. Based on the two-level architecture of the system, the C-light input language is translated into the intermediate C-kernel language. The meta generator of the correctness conditions receives the C-kernel program and Hoare logic for the C-kernel as input. To solve the well-known problem of determining loop invariants, the definite iteration approach was chosen. The body of the definite iteration loop is executed once for each element of the finite dimensional data structure, and the inference rule for them uses the substitution operation rep, which represents the action of the cycle in symbolic form. Also, in our meta generator, the method of semantic markup of correctness conditions has been implemented and expanded. It allows to generate explanations for unproven conditions and simplifies the errors localization. Finally, if the theorem prover fails to determine the truth of the condition, we can focus on proving its falsity. Thus a method of proving the falsity of the correctness conditions in the ACL2 system was developed. The need for more detailed explanations of the correctness conditions containing the replacement operation rep has led to a change of the algorithms for generating the replacement operation, and the generation of explanations for unproven correctness conditions. Modifications of these algorithms are presented in the article. They allow marking rep definition with semantic labels, extracting semantic labels from rep definition and generating description of break execution condition.В ИСИ СО РАН разрабатывается система C-lightVer для дедуктивной верификации С-программ. Исходя из двухуровневой архитектуры системы, входной язык C-light транслируется в промежуточный язык C-kernel. Метагенератор условий корректности принимает на вход C-kernel программу и логику Хоара для C-kernel. Для решения известной проблемы задания инвариантов циклов выбран подход финитных итераций. Тело цикла финитной итерации исполняется один раз для каждого элемента структуры данных конечной размерности, а правило вывода для них использует операцию замены rep, выражающую действие цикла в символической форме. Также в нашем метагенераторе внедрен и расширен метод семантической разметки условий корректности. Он позволяет порождать пояснения для недоказанных условий и упрощает локализацию ошибок. Наконец, если система ACL2 не справляется с установлением истинности условия, можно сосредоточиться на доказательстве его ложности. Ранее нами был разработан способ доказательства ложности условий корректности для системы ACL2. Необходимость в более подробных объяснениях условий корректности, содержащих операцию замены rep, привела к изменению алгоритмов генерации операции замены, извлечения семантических меток и генерации объяснений недоказанных условий корректности. В статье представлены модификации данных алгоритмов. Эти изменения позволяют пометить исходный код функции rep семантическими метками, извлекать семантические метки из определения rep, а также генерировать описание условия исполнения инструкции break

Automating Event-B invariant proofs by rippling and proof patching

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