Fifty years of Hoare’s logic

Apt, Krzysztof R.; Olderog, Ernst-Rüdiger

doi:10.1007/s00165-019-00501-3

Cited by 41 publications

(14 citation statements)

References 189 publications

(291 reference statements)

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“…Для задания аксиоматической семантики языка Cloud-Sisal-kernel используется метод слабейшего предусловия [7]. Данный метод, как и символический метод верификации финитных итераций, основан на замене переменных их значениями, вычисленными символически.…”

Section: аксиоматическая семантика языка Cloud-sisal-kernelunclassified

“…Система C-lightVer [1][2][3][4][5] разрабатывается в Институте систем информатики СО РАН для верификации C-программ. Данная система основана на методе дедуктивной верификации [6][7][8][9]. Представительное подмножество языка C (C-light) [10] является входным языком системы C-lightVer.…”

Section: Introductionunclassified

Towards Automatic Deductive Verification of C Programs with Sisal Loops Using the C-lightVer System

Kondratyev

2021

Model. anal. inf. sist.

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The C-lightVer system is developed in IIS SB RAS for C-program deductive verification. C-kernel is an intermediate verification language in this system. Cloud parallel programming system (CPPS) is also developed in IIS SB RAS. Cloud Sisal is an input language of CPPS. The main feature of CPPS is implicit parallel execution based on automatic parallelization of Cloud Sisal loops. Cloud-Sisal-kernel is an intermediate verification language in the CPPS system. Our goal is automatic parallelization of such a superset of C that allows implementing automatic verification. Our solution is such a superset of C-kernel as C-Sisal-kernel. The first result presented in this paper is an extension of C-kernel by Cloud-Sisal-kernel loops. We have obtained the C-Sisal-kernel language. The second result is an extension of C-kernel axiomatic semantics by inference rule for Cloud-Sisal-kernel loops. The paper also presents our approach to the problem of deductive verification automation in the case of finite iterations over data structures. This kind of loops is referred to as definite iterations. Our solution is a composition of symbolic method of verification of definite iterations, verification condition metageneration and mixed axiomatic semantics method. Symbolic method of verification of definite iterations allows defining inference rules for these loops without invariants. Symbolic replacement of definite iterations by recursive functions is the base of this method. Obtained verification conditions with applications of recursive functions correspond to logical base of ACL2 prover. We use ACL2 system based on computable recursive functions. Verification condition metageneration allows simplifying implementation of new inference rules in a verification system. The use of mixed axiomatic semantics results to simpler verification conditions in some cases.

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“…our textbook [3]. These historical developments are traced in the recent survey [5]. Also, formalization of Hoare's logic in various interactive theorem provers, e.g., Coq (see, e.g., [7]), led to a computer aided verification of several programs.…”

Section: Background and Motivationmentioning

confidence: 99%

Reasoning about call-by-value: a missing result in the history of Hoare's logic

Apt¹,

Boer²

2019

Preprint

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We provide a sound and relatively complete Hoare-like proof system for reasoning about partial correctness of recursive procedures in presence of local variables and the call-by-value parameter mechanism, and in which the correctness proofs are linear in the length of the program. We argue that in spite of the fact that Hoare-like proof systems for recursive procedures were intensively studied, no such proof system has been proposed in the literature.

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“…Hence, verification is complete modulo checking whether the inequality д ⪯ h between two functions in our language holds. Indeed, Hoare logic is also only complete modulo deciding an implication between two formulae in the language of first-order arithmetic [Apt and Olderog 2019].…”

Section: Introductionmentioning

confidence: 99%

Relatively complete verification of probabilistic programs: an expressive language for expectation-based reasoning

Batz

Kaminski

Katoen

et al. 2021

Proc. ACM Program. Lang.

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We study a syntax for specifying quantitative assertions —functions mapping program states to numbers—for probabilistic program verification. We prove that our syntax is expressive in the following sense: Given any probabilistic program C , if a function f is expressible in our syntax, then the function mapping each initial state σ to the expected value of evaluated in the final states reached after termination of C on σ (also called the weakest preexpectation wp[ C ]( f )) is also expressible in our syntax. As a consequence, we obtain a relatively complete verification system for reasoning about expected values and probabilities in the sense of Cook: Apart from proving a single inequality between two functions given by syntactic expressions in our language, given f , g , and C , we can check whether g ≼ wp[ C ]( f ).

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“…На первом этапе аннотированная C-light программа транслируется в эквивалентную программу на языке C-kernel. Далее, с помощью аксиоматической семантики выводятся условия корректности (УК) [2]. Затем происходит доказательство полученных УК с помощью системы автоматизированного доказательства теорем.…”

Section: Introductionunclassified

The Complex Approach of the C-lightVer System to the Automated Error Localization in C-programs

Кондратьев

Промский

2019

Model. anal. inf. sist.

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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.

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Fifty years of Hoare’s logic

Abstract: We present a history of Hoare's logic.

Cited by 41 publications

References 189 publications

Towards Automatic Deductive Verification of C Programs with Sisal Loops Using the C-lightVer System

Reasoning about call-by-value: a missing result in the history of Hoare's logic

Relatively complete verification of probabilistic programs: an expressive language for expectation-based reasoning

The Complex Approach of the C-lightVer System to the Automated Error Localization in C-programs

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