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1.
We propose a decision procedure for algebraically closed fields based on a quantifier elimination method. The procedure is intended to build proofs for systems of polynomial equations and inequations. We describe how this procedure can be carried out in a proof assistant using a Computer Algebra system in a purely skeptical way. We present an implementation in the particular framework of Coq and Maple giving some details regarding the interface between the two tools. This allows us to show that a Computer Algebra system can be used not only to bring additional computational power to a proof assistant but also to enhance the automation of such tools.  相似文献
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This paper presents a formalization in Coq of Common Knowledge Logic and checks its adequacy on case studies. Those studies allow exploring experimentally the proof-theoretic side of Common Knowledge Logic. This work is original in that nobody has considered Higher Order Common Knowledge Logic from the point of view of proofs performed on a proof assistant. As a matter of facts, it is experimental by nature as it tries to draw conclusions from experiments.   相似文献
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The paper describes the general philosophy and the main architectural and technological solutions adopted in the HELM Project for the management of large repositories of mathematical knowledge. The leitmotiv is the extensive use of XML technology, and the exploitation of information in the Web way, that is without a central authority, with few basic rules, in a scalable, adaptable, and extensible manner.  相似文献
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We formalize natural deduction for first-order logic in the proof assistant Coq, using de Bruijn indices for variable binding. The main judgment we model is of the form d[:], stating that d is a proof term of formula under hypotheses it can be viewed as a typing relation by the Curry–Howard isomorphism. This relation is proved sound with respect to Coq's native logic and is amenable to the manipulation of formulas and of derivations. As an illustration, we define a reduction relation on proof terms with permutative conversions and prove the property of subject reduction.  相似文献
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We present a formal proof (at the implementation level) of an efficient algorithm proposed by P. Zimmermann in 1999 to compute square roots of arbitrarily large integers. This program, which is part of the GNU Multiple Precision Arithmetic Library, is completely proven within the COQ system. Proofs are developed using the CORRECTNESS tool to deal with imperative features of the program. The formalization is rather large (more than 13,000 lines) and requires some advanced techniques for proof management and reuse.  相似文献
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This paper reports on the first steps towards the formal verification of correctness proofs of real-life protocols in process algebra. We show that such proofs can be verified, and partly constructed, by a general purpose proof checker. The process algebra we use isCRL, ACP augmented with data, which is expressive enough for the specification of real-life protocols. The proof checker we use is Coq, which is based on the Calculus of Constructions, an extension of simply typed lambda calculus. The focus is on the translation of the proof theory ofCRL andCRL-specifications to Coq. As a case study, we verified the Alternating Bit Protocol.  相似文献
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对可靠程序的需求随着高可信软件在信息社会中的作用日益重要而增加。基于形式化证明工具构造携带证明的安全程序,给出严格的程序规范及其证明是提高软件可靠性的重要途径。论文介绍使用形式化证明工具Coq构造安全程序的过程和经验。  相似文献
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以μC/OS-Ⅲ内核中的任务调度器为研究对象,选取调度相关的核心代码,验证调度器代码满足优先调度最高优先级任务的性质。基于分离逻辑与SCAP验证理论,利用Coq辅助证明工具,通过定义机器模型、操作语义、逻辑断言以及推导规则构建验证框架。在验证框架中,定义内核数据结构和内核相关性质的逻辑描述,模块化地对内核代码进行推理。验证结果表明,μC/OS-Ⅲ任务调度器满足可靠性要求,并且可以通过机器的自动检查。  相似文献
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