摘要
定理证明是一种形式化方法,在高可靠性系统验证中起着越来越重要的作用。分数阶微积分是高可靠性系统分析的基础,实数二项式系数是分数阶微积分定义的重要组成部分。在高阶逻辑定理库中还没有实数二项式系数的形式化。提出实数二项式系数高阶逻辑形式化方法。首先研究阶乘幂在HOL4中的形式化,然后利用阶乘幂的高阶逻辑形式分析实数二项式系数,最后将实数二项式系数应用于分数阶微积分的形式化。分数阶微积分的形式化分析表明了实数二项式系数及其运算性质形式化的正确性和有效性。
The theorem proving is a formal method and plays an important role in the verification of safety-critical system.The fractional calculus is the basis of the complex system＇s analysis. The real binomial coefficient is an important part of the fractional calculus GL definition. Currently, there is not the formalization of real binomial coefficient in high- er-order-logic theorem library. This paper presented the formalization of the real binomial coefficients. The factorial power was firstly formalized in HOIA. And the real binomial coefficient was formalized using the formalization of facto- rial power. The paper also presented the formal verification of the fractional calculus. At the same time it illustrateed the practical effectiveness and utilization of our approach.
出处
《计算机科学》
CSCD
北大核心
2014年第2期15-18,共4页
Computer Science
基金
国际科技合作计划(2010DFB10930
2011DFG13000)
国家自然科学基金项目(6087 3006
61070049
61170304
61104035
61174145
61201378)
北京市自然科学基金
北京市优秀人才项目(4122017
KZ201210028036
KM2010 10028021
2012D005016000011)资助
