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arXiv 1901.03414cs.LO
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面向平台无关的标准三角函数规范和验证

Towards platform-independent specification and verification of the standard trigonometry functions

Nikolay V. Shilov, Boris L. Faifel, Svetlana O. Shilova, Aleksey V. Promsky

摘要:

研究计划“标准数学函数形式化规范与验证的平台无关方法”旨在开发一种增量式组合方法来规范和验证标准数学函数,如sqrt,cos,sin等。平台无关意味着我们试图设计一种相对简单的计算机算法公理化,和整数算术(即实数和有理数的域R和Q,整数环Z),但既不指定计算机算术的基,也不指定数字表示的格式。递增性意味着我们从最简单的最简单的规范开始,最简单的易于验证的实数算法,并以计算机算法的现实规范和验证结束。我们称我们的方法为组合,因为我们从手册开始(纸笔)验证某些选定的实数算法,然后将这些算法和验证作为计算机算法及其人工验证的草稿和证明大纲,最后,利用计算机辅助校对系统对手工校对进行了验证(以避免诉诸“显而易见”,这在人类携带的证据中非常常见)。在本文中,我们提出了第一个步骤,对一个平台无关的增量相结合的方法,规范和验证的标准函数的cos和sin,实现数学三角函数的cos和sin。

英文摘要:

Research project "Platform-independent approach to formal specification and verification of standard mathematical functions" is aimed onto a development of an incremental combined approach to the specification and verification of the standard mathematical functions like sqrt, cos, sin, etc. Platform-independence means that we attempt to design a relatively simple axiomatization of the computer arithmetic in terms of real, rational, and integer arithmetic (i.e. the fields R and Q of real and rational numbers, the ring Z of integers) but don't specify neither base of the computer arithmetic, nor a format of numbers' representation. Incrementality means that we start with the most straightforward specification of the simplest easy to verify algorithm in real numbers and finish with a realistic specification and a verification of an algorithm in computer arithmetic. We call our approach combined because we start with a manual (pen-and-paper) verification of some selected algorithm in real numbers, then use these algorithm and verification as a draft and proof-outlines for the algorithm in computer arithmetic and its manual verification, and finish with a computer-aided validation of our manual proofs with some proof-assistant system (to avoid appeals to "obviousness" that are very common in human-carried proofs). In the paper we present first steps towards a platform-independent incremental combined approach to specification and verification of the standard functions cos and sin that implement mathematical trigonometric functions cos and sin.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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