A monadic, functional implementation of real numbers
A monadic, functional implementation of real numbers
复制标题
实数的一元函数实现
DOI：
10.1017/s0960129506005871
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发表时间：
2006
影响因子：
0.5
通讯作者：
Russell O'Connor
中科院分区：
文献类型：
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作者：
Russell O'Connor
大规模真实的数计算是现代数学证明中的一个重要组成部分。由于这种冗长的计算无法通过手工验证，一些数学家希望使用软件证明助手来验证这些证明的正确性。本文利用度量空间上完备化运算的单子性质，给出了构造性真实的数和初等函数的一种新的证明方法。Bishop和Bridges关于正则序列的概念（Bishop and Bridges 1985）被推广到我称之为正则函数的东西，它构成了任何度量空间的完备化。使用单子运算，通过提升原始空间上的连续函数来创建长度空间（这是度量空间的一个常见子类）上的连续函数。一个原型Haskell实现已经创建。我相信这种方法产生了一个真实的数字库，它对于计算来说相当有效，并且仍然足够简单，可以很容易地验证其正确性。
Large scale real number computation is an essential ingredient in several modern mathematical proofs. Because such lengthy computations cannot be verified by hand, some mathematicians want to use software proof assistants to verify the correctness of these proofs. This paper develops a new implementation of the constructive real numbers and elementary functions for such proofs by using the monad properties of the completion operation on metric spaces. Bishop and Bridges's notion (Bishop and Bridges 1985) of regular sequences is generalised to what I call regular functions, which form the completion of any metric space. Using the monad operations, continuous functions on length spaces (which are a common subclass of metric spaces) are created by lifting continuous functions on the original space. A prototype Haskell implementation has been created. I believe that this approach yields a real number library that is reasonably efficient for computation, and still simple enough to verify its correctness easily.
2002年北京德国德国大会
DOI：
--
发表时间：
2003
期刊：
影响因子：
--
作者：
Yukinobu;Umenai
通讯作者：
Umenai