内涵构造数：算法概念的形式化
Intensional Constructed Numbers: Towards Formalizing the Notion of Algorithm
摘要：
这项工作的目的是一个步骤的正式定义的概念的算法，在这个意义上的等价类的程序工作“以类似的方式”。但是，我们不是直接在程序上定义等价变换，而是查看每个特定参数的计算并给它一个结构。这导致了构造数的概念：计算的结果是一个构造数，其构造函数（0，后继者）携带了其计算的历史条件（或轨迹）。这些条件与构造数之间存在等价关系。两个程序是等价的，如果它们为每个参数产生等价的构造数。
英文摘要：
This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs, we look at the computation for each particular argument and give it a structure. This leads to the notion of constructed number: the result of the computation is a constructed number whose constructors (0, successor) carry a history condition (or trace) of their computation. There are equivalence relations on these conditions and on constructed numbers. Two programs are equivalent if they produce equivalent constructed numbers for each argument.
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。
