In this work, we propose the concept of Construction Defining Functionality (CDF), which characterizes functions by the structural spaces they generate through iteration,recursion, and logical application. By viewing functions as generators of hierarchical structures, we formalize these generated structural spaces and organize a framework to classify and mathematically model their properties. The organized CDF framework captures the intrinsic constructive behaviors of functions via their generated structural spaces.

翻译：本文提出构造定义功能性（CDF）的概念，该概念通过函数在迭代、递归及逻辑应用过程中生成的结构空间来刻画函数特性。通过将函数视为层次化结构的生成器，我们形式化这些生成的结构空间，并构建了一个用于分类和数学建模其性质的框架。所构建的CDF框架通过函数生成的结构空间捕捉了函数内在的构造性行为。