Construction Defining Functionality:A Constructive Perspective on Functions through Their Generated Structures

Abstract

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.