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

TL;DR

This paper introduces Construction Defining Functionality (CDF), a framework that characterizes functions based on the hierarchical structures they generate through iteration and recursion, providing a new constructive perspective.

Contribution

It formalizes the concept of functions as generators of structural spaces and develops a classification framework for their constructive behaviors.

Findings

Formalization of structural spaces generated by functions

Framework for classifying functions based on their constructive properties

Mathematical modeling of hierarchical structures from functions

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.