Semantic Deconstruction and Operator Reconfiguration: An Architecture of Morphic Computation Based on Inverse Categorical Compilation Theory

Abstract

This paper presents the Inverse Categorical Compilation Theory (ICCT), a paradigm shift that redefines compilation from a linear transformation of source code to a reverse reconstruction process of computational intent. Moving beyond the traditional generative grammar framework, we propose that the relationship between machine instruction sets and high-level semantics is governed by adjoint functors within a structured category-theoretic domain. We introduce the "Semantic-Instruction Duality," establishing that execution traces possess inherent holographic properties that allow for the unique recovery of primitive operators. By modeling program execution as a topological movement within a manifold and utilizing an inverse folding operator, we demonstrate that optimal program logic can be reconstructed from binary streams without the prerequisite of source code. This theoretical framework provides a rigorous foundation for autonomous logic reconfiguration, proving that computational optimization is mathematically equivalent to the inverse projection of operator spaces. Our results suggest that compilation is not an entropy-increasing translation, but rather an entropy-decreasing process of intent-extraction, establishing a new foundation for software engineering where binary execution is recognized as a direct manifestation of canonical logical representation.