# Formalization of Transform Methods using HOL Light

## TL;DR

This paper discusses the ongoing formalization of transform methods like Laplace and Fourier in HOL Light to improve the rigor and reliability of analyzing dynamical systems.

## Contribution

It introduces a higher-order logic formalization of transform methods using HOL Light, detailing progress, challenges, and future plans.

## Key findings

- Initial formalizations completed in HOL Light
- Identified key challenges in formalizing transform methods
- Roadmap for full formalization and verification

## Abstract

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.