# Applications of the analogy between formulas and exponential polynomials to equivalence and normal forms

## TL;DR

This paper explores the analogy between formulas and exponential polynomials to develop methods for formula equivalence, isomorphism, and normal forms, applicable in both classical and intuitionistic logic.

## Contribution

It introduces a novel approach linking formulas to exponential polynomials, enabling new techniques for proving equivalence and constructing normal forms.

## Key findings

- A method for proving formula isomorphism and equivalence via inequality checks
- A constructive analogue of the arithmetical hierarchy using exp-log normal form
- Results valid in both intuitionistic and classical logic

## Abstract

We show some applications of the formulas-as-polynomials correspondence: 1) a method for (dis)proving formula isomorphism and equivalence based on showing (in)equality; 2) a constructive analogue of the arithmetical hierarchy, based on the exp-log normal form. The results are valid intuitionistically, as well as classically.