A library of Taylor models for PVS automatic proof checker

TL;DR

This paper introduces a library for Taylor models integrated with the PVS proof assistant, enabling both numerical computation and formal proof validation for safety-critical applications.

Contribution

It presents a novel library that extends PVS with Taylor models, allowing for verified computations and proofs in differential equations and interval arithmetic.

Findings

Library enables proof validation alongside numerical results

Designed for small to medium safety-critical applications

Integrates Taylor models with PVS for formal verification

Abstract

We present in this paper a library to compute with Taylor models, a technique extending interval arithmetic to reduce decorrelation and to solve differential equations. Numerical software usually produces only numerical results. Our library can be used to produce both results and proofs. As seen during the development of Fermat's last theorem reported by Aczel 1996, providing a proof is not sufficient. Our library provides a proof that has been thoroughly scrutinized by a trustworthy and tireless assistant. PVS is an automatic proof assistant that has been fairly developed and used and that has no internal connection with interval arithmetic or Taylor models. We built our library so that PVS validates each result as it is produced. As producing and validating a proof, is and will certainly remain a bigger task than just producing a numerical result our library will never be a replacement to imperative implementations of Taylor models such as Cosy Infinity. Our library should mainly be used to validate small to medium size results that are involved in safety or life critical applications.