Checking Zenon Modulo Proofs in Dedukti

TL;DR

This paper presents a method to verify Zenon Modulo proofs within Dedukti, enhancing trust in automated proof generation by embedding proofs into a universal proof checker.

Contribution

It introduces a shallow embedding of Zenon Modulo proofs into Dedukti, enabling independent verification and increasing confidence in automated theorem proving.

Findings

Successful embedding of Zenon Modulo proofs into Dedukti.

Improved confidence in automated proof verification.

Applicable to both academic and industrial proof verification.

Abstract

Dedukti has been proposed as a universal proof checker. It is a logical framework based on the lambda Pi calculus modulo that is used as a backend to verify proofs coming from theorem provers, especially those implementing some form of rewriting. We present a shallow embedding into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deduction modulo and typing. Zenon Modulo is applied to the verification of programs in both academic and industrial projects. The purpose of our embedding is to increase the confidence in automatically generated proofs by separating untrusted proof search from trusted proof verification.