A Framework for Proof-carrying Logical Transformations

TL;DR

This paper introduces a modular framework for proof-carrying logical transformations that enhances trustworthiness by generating and verifying certificates independently, applicable in higher-order logic with polymorphism and built-in theories.

Contribution

It presents a novel framework for proof-carrying logical transformations with independent certificate generation and verification in higher-order logic.

Findings

Framework enables independent certificate checking

Supports higher-order logic with polymorphism

Improves confidence in logical transformations

Abstract

In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In this paper, we develop a framework to improve confidence in their results. We follow a modular and skeptical approach: transformations are instrumented independently of each other and produce certificates that are checked by a third-party tool. Logical transformations are considered in a higher-order logic, with type polymorphism and built-in theories such as equality and integer arithmetic. We develop a language of proof certificates for them and use it to implement the full chain of certificate generation and certificate verification.