HOL Light QE

TL;DR

HOL Light QE extends the HOL Light proof assistant with quotation and evaluation operators inspired by ${ m CTT}_{ m qe}$, enabling manipulation of mathematical expressions in a syntactically meaningful way, with a focus on implementation and benefits.

Contribution

The paper introduces HOL Light QE, a new system that incorporates quotation and evaluation into HOL Light, demonstrating the feasibility and advantages of these features in a proof assistant.

Findings

Successfully implemented quotation and evaluation in HOL Light

Demonstrated benefits of syntactic manipulation in formal proofs

Provided open access to the HOL Light QE system

Abstract

We are interested in algorithms that manipulate mathematical expressions in mathematically meaningful ways. Expressions are syntactic, but most logics do not allow one to discuss syntax. ${\rm CTT}_{\rm qe}$ is a version of Church's type theory that includes quotation and evaluation operators, akin to quote and eval in the Lisp programming language. Since the HOL logic is also a version of Church's type theory, we decided to add quotation and evaluation to HOL Light to demonstrate the implementability of ${\rm CTT}_{\rm qe}$ and the benefits of having quotation and evaluation in a proof assistant. The resulting system is called HOL Light QE. Here we document the design of HOL Light QE and the challenges that needed to be overcome. The resulting implementation is freely available.