HOL Light

The HOL Light theorem prover

Written by John Harrison drawing on the work of
Mike Gordon Tom Melham Robin Milner Larry Paulson Konrad Slind
and many other HOL and LCF researchers

HOL Light is a computer program to help users prove interesting mathematical theorems completely formally in higher order logic. It sets a very exacting standard of correctness, but provides a number of automated tools and pre-proved mathematical theorems (e.g. about arithmetic, basic set theory and real analysis) to save the user work. It is also fully programmable, so users can extend it with new theorems and inference rules without compromising its soundness. There are a number of versions of HOL, going back to Mike Gordon's work in the early 80s. Compared with other HOL systems, HOL Light uses a much simpler logical core and has little legacy code, giving the system a simple and uncluttered feel. Despite its simplicity, it offers theorem proving power comparable to, and in some areas greater than, other versions of HOL, and has been used for some significant industrial-scale verification applications.

HOL Light is now hosted on Github so you can get the sources from the Github repository. You can browse individual source files online, or check out all the code using git. For example, the following command will copy all the code from the Github repository into a new directory hol-light (assumed not to exist already):

git clone https://github.com/jrh13/hol-light.git

If you use a debian-based Linux distribution, then you can get a ready-to-use HOL Light system together with useful auxiliary tools simply by installing the hol-light package (thanks to Hendrik Tews ). For example

sudo apt-get install hol-light

Otherwise, you can always install it yourself. HOL Light is written in Objective CAML (OCaml), and it should work with any reasonably recent version. To build with OCaml 3.10 and later you will also need to install camlp5, version 5.07 or higher. See the README file in the distribution for detailed installation instructions.

The following lists some available documentation and resources:

Reference Manual available as online crosslinked HTML or as one PDF file (also an older variant keyed to version 2.20).
Tutorial, which tries to teach HOL Light through examples.
Quick Reference Guide compiled by Freek Wiedijk (text, PDF, Postscript, DVI, LaTeX)
Jeremy Bem's hol-online, and the earlier project Formalpedia, use a processed version of HOL Light to produce an online repository of software and formal mathematics.
Summary of many HOL source files, written by Carl Witty (text)
Old user manual, not fully updated from the older CAML Light version (DVI, Postscript and PDF).
The hol-info mailing list is a good place for HOL-related discussion
Josef Urban's HOL Proof Advisor uses automated data mining to produce proof advice.

Here are some applications of HOL Light:

Formalization of floating-point arithmetic, and the formal verification of several floating-point algorithms at Intel.
See this paper for a quick summary and more references, and this one for a more detailed presentation.
The Flyspeck project to machine-check Tom Hales's proof of the Kepler conjecture.
Tom has already proved the Jordan Curve Theorem and other relevant results in HOL Light.
Many other mathematical results of varying degrees of difficulty have been verified in HOL Light.
See for example the HOL Light entries on the Formalizing 100 Theorems page.

HOL Light is free open source software. It comes with no warranty of any kind (see the LICENCE file in the distribution), and no guarantee of maintainance. However, please feel free to send any comments or questions to the author at

Last updated by John Harrison on Fri 13th January 2017.