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
git clone https://github.com/jrh13/hol-light.git
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
For those who prefer to download a packaged version directly instead of using
subversion, a snapshot from 10th January 2010 is available as
a gzipped tar file or as a zip file. The last numbered release, now quite
old, is 2.20, which you can get here.
(Note that 2.20 doesn't work under OCaml >= 3.10, owing to changes to
camlp4. If you really want to use HOL Light with these versions of OCaml, use
one of the more recent versions listed above.)
Experimental Linux binaries for version 2.20 are also now available, created
using CryoPID. NB: I'm not sure how
portable these are across Linux versions; better to build from source if you
can. The files are hol (core system), hol.sosa (preloaded with analysis and sum-of-squares
tools), hol.multivariate (preloaded with
multivariate analysis) and hol.card (preloaded with
cardinal arithmetic). Note that although these work as standalone executables,
if you are planning to work much with the system, you'll probably still want to
download the HOL sources to give access to additional library directories and
to the help files. For example, if you download the HOL Light source tree to
"/home/myself/hol_light", you might start a HOL Light session with the
following so that HOL Light can find all the files (# is the OCaml
# hol_dir := "/home/myself/hol_light";;
val it : unit = ()
# load_path := ["."; !hol_dir];;
val it : unit = ()
The following lists some available documentation and resources:
Here are some applications of HOL Light:
- 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
- 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
- Summary of many HOL source files,
written by Carl Witty (text)
- Old user manual, not fully updated from the older CAML Light
- 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.
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
- 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
- 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.
Last updated by John Harrison
on 19th October 2015.