This coq library aims to formalize a substantial body of mathematics using the univalent point of view.
In this section, we explain how to prepare your computer for the compilation of UniMath under Mac OS X, under Ubuntu/Debian, and under Arch/Manjaro Linux.
The simplest method, recommended for most users, is to first install Coq, Emacs, and Proof General, and then build and install UniMath.
Coq can be installed using the package manager Homebrew:
brew install coq
Alternatively, you can install Coq in any other standard way; or you can ask UniMath to build its own copy of Coq, which may be useful if your globally installed Coq is a version incompatible with UniMath. If you plan to do this, then you must first install its dependencies, e.g. with the Homebrew command:
brew install bash objective-caml ocaml-num ocaml-findlib camlp5
or, for more customisability, using the “opam” OCaml package manager, according to the detailed instructions in INSTALL_OPAM.md
.
Emacs may be installed using https://emacsformacosx.com/, http://aquamacs.org, or any other flavour of Emacs you prefer.
Now you may proceed to the instructions for Installation of Proof General and Installing UniMath below.
The automated sanity checks (for contributions to UniMath) may require a more recent version of bash than the one preinstalled on Mac OS; this can be installed with brew install bash
.
Under Ubuntu or Debian, you may install Coq with the following shell command.
sudo apt-get install coq
(Ubuntu 21.10 provides Coq version 8.12.0.)
Alternatively, if you wish to compile a version of Coq known to work with Unimath, you may install OCaml with the following shell command.
sudo apt-get install build-essential git ocaml ocaml-nox ocaml-native-compilers camlp5 libgtk2.0 libgtksourceview2.0 liblablgtk-extras-ocaml-dev ocaml-findlib libnum-ocaml-dev emacs
Now proceed with Installation of Proof General and Installing UniMath below.
Under Arch Linux or Manjaro Linux you may install OCaml and Emacs with the following shell commands.
sudo pacman --sync --needed archlinux-keyring
sudo pacman-key --populate archlinux
sudo pacman --sync --needed ocaml camlp5 ocaml-findlib ocaml-num
sudo pacman -S emacs
Now proceed with Installation of Proof General and Installing UniMath below.
You may obtain Proof General by using the quick installation instructions at http://proofgeneral.inf.ed.ac.uk/ or at https://proofgeneral.github.io/. Your version of emacs determines which version of Proof General you need, roughly, so some experimentation may be required; you may even need the current development version if your emacs is recent.
For those unfamiliar with Emacs, M-x
means “hold Alt, press x”.
Similarly, C-g
means “hold Ctrl, press g”. This cancels any action you have
started.
Finally, RET
means “press Enter”.
Hence, the first Proof General installation instruction
M-x package-refresh-contents RET
reads “hold Alt, press x; type package-refresh-contents; press Enter”.
Optional: some useful Proof General add-ons are available for installation at https://github.com/cpitclaudel/company-coq/.
To download UniMath, issue the following shell commands.
$ git clone https://github.com/UniMath/UniMath
$ cd UniMath
To compile the Coq formalizations (in all the packages), issue the following shell command (in this directory).
make
Once this is done, you can start browsing and editing UniMath. Below, we explain how to compile individual packages of UniMath, and how to create HTML documentation.
CategoryTheory
, issue
$ make CategoryTheory
CategoryTheory/Categories.v
, issue
$ make UniMath/CategoryTheory/Categories.vo
Note the extension *.vo
required in the command.
$ make html
The documentation is created in the subdirectory html
.
$ make doc
In this version of the documentation, any proof enclosed within Proof.
and Qed.
/Defined.
is replaced by a button Show proof.
.
Clicking on this button unveils (unfolds) the corresponding proof. A Hide proof
button can be used to fold the proof again.
The documentation is created in the subdirectory enhanced-html
.
(This feature requires the use of the otherwise optional Proof
command of
the Coq vernacular language to indicate the beginning of the proof. Toggling
of proofs requires an internet connection for downloading the jquery
library.)
user-contrib
directory of Coq, for use by other developments:
$ make install
The path to that directory from here, by default, is ./sub/coq/user-contrib/.
Emacs (which every UniMath user should become expert with) includes a facility
called “tags” which enables easy navigation between Coq proof files. For
example, you may be examining a proof containing a reference to a symbol such
as “has_homsets”, and you may wonder where the source code of its definition
is. To do that, one positions the cursor on the symbol, presses M-.
,
accepts (or modifies) the proffered string, and presses return. Emacs then
takes you to the source code of the definition. One may repeat that as often
as desired, and return one level upward in the chain of locations visited with
M-*
.
Another use of the tags file is to search through all the source files for the
occurrence of text matching a given regular expression. For example, you can use
M-x tags-search
with the regular expression ^Notation *" *\[ *. *\(, *[[:alpha:]]+ *\)*\]"
to locate the following lines in various files:
Notation "[ C , D , hs ]" := (functor_precategory C D hs) : cat.
Notation "[ C , D , hs ]" := (functor_precategory C D hs) : cat.
Notation "[ C , D ]" := (functor_category C D) : cat.
Notation "[ C , D ]" := (functor_category C D) : cat.
In order to enable this facility, make a “TAGS” file as follows.
To make a TAGS file for use with emacs etags
commands:
$ make TAGS
To make a TAGS file dealing with a single package, for example, Foundations
:
$ make TAGS-Foundations
The first time the tags facility is used, the user will be prompted for the location of a TAGS file to use – it will be in the top-level directory of UniMath.
To obtain information about the compilation time of each file, add
TIMED=yes
to the make
command line. For this to work, you need the
GNU time
utility installed on your system in /usr/bin
. Alternatively,
add TIMECMD=time
to the make
command line, where time
is a
time command that works on your system.
On both Linux and Mac OS X systems, time
is a built-in bash shell command
that differs from GNU time, available on Linux systems as \time
. Under
Mac OS X, you can install GNU time as gtime
by running brew install
gnu-time
.
Since make
variables can be included in the time command, the following
example (using GNU time gtime
) shows how to display the user time and the name of the
file on the same line.
$ time make TIMECMD='gtime -f "user time %U: $*"'
The first time
command provides overall time for the whole build.
Timing of execution of individual tactics and vernacular commands can be obtained by
$ make MOREFLAGS=-time
For postprocessing of the (huge) output, use our utility slowest
, like this:
$ make MOREFLAGS=-time TIMECMD='util/slowest 10 0.5'
For each Coq file compiled, the timing of the 10 slowest steps taking at least 0.5 seconds will be displayed.
You may time both steps and files like this:
$ make MOREFLAGS=-time TIMECMD='gtime -f "user time %U: $(basename $*)" util/slowest 10 0.5'
To speed up execution on a machine with multiple cores or pseudo-cores, specify the use of multiple processes in parallel, e.g., 4, as follows.
$ make -j4
The correct version of Coq is built and used automatically by the command
make
. (If you wish to bypass the building of Coq and use your own version,
then follow the instructions in the file build/Makefile-configuration-template.)
The file UniMath/.dir-locals.el
contains code that arranges for
Proof General to use the Coq programs built by make
when one of the proof
files of UniMath is opened in emacs; in order to use them more generally, such
as from the command line, then add the full path for the directory
./sub/coq/bin
to your PATH
environment variable, or set the emacs
variable coq-prog-name
in your emacs initialization file, .emacs
.
The various *.v files are compiled by Coq in such a way that the fully
qualified name of each identifier begins with UniMath. For example, the fully
qualified name of maponpaths
in uu0.v is UniMath.Foundations.Basics.PartA.maponpaths
.
The preferred way to interact with the Coq code is with Proof General, running
in a modern version of emacs. The file UniMath/.dir-locals.el will set the
emacs variable coq-prog-args
appropriately. In particular, it will add the
directory UniMath to the path, using the -R
option, and it will arrange for
files with names of the form *.v
to be edited in “Coq mode”.
We are using some Unicode characters in our Coq files. One way to type such
characters easily is with the “Agda input method”: to type σ, for example, one
types \sigma, which is automatically replaced by σ. We have arranged for the
Agda input method to be automatically enabled in buffers containing one of the
UniMath Coq files. The emacs command for viewing the typing shortcuts offered
by the Agda input method is C-H I
.
In this section we describe some problems that have been encountered during compilation, and how to fix them.
The following type mismatch error during compilation of Coq results from a mismatch between the version of OCaml used and the version of Coq being compiled.
"/usr/local/bin/ocamlfind" opt -rectypes -dtypes -w -3-52-56 -I config -I lib -I kernel -I kernel/byterun -I library -I proofs -I tactics -I pretyping -I interp -I stm -I toplevel -I parsing -I printing -I intf -I engine -I ltac -I tools -I tools/coqdoc -I plugins/omega -I plugins/romega -I plugins/micromega -I plugins/quote -I plugins/setoid_ring -I plugins/extraction -I plugins/fourier -I plugins/cc -I plugins/funind -I plugins/firstorder -I plugins/derive -I plugins/rtauto -I plugins/nsatz -I plugins/syntax -I plugins/decl_mode -I plugins/btauto -I plugins/ssrmatching -I plugins/ltac -I "/usr/local/Cellar/camlp5/7.03_1/lib/ocaml/camlp5" -thread -g -c lib/pp_control.ml
File "lib/pp_control.ml", line 61, characters 22-33:
Error: This expression has type bytes -> int -> int -> unit
but an expression was expected of type string -> int -> int -> unit
Type bytes is not compatible with type string
For example, Coq 8.6.1 cannot be compiled by OCaml 4.06.0, and must instead be compiled by an older version. In the instructions above, we arrange for OCaml 4.02.3 to be used to compile Coq 8.6.1.
When calling make
, various files are read, some of them not under version control by git.
If those files are ill-formed, make
stops working; in particular, make
cannot be used to delete and recreate those files.
When such a situation arises, one solution is to try cleaning everything with this command:
$ make INCLUDE=no distclean
Another solution is to let git do the cleaning, by running:
$ git clean -Xdfq
$ git submodule foreach git clean -Xdfq
The Makefile provides this pair of commands, too:
$ make INCLUDE=no git-clean
If you get error messages involving the command line option -fno-defer-pop
, you
might be running Mac OS X 10.9 with an OCaml compiler installed by brew
. In
that case try
brew update
brew upgrade objective-caml
If that doesn’t work, try
brew remove objective-caml
brew install objective-caml
If you get the error message Error: cannot find 'ocamlc.opt' in your path!
, you need to install ocaml-native-compilers
, e.g., by running
$ sudo apt-get install ocaml-native-compilers
This package is not among the build dependencies for older versions of Coq.
To regularly update the TAGS file, you may build with the command make TAGS all
.
Before submitting a pull request, developers should run the sanity checks that are specified
in the Makefile by adding sanity-checks
to the “make” command line.
One of the sanity checks checks that all proof files in the directory tree
are listed in the corresponding package, but it will complain even about
files you haven’t checked in; to disable the test, add -o
check-listing-of-proof-files
to the “make” command line. Other sanity
checks can be skipped the same way. For example, if you intend to make a
change to the Foundations package, then you can add -o
check-for-change-to-Foundations
to the “make” command line.
Memory limits: pull requests are tested automatically by GitHub CI,
and at that point, a memory limit is imposed to ensure reproducibility of
results and to prevent excessive memory usage. To apply the same memory
limit on your own machine before submitting a pull request, add
LIMIT_MEMORY=yes
to the make
command line. Unfortunately, under Mac OS
X, such memory limits are ineffective, so you may prefer to run the test
under Linux.