# UniMath

This coq library aims to formalize a substantial body of mathematics using the univalent point of view.

View the Project on GitHub UniMath/UniMath

# Installation of UniMath on Unix-like systems

## Remarks

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.

### Preparing for the installation under Mac OS X

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:

1. Install Homebrew according to the instructions at http://brew.sh/.
2. Install Coq from Homebrew with the command
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.

### Preparing for the installation under Ubuntu or Debian (Linux)

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.

### Preparing for the installation under Arch Linux or Manjaro Linux

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.

## Installation of Proof General (all operating systems)

You may obtain Proof General from 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/.

## Installing UniMath

$git clone https://github.com/UniMath/UniMath$ cd UniMath


To compile the Coq formalizations (in all the packages), issue the following shell command (in this directory).

make


Alternatively, if you want to build a specific version of Coq for UniMath (not usually needed, but sometimes useful for compatibility reasons), and you have installed its dependencies as described above, you may issue the following command.

make BUILD_COQ=yes


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.

### Building individual packages and HTML documentation

• To compile an individual package and the files it depends on, e.g., the package CategoryTheory, issue
 $make CategoryTheory  • To compile an individual file and the files it depends on, e.g., the file CategoryTheory/Categories.v, issue $ make UniMath/CategoryTheory/Categories.vo


Note the extension *.vo required in the command.

• To create the standard HTML documentation provided by coqdoc:
 $make html  The documentation is created in the subdirectory html. • To create HTML documentation with “hidden” proofs: $ 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.)

• To install UniMath in the user-contrib directory of Coq, for use by other developments:
 $make install  The path to that directory from here, by default, is ./sub/coq/user-contrib/. • To install CoqIDE, see INSTALL_COQIDE. ## TAGS files Emacs (which every UniMath user should become expert with) includes a facility called “tags” which enables easy navigation between Coq proof files. For example, you may be examining a proof containing a reference to a symbol such as “has_homsets”, and you may wonder where the source code of its definition is. To do that, one positions the cursor on the symbol, presses M-., accepts (or modifies) the proffered string, and presses return. Emacs then takes you to the source code of the definition. One may repeat that as often as desired, and return one level upward in the chain of locations visited with M-*. Another use of the tags file is to search through all the source files for the occurrence of text matching a given regular expression. For example, you can use M-x tags-search with the regular expression ^Notation *" *$*. *$$, *[[:alpha:]]+ *$$*$" 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. ## Measuring compilation time 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 paralle, e.g, 4, as follows.

$make -j4  ## Further details 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. ## Problems In this section we describe some problems that have been encountered during compilation, and how to fix them. ### Errors while compiling Coq 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. ### Problems caused by ill-formed input to make 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  ### Problems specific to MacOS 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  ### Problems specific to Linux (e.g., Debian and Ubuntu) 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.

### Hints for developers

• 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 “travis” at github, and at that point, a memory limit is imposed to ensure reproducibility of results to 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.