\[\begin{split}\newcommand{\as}{\kw{as}} \newcommand{\Assum}[3]{\kw{Assum}(#1)(#2:#3)} \newcommand{\case}{\kw{case}} \newcommand{\cons}{\textsf{cons}} \newcommand{\consf}{\textsf{consf}} \newcommand{\Def}[4]{\kw{Def}(#1)(#2:=#3:#4)} \newcommand{\emptyf}{\textsf{emptyf}} \newcommand{\End}{\kw{End}} \newcommand{\kwend}{\kw{end}} \newcommand{\even}{\textsf{even}} \newcommand{\evenO}{\textsf{even}_\textsf{O}} \newcommand{\evenS}{\textsf{even}_\textsf{S}} \newcommand{\Fix}{\kw{Fix}} \newcommand{\fix}{\kw{fix}} \newcommand{\for}{\textsf{for}} \newcommand{\forest}{\textsf{forest}} \newcommand{\Functor}{\kw{Functor}} \newcommand{\In}{\kw{in}} \newcommand{\Ind}[4]{\kw{Ind}[#2](#3:=#4)} \newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} \newcommand{\Indp}[5]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)} \newcommand{\Indpstr}[6]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)/{#6}} \newcommand{\injective}{\kw{injective}} \newcommand{\kw}[1]{\textsf{#1}} \newcommand{\length}{\textsf{length}} \newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} \newcommand{\List}{\textsf{list}} \newcommand{\lra}{\longrightarrow} \newcommand{\Match}{\kw{match}} \newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} \newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} \newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} \newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} \newcommand{\mto}{.\;} \newcommand{\nat}{\textsf{nat}} \newcommand{\Nil}{\textsf{nil}} \newcommand{\nilhl}{\textsf{nil\_hl}} \newcommand{\nO}{\textsf{O}} \newcommand{\node}{\textsf{node}} \newcommand{\nS}{\textsf{S}} \newcommand{\odd}{\textsf{odd}} \newcommand{\oddS}{\textsf{odd}_\textsf{S}} \newcommand{\ovl}[1]{\overline{#1}} \newcommand{\Pair}{\textsf{pair}} \newcommand{\plus}{\mathsf{plus}} \newcommand{\SProp}{\textsf{SProp}} \newcommand{\Prop}{\textsf{Prop}} \newcommand{\return}{\kw{return}} \newcommand{\Set}{\textsf{Set}} \newcommand{\Sort}{\mathcal{S}} \newcommand{\Str}{\textsf{Stream}} \newcommand{\Struct}{\kw{Struct}} \newcommand{\subst}[3]{#1\{#2/#3\}} \newcommand{\tl}{\textsf{tl}} \newcommand{\tree}{\textsf{tree}} \newcommand{\trii}{\triangleright_\iota} \newcommand{\Type}{\textsf{Type}} \newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} \newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} \newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} \newcommand{\WFE}[1]{\WF{E}{#1}} \newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} \newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} \newcommand{\with}{\kw{with}} \newcommand{\WS}[3]{#1[] \vdash #2 <: #3} \newcommand{\WSE}[2]{\WS{E}{#1}{#2}} \newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} \newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} \newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} \newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} \newcommand{\zeroone}[1]{[{#1}]} \end{split}\]


The distribution provides utilities to simplify some tedious works beside proof development, tactics writing or documentation.

Using Coq as a library

In previous versions, coqmktop was used to build custom toplevels - for example for better debugging or custom static linking. Nowadays, the preferred method is to use ocamlfind.

The most basic custom toplevel is built using:

% ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg \
              -package coq.toplevel \
              topbin/coqtop_bin.ml -o my_toplevel.native

For example, to statically link Ltac, you can just do:

% ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg \
              -package coq.toplevel,coq.plugins.ltac \
              topbin/coqtop_bin.ml -o my_toplevel.native

and similarly for other plugins.

Building a Coq project

As of today it is possible to build Coq projects using two tools:

  • coq_makefile, which is distributed by Coq and is based on generating a makefile,

  • Dune, the standard OCaml build tool, which, since version 1.9, supports building Coq libraries.

Building a Coq project with coq_makefile

The majority of Coq projects are very similar: a collection of .v files and eventually some .ml ones (a Coq plugin). The main piece of metadata needed in order to build the project are the command line options to coqc (e.g. -R, Q, -I, see command line options). Collecting the list of files and options is the job of the _CoqProject file.

A simple example of a _CoqProject file follows:

-R theories/ MyCode
-arg -w
-arg all
-I src/

where options -R, -Q and -I are natively recognized, as well as file names. The lines of the form -arg foo are used in order to tell to literally pass an argument foo to coqc: in the example, this allows to pass the two-word option -w all (see command line options).

CoqIDE, Proof-General and VSCoq all understand _CoqProject files and can be used to invoke Coq with the desired options.

The coq_makefile utility can be used to set up a build infrastructure for the Coq project based on makefiles. The recommended way of invoking coq_makefile is the following one:

coq_makefile -f _CoqProject -o CoqMakefile

Such command generates the following files:


is a makefile for GNU Make with targets to build the project (e.g. generate .vo or .html files from .v or compile .ml* files) and install it in the user-contrib directory where the Coq library is installed. Run make with the -f CoqMakefile option to use CoqMakefile.


contains make variables assignments that reflect the contents of the _CoqProject file as well as the path relevant to Coq.

An optional file CoqMakefile.local can be provided by the user in order to extend CoqMakefile. In particular one can declare custom actions to be performed before or after the build process. Similarly one can customize the install target or even provide new targets. Extension points are documented in paragraph CoqMakefile.local.

The extensions of the files listed in _CoqProject is used in order to decide how to build them. In particular:

  • Coq files must use the .v extension

  • OCaml files must use the .ml or .mli extension

  • OCaml files that require pre processing for syntax extensions (like VERNAC EXTEND) must use the .mlg extension

  • In order to generate a plugin one has to list all OCaml modules (i.e. Baz for baz.ml) in a .mlpack file (or .mllib file).

The use of .mlpack files has to be preferred over .mllib files, since it results in a “packed” plugin: All auxiliary modules (as Baz and Bazaux) are hidden inside the plugin’s "namespace" (Qux_plugin). This reduces the chances of begin unable to load two distinct plugins because of a clash in their auxiliary module names.


The optional file CoqMakefile.local is included by the generated file CoqMakefile. It can contain two kinds of directives.

Variable assignment

The variable must belong to the variables listed in the Parameters section of the generated makefile. Here we describe only few of them.


can be used to specify third party findlib packages, and is passed to the OCaml compiler on building or linking of modules. Eg: -package yojson.


can be used to specify additional flags to the OCaml compiler, like -bin-annot or -w....


it contains a default of -warn-error +a-3, useful to modify this setting; beware this is not recommended for projects in Coq's CI.


can be set in order to use alternative binaries (e.g. wrappers)


can be extended by including other paths in which *.cm* files are searched. For example COQ_SRC_SUBDIRS+=user-contrib/Unicoq lets you build a plugin containing OCaml code that depends on the OCaml code of Unicoq


override the flags passed to coqc. By default -q.


extend the flags passed to coqc


override the flags passed to coqchk. By default -silent -o.


extend the flags passed to coqchk


override the flags passed to coqdoc. By default -interpolate -utf8.


extend the flags passed to coqdoc

Rule extension

The following makefile rules can be extended.


        echo "This line is print before making the all target"
        cp ThisExtraFile /there/it/goes

run before the all target. One can use this to configure the project, or initialize sub modules or check dependencies are met.


run after the all target. One can use this to run a test suite, or compile extracted code.


run after install. One can use this to install extra files.


One can use this to install extra doc.







One can append lines to the generated .merlin file extending this target.

Timing targets and performance testing

The generated Makefile supports the generation of two kinds of timing data: per-file build-times, and per-line times for an individual file.

The following targets and Makefile variables allow collection of per- file timing data:

  • TIMED=1

    passing this variable will cause make to emit a line describing the user-space build-time and peak memory usage for each file built.


    On Mac OS, this works best if you’ve installed gnu-time.


    For example, the output of make TIMED=1 may look like this:

    COQDEP Fast.v
    COQDEP Slow.v
    COQC Slow.v
    Slow.vo (user: 0.34 mem: 395448 ko)
    COQC Fast.v
    Fast.vo (user: 0.01 mem: 45184 ko)
  • pretty-timed

    this target stores the output of make TIMED=1 into time-of-build.log, and displays a table of the times and peak memory usages, sorted from slowest to fastest, which is also stored in time-of-build-pretty.log. If you want to construct the log for targets other than the default one, you can pass them via the variable TGTS, e.g., make pretty-timed TGTS="a.vo b.vo".


    This target requires python to build the table.


    This target will append to the timing log; if you want a fresh start, you must remove the file time-of-build.log or run make cleanall.


    By default the table displays user times. If the build log contains real times (which it does by default), passing TIMING_REAL=1 to make pretty-timed will use real times rather than user times in the table.


    Passing TIMING_INCLUDE_MEM=0 to make will result in the tables not including peak memory usage information. Passing TIMING_SORT_BY_MEM=1 to make will result in the tables be sorted by peak memory usage rather than by the time taken.


    For example, the output of make pretty-timed may look like this:

    COQC Slow.v
    Slow.vo (real: 0.52, user: 0.39, sys: 0.12, mem: 394648 ko)
    COQC Fast.v
    Fast.vo (real: 0.06, user: 0.02, sys: 0.03, mem: 56980 ko)
        Time |  Peak Mem | File Name
    0m00.41s | 394648 ko | Total Time / Peak Mem
    0m00.39s | 394648 ko | Slow.vo
    0m00.02s |  56980 ko | Fast.vo
  • print-pretty-timed-diff

    this target builds a table of timing changes between two compilations; run make make-pretty-timed-before to build the log of the “before” times, and run make make-pretty-timed-after to build the log of the “after” times. The table is printed on the command line, and stored in time-of-build-both.log. This target is most useful for profiling the difference between two commits in a repository.


    This target requires python to build the table.


    The make-pretty-timed-before and make-pretty-timed-after targets will append to the timing log; if you want a fresh start, you must remove the files time-of-build-before.log and time-of-build-after.log or run make cleanall before building either the “before” or “after” targets.


    The table will be sorted first by absolute time differences rounded towards zero to a whole-number of seconds, then by times in the “after” column, and finally lexicographically by file name. This will put the biggest changes in either direction first, and will prefer sorting by build-time over subsecond changes in build time (which are frequently noise); lexicographic sorting forces an order on files which take effectively no time to compile.

    If you prefer a different sorting order, you can pass TIMING_SORT_BY=absolute to sort by the total time taken, or TIMING_SORT_BY=diff to sort by the signed difference in time.


    Just like pretty-timed, this table defaults to using user times. Pass TIMING_REAL=1 to make on the command line to show real times instead.


    Just like pretty-timed, passing TIMING_INCLUDE_MEM=0 to make will result in the tables not including peak memory usage information. Passing TIMING_SORT_BY_MEM=1 to make will result in the tables be sorted by peak memory usage rather than by the time taken.


    For example, the output table from make print-pretty-timed-diff may look like this:

       After |  Peak Mem | File Name             |   Before |  Peak Mem ||    Change || Change (mem) |  % Change | % Change (mem)
    0m00.43s | 394700 ko | Total Time / Peak Mem | 0m00.41s | 394648 ko || +0m00.01s ||        52 ko |    +4.87% |         +0.01%
    0m00.39s | 394700 ko | Fast.vo               | 0m00.02s |  56980 ko || +0m00.37s ||    337720 ko | +1850.00% |       +592.69%
    0m00.04s |  56772 ko | Slow.vo               | 0m00.39s | 394648 ko || -0m00.35s ||   -337876 ko |   -89.74% |        -85.61%

The following targets and Makefile variables allow collection of per- line timing data:

  • TIMING=1

    passing this variable will cause make to use coqc -time to write to a .v.timing file for each .v file compiled, which contains line-by-line timing information.


    For example, running make all TIMING=1 may result in a file like this:

    Chars 0 - 26 [Require~Coq.ZArith.BinInt.] 0.157 secs (0.128u,0.028s)
    Chars 27 - 68 [Declare~Reduction~comp~:=~vm_c...] 0. secs (0.u,0.s)
    Chars 69 - 162 [Definition~foo0~:=~Eval~comp~i...] 0.153 secs (0.136u,0.019s)
    Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] 0.239 secs (0.236u,0.s)
  • print-pretty-single-time-diff

    print-pretty-single-time-diff AFTER=path/to/file.v.after-timing BEFORE=path/to/file.v.before-timing

    this target will make a sorted table of the per-line timing differences between the timing logs in the BEFORE and AFTER files, display it, and save it to the file specified by the TIME_OF_PRETTY_BUILD_FILE variable, which defaults to time-of-build-pretty.log. To generate the .v.before-timing or .v.after-timing files, you should pass TIMING=before or TIMING=after rather than TIMING=1.


    The sorting used here is the same as in the print-pretty-timed-diff target.


    This target requires python to build the table.


    This target follows the same sorting order as the print-pretty-timed-diff target, and supports the same options for the TIMING_SORT_BY variable.


    By default, two lines are only considered the same if the character offsets and initial code strings are identical. Passing TIMING_FUZZ=N relaxes this constraint by allowing the character locations to differ by up to N, as long as the total number of characters and initial code strings continue to match. This is useful when there are small changes to a file, and you want to match later lines that have not changed even though the character offsets have changed.


    By default the table picks up real times, under the assumption that when comparing line-by-line, the real time is a more accurate representation as it includes disk time and time spent in the native compiler. Passing TIMING_REAL=0 to make will use user times rather than real times in the table.


    For example, running print-pretty-single-time-diff might give a table like this:

    After     | Code                                                | Before    || Change    | % Change
    0m00.50s  | Total                                               | 0m04.17s  || -0m03.66s | -87.96%
    0m00.145s | Chars 069 - 162 [Definition~foo0~:=~Eval~comp~i...] | 0m00.192s || -0m00.04s | -24.47%
    0m00.126s | Chars 000 - 026 [Require~Coq.ZArith.BinInt.]        | 0m00.143s || -0m00.01s | -11.88%
       N/A    | Chars 027 - 068 [Declare~Reduction~comp~:=~nati...] | 0m00.s    || +0m00.00s | N/A
    0m00.s    | Chars 027 - 068 [Declare~Reduction~comp~:=~vm_c...] |    N/A    || +0m00.00s | N/A
    0m00.231s | Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] | 0m03.836s || -0m03.60s | -93.97%
  • all.timing.diff, path/to/file.v.timing.diff

    The path/to/file.v.timing.diff target will make a .v.timing.diff file for the corresponding .v file, with a table as would be generated by the print-pretty-single-time-diff target; it depends on having already made the corresponding .v.before-timing and .v.after-timing files, which can be made by passing TIMING=before and TIMING=after. The all.timing.diff target will make such timing difference files for all of the .v files that the Makefile knows about. It will fail if some .v.before-timing or .v.after-timing files don’t exist.


    This target requires python to build the table.

Reusing/extending the generated Makefile

Including the generated makefile with an include directive is discouraged. The contents of this file, including variable names and status of rules shall change in the future. Users are advised to include Makefile.conf or call a target of the generated Makefile as in make -f Makefile target from another Makefile.

One way to get access to all targets of the generated CoqMakefile is to have a generic target for invoking unknown targets.


# KNOWNTARGETS will not be passed along to CoqMakefile
KNOWNTARGETS := CoqMakefile extra-stuff extra-stuff2
# KNOWNFILES will not get implicit targets from the final rule, and so
# depending on them won't invoke the submake
# Warning: These files get declared as PHONY, so any targets depending
# on them always get rebuilt
KNOWNFILES   := Makefile _CoqProject

.DEFAULT_GOAL := invoke-coqmakefile

CoqMakefile: Makefile _CoqProject
        $(COQBIN)coq_makefile -f _CoqProject -o CoqMakefile

invoke-coqmakefile: CoqMakefile
        $(MAKE) --no-print-directory -f CoqMakefile $(filter-out $(KNOWNTARGETS),$(MAKECMDGOALS))

.PHONY: invoke-coqmakefile $(KNOWNFILES)

##                      Your targets here                         ##

# This should be the last rule, to handle any targets not declared above
%: invoke-coqmakefile

Building a subset of the targets with -j

To build, say, two targets foo.vo and bar.vo in parallel one can use make only TGTS="foo.vo bar.vo" -j.


make foo.vo bar.vo -j has a different meaning for the make utility, in particular it may build a shared prerequisite twice.


For users of coq_makefile with version < 8.7

  • Support for "subdirectory" is deprecated. To perform actions before or after the build (like invoking make on a subdirectory) one can hook in pre-all and post-all extension points.

  • -extra-phony and -extra are deprecated. To provide additional target (.PHONY or not) please use CoqMakefile.local.

Precompiling for native_compute

To compile files for native_compute, one can use the -native-compiler yes option of Coq, for instance by putting the following in a CoqMakefile.local file:

COQEXTRAFLAGS += -native-compiler yes

The generated CoqMakefile installation target will then take care of installing the extra .coq-native directories.


As an alternative to modifying any file, one can set the environment variable when calling make:

COQEXTRAFLAGS="-native-compiler yes" make

This can be useful when files cannot be modified, for instance when installing via OPAM a package built with coq_makefile:

COQEXTRAFLAGS="-native-compiler yes" opam install coq-package


This requires all dependencies to be themselves compiled with -native-compiler yes.

Building a Coq project with Dune


Dune's Coq support is still experimental; we strongly recommend using Dune 2.3 or later.


The canonical documentation for the Coq Dune extension is maintained upstream; please refer to the Dune manual for up-to-date information. This documentation is up to date for Dune 2.3.

Building a Coq project with Dune requires setting up a Dune project for your files. This involves adding a dune-project and pkg.opam file to the root (pkg.opam can be empty or generated by Dune itself), and then providing dune files in the directories your .v files are placed. For the experimental version "0.1" of the Coq Dune language, Coq library stanzas look like:

 (name <module_prefix>)
 (package <opam_package>)
 (synopsis <text>)
 (modules <ordered_set_lang>)
 (libraries <ocaml_libraries>)
 (flags <coq_flags>))

This stanza will build all .v files in the given directory, wrapping the library under <module_prefix>. If you declare an <opam_package>, an .install file for the library will be generated; the optional (modules <ordered_set_lang>) field allows you to filter the list of modules, and (libraries <ocaml_libraries>) allows the Coq theory depend on ML plugins. For the moment, Dune relies on Coq's standard mechanisms (such as COQPATH) to locate installed Coq libraries.

By default Dune will skip .v files present in subdirectories. In order to enable the usual recursive organization of Coq projects add

(include_subdirs qualified)

to you dune file.

Once your project is set up, dune build will generate the pkg.install files and all the files necessary for the installation of your project.


A typical stanza for a Coq plugin is split into two parts. An OCaml build directive, which is standard Dune:

 (name equations_plugin)
 (public_name equations.plugin)
 (flags :standard -warn-error -3-9-27-32-33-50)
 (libraries coq.plugins.cc coq.plugins.extraction))

(coq.pp (modules g_equations))

And a Coq-specific part that depends on it via the libraries field:

 (name Equations) ; -R flag
 (package equations)
 (synopsis "Equations Plugin")
 (libraries coq.plugins.extraction equations.plugin)
 (modules :standard \ IdDec NoCycle)) ; exclude some modules that don't build

(include_subdirs qualified)

Computing Module dependencies

In order to compute module dependencies (to be used by make or dune), Coq provides the coqdep tool.

coqdep computes inter-module dependencies for Coq programs, and prints the dependencies on the standard output in a format readable by make. When a directory is given as argument, it is recursively looked at.

Dependencies of Coq modules are computed by looking at Require commands (Require, Require Export, Require Import), but also at the command Declare ML Module.

See the man page of coqdep for more details and options.

Both Dune and coq_makefile use coqdep to compute the dependencies among the files part of a Coq project.

Embedded Coq phrases inside LaTeX documents

When writing documentation about a proof development, one may want to insert Coq phrases inside a LaTeX document, possibly together with the corresponding answers of the system. We provide a mechanical way to process such Coq phrases embedded in LaTeX files: the coq-tex filter. This filter extracts Coq phrases embedded in LaTeX files, evaluates them, and insert the outcome of the evaluation after each phrase.

Starting with a file file.tex containing Coq phrases, the coq-tex filter produces a file named file.v.tex with the Coq outcome.

There are options to produce the Coq parts in smaller font, italic, between horizontal rules, etc. See the man page of coq-tex for more details.

Man pages

There are man pages for the commands coqdep and coq-tex. Man pages are installed at installation time (see installation instructions in file INSTALL, step 6).