Chapter 15  Utilities

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

15.1  Building a toplevel extended with user tactics

The native-code version of Coq cannot dynamically load user tactics using Objective Caml code. It is possible to build a toplevel of Coq, with Objective Caml code statically linked, with the tool coqmktop.

For example, one can build a native-code Coq toplevel extended with a tactic which source is in tactic.ml with the command

     % coqmktop -opt -o mytop.out tactic.cmx

where tactic.ml has been compiled with the native-code compiler ocamlopt. This command generates an executable called mytop.out. To use this executable to compile your Coq files, use coqc -image mytop.out.

A basic example is the native-code version of Coq (coqtop.opt), which can be generated by coqmktop -opt -o coqopt.opt.

Application: how to use the Objective Caml debugger with Coq.

One useful application of coqmktop is to build a Coq toplevel in order to debug your tactics with the Objective Caml debugger. You need to have configured and compiled Coq for debugging (see the file INSTALL included in the distribution). Then, you must compile the Caml modules of your tactic with the option -g (with the bytecode compiler) and build a stand-alone bytecode toplevel with the following command:

% coqmktop -g -o coq-debug <your .cmo files>

To launch the Objective Caml debugger with the image you need to execute it in an environment which correctly sets the COQLIB variable. Moreover, you have to indicate the directories in which ocamldebug should search for Caml modules.

A possible solution is to use a wrapper around ocamldebug which detects the executables containing the word coq. In this case, the debugger is called with the required additional arguments. In other cases, the debugger is simply called without additional arguments. Such a wrapper can be found in the dev/ subdirectory of the sources.

15.2  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, -I,
See also: Section 14.3.3). 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
theories/foo.v
theories/bar.v
-I src/
src/baz.ml4
src/bazaux.ml
src/qux_plugin.mlpack

Currently, both CoqIDE and Proof General (version ≥ 4.3pre) understand _CoqProject files and 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:

CoqMakefile
is a generic makefile for GNU Make that provides targets to build the project (both .v and .ml* files), to install it system-wide in the coq-contrib directory (i.e. where Coq is installed) as well as to invoke coqdoc to generate html documentation.

CoqMakefile.conf
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 15.2.

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

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 “name space” (Qux_plugin). This reduces the chances of begin unable to load two distinct plugins because of a clash in their auxiliary module names.

CoqMakefile.local

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

Variable assignment
to the variables listed in the Parameters section of the generated makefile. Here we describe only few of them.
CAMLPKGS
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.
CAMLFLAGS
can be used to specify additional flags to the OCaml compiler, like -bin-annot or -w....
COQC, COQDEP, COQDOC
can be set in order to use alternative binaries (e.g. wrappers)
Rule extension
The following makefile rules can be extended. For example
pre-all::
        echo "This line is print before making the all target"
install-extra::
        cp ThisExtraFile /there/it/goes
pre-all::
run before the all target. One can use this to configure the project, or initialize sub modules or check dependencies are met.
post-all::
run after the all target. One can use this to run a test suite, or compile extracted code.
install-extra::
run after install. One can use this to install extra files.
install-doc::
One can use this to install extra doc.
uninstall::
uninstall-doc::
clean::
cleanall::
archclean::
merlin-hook::
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:

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

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. For example:

# 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
 @true
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.

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

Notes for users of coq_makefile with version < 8.7

15.3  Modules dependencies

In order to compute modules dependencies (so to use make), Coq comes with an appropriate tool, coqdep.

coqdep computes inter-module dependencies for Coq and Objective Caml 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.

Dependencies of Objective Caml modules are computed by looking at open commands and the dot notation module.value. However, this is done approximately and you are advised to use ocamldep instead for the Objective Caml modules dependencies.

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

The build infrastructure generated by coq_makefile uses coqdep to automatically compute the dependencies among the files part of the project.

15.4  Documenting Coq files with coqdoc

coqdoc is a documentation tool for the proof assistant Coq, similar to javadoc or ocamldoc. The task of coqdoc is

  1. to produce a nice LATEX and/or HTML document from the Coq sources, readable for a human and not only for the proof assistant;
  2. to help the user navigating in his own (or third-party) sources.

15.4.1  Principles

Documentation is inserted into Coq files as special comments. Thus your files will compile as usual, whether you use coqdoc or not. coqdoc presupposes that the given Coq files are well-formed (at least lexically). Documentation starts with (**, followed by a space, and ends with the pending *). The documentation format is inspired by Todd A. Coram’s Almost Free Text (AFT) tool: it is mainly ASCII text with some syntax-light controls, described below. coqdoc is robust: it shouldn’t fail, whatever the input is. But remember: “garbage in, garbage out”.

Coq material inside documentation.

Coq material is quoted between the delimiters [ and ]. Square brackets may be nested, the inner ones being understood as being part of the quoted code (thus you can quote a term like fun x => u by writing [fun x => u]). Inside quotations, the code is pretty-printed in the same way as it is in code parts.

Pre-formatted vernacular is enclosed by [[ and ]]. The former must be followed by a newline and the latter must follow a newline.

Pretty-printing.

coqdoc uses different faces for identifiers and keywords. The pretty-printing of Coq tokens (identifiers or symbols) can be controlled using one of the following commands:

(** printing token %...LATEX...% #...HTML...# *)

or

(** printing token $...LATEX math...$ #...HTML...# *)

It gives the LATEX and HTML texts to be produced for the given Coq token. One of the LATEX or HTML text may be omitted, causing the default pretty-printing to be used for this token.

The printing for one token can be removed with

(** remove printing token *)

Initially, the pretty-printing table contains the following mapping:

->         <-         *×         
<=         >=         =>        
<>         <->         |-        
\/         /\         ~¬         

Any of these can be overwritten or suppressed using the printing commands.

Important note: the recognition of tokens is done by a (ocaml)lex automaton and thus applies the longest-match rule. For instance, ->~ is recognized as a single token, where Coq sees two tokens. It is the responsibility of the user to insert space between tokens or to give pretty-printing rules for the possible combinations, e.g.

(** printing ->~ %\ensuremath{\rightarrow\lnot}% *)
Sections.

Sections are introduced by 1 to 4 leading stars (i.e. at the beginning of the line) followed by a space. One star is a section, two stars a sub-section, etc. The section title is given on the remaining of the line. Example:

    (** * Well-founded relations
  
        In this section, we introduce...  *)
Lists.

List items are introduced by a leading dash. coqdoc uses whitespace to determine the depth of a new list item and which text belongs in which list items. A list ends when a line of text starts at or before the level of indenting of the list’s dash. A list item’s dash must always be the first non-space character on its line (so, in particular, a list can not begin on the first line of a comment - start it on the second line instead).

Example:

     We go by induction on [n]:
     - If [n] is 0...
     - If [n] is [S n'] we require...

       two paragraphs of reasoning, and two subcases:

       - In the first case...
       - In the second case...

     So the theorem holds.
Rules.

More than 4 leading dashes produce a horizontal rule.

Emphasis.

Text can be italicized by placing it in underscores. A non-identifier character must precede the leading underscore and follow the trailing underscore, so that uses of underscores in names aren’t mistaken for emphasis. Usually, these are spaces or punctuation.

    This sentence contains some _emphasized text_.
Escaping to LATEX and HTML.

Pure LATEX or HTML material can be inserted using the following escape sequences:

Note: to simply output the characters $, % and # and escaping their escaping role, these characters must be doubled.

Verbatim.

Verbatim material is introduced by a leading << and closed by >> at the beginning of a line. Example:

Here is the corresponding caml code:
<<
  let rec fact n = 
    if n <= 1 then 1 else n * fact (n-1)
>>
Hyperlinks.

Hyperlinks can be inserted into the HTML output, so that any identifier is linked to the place of its definition.

coqc file.v automatically dumps localization information in file.glob or appends it to a file specified using option --dump-glob file. Take care of erasing this global file, if any, when starting the whole compilation process.

Then invoke coqdoc or coqdoc --glob-from file to tell coqdoc to look for name resolutions into the file file (it will look in file.glob by default).

Identifiers from the Coq standard library are linked to the Coq web site at http://coq.inria.fr/library/. This behavior can be changed using command line options --no-externals and --coqlib; see below.

Hiding / Showing parts of the source.

Some parts of the source can be hidden using command line options -g and -l (see below), or using such comments:

(* begin hide *)
some Coq material
(* end hide *)

Conversely, some parts of the source which would be hidden can be shown using such comments:

(* begin show *)
some Coq material
(* end show *)

The latter cannot be used around some inner parts of a proof, but can be used around a whole proof.

15.4.2  Usage

coqdoc is invoked on a shell command line as follows:

  coqdoc <options and files>

Any command line argument which is not an option is considered to be a file (even if it starts with a -). Coq files are identified by the suffixes .v and .g and LATEX files by the suffix .tex.

HTML output
 

This is the default output. One HTML file is created for each Coq file given on the command line, together with a file index.html (unless option -no-index is passed). The HTML pages use a style sheet named style.css. Such a file is distributed with coqdoc.

LATEX output
 

A single LATEX file is created, on standard output. It can be redirected to a file with option -o. The order of files on the command line is kept in the final document. LATEX files given on the command line are copied ‘as is’ in the final document . DVI and PostScript can be produced directly with the options -dvi and -ps respectively.

TEXmacs output
 

To translate the input files to TEXmacs format, to be used by the TEXmacs Coq interface.

Command line options

Overall options
--html
 

Select a HTML output.

--latex
 

Select a LATEX output.

--dvi
 

Select a DVI output.

--ps
 

Select a PostScript output.

--texmacs
 

Select a TEXmacs output.

--stdout
 

Write output to stdout.

-o file, --output file
 

Redirect the output into the file ‘file’ (meaningless with -html).

-d dir, --directory dir
 

Output files into directory ‘dir’ instead of current directory (option -d does not change the filename specified with option -o, if any).

--body-only
 

Suppress the header and trailer of the final document. Thus, you can insert the resulting document into a larger one.

-p string, --preamble string
 

Insert some material in the LATEX preamble, right before \begin{document} (meaningless with -html).

--vernac-file file, --tex-file file
 

Considers the file ‘file’ respectively as a .v (or .g) file or a .tex file.

--files-from file
 

Read file names to process in file ‘file’ as if they were given on the command line. Useful for program sources split up into several directories.

-q, --quiet
 

Be quiet. Do not print anything except errors.

-h, --help
 

Give a short summary of the options and exit.

-v, --version
 

Print the version and exit.

Index options

Default behavior is to build an index, for the HTML output only, into index.html.

--no-index
 

Do not output the index.

--multi-index
 

Generate one page for each category and each letter in the index, together with a top page index.html.

--index string
 

Make the filename of the index string instead of “index”. Useful since “index.html” is special.

Table of contents option
-toc, --table-of-contents
 

Insert a table of contents. For a LATEX output, it inserts a \tableofcontents at the beginning of the document. For a HTML output, it builds a table of contents into toc.html.

--toc-depth int
 

Only include headers up to depth int in the table of contents.

Hyperlinks options
--glob-from file
 

Make references using Coq globalizations from file file. (Such globalizations are obtained with Coq option -dump-glob).

--no-externals
 

Do not insert links to the Coq standard library.

--external url coqdir
 

Use given URL for linking references whose name starts with prefix coqdir.

--coqlib url
 

Set base URL for the Coq standard library (default is http://coq.inria.fr/library/). This is equivalent to --external url Coq.

-R dir coqdir
 

Map physical directory dir to Coq logical directory coqdir (similarly to Coq option -R).

Note: option -R only has effect on the files following it on the command line, so you will probably need to put this option first.

Title options
-s , --short
 

Do not insert titles for the files. The default behavior is to insert a title like “Library Foo” for each file.

--lib-name string
 

Print “string Foo” instead of “Library Foo” in titles. For example “Chapter” and “Module” are reasonable choices.

--no-lib-name
 

Print just “Foo” instead of “Library Foo” in titles.

--lib-subtitles
 

Look for library subtitles. When enabled, the beginning of each file is checked for a comment of the form:

(** * ModuleName : text *)

where ModuleName must be the name of the file. If it is present, the text is used as a subtitle for the module in appropriate places.

-t string, --title string
 

Set the document title.

Contents options
-g, --gallina
 

Do not print proofs.

-l, --light
 

Light mode. Suppress proofs (as with -g) and the following commands:

  • [Recursive] Tactic Definition
  • Hint / Hints
  • Require
  • Transparent / Opaque
  • Implicit Argument / Implicits
  • Section / Variable / Hypothesis / End

The behavior of options -g and -l can be locally overridden using the (* begin show *)(* end show *) environment (see above).

There are a few options to drive the parsing of comments:

--parse-comments
 

Parses regular comments delimited by (* and *) as well. They are typeset inline.

--plain-comments
 

Do not interpret comments, simply copy them as plain-text.

--interpolate
 

Use the globalization information to typeset identifiers appearing in Coq escapings inside comments.

Language options

Default behavior is to assume ASCII 7 bits input files.

-latin1, --latin1
 

Select ISO-8859-1 input files. It is equivalent to --inputenc latin1 --charset iso-8859-1.

-utf8, --utf8
 

Set --inputenc utf8x for LATEX output and --charset utf-8 for HTML output. Also use Unicode replacements for a couple of standard plain ASCII notations such as → for -> and ∀ for forall. LATEX UTF-8 support can be found at http://www.ctan.org/pkg/unicode.

For the interpretation of Unicode characters by LATEX, extra packages which coqdoc does not provide by default might be required, such as textgreek for some Greek letters or stmaryrd for some mathematical symbols. If a Unicode character is missing an interpretation in the utf8x input encoding, add \DeclareUnicodeCharacter{code}{latex-interpretation}. Packages and declarations can be added with option -p.

--inputenc string
 

Give a LATEX input encoding, as an option to LATEX package inputenc.

--charset string
 

Specify the HTML character set, to be inserted in the HTML header.

15.4.3  The coqdoc LATEX style file

In case you choose to produce a document without the default LATEX preamble (by using option --no-preamble), then you must insert into your own preamble the command

\usepackage{coqdoc}

The package optionally takes the argument [color] to typeset identifiers with colors (this requires the xcolor package).

Then you may alter the rendering of the document by redefining some macros:

coqdockw, coqdocid, …
 

The one-argument macros for typesetting keywords and identifiers. Defaults are sans-serif for keywords and italic for identifiers.

For example, if you would like a slanted font for keywords, you may insert

     \renewcommand{\coqdockw}[1]{\textsl{#1}}

anywhere between \usepackage{coqdoc} and \begin{document}.

coqdocmodule
 

One-argument macro for typesetting the title of a .v file. Default is

\newcommand{\coqdocmodule}[1]{\section*{Module #1}}

and you may redefine it using \renewcommand.

15.5  Embedded Coq phrases inside LATEX documents

When writing a 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.


Remark. This Reference Manual and the Tutorial have been completely produced with coq-tex.

15.6  Coq and GNU Emacs

15.6.1  The Coq Emacs mode

Coq comes with a Major mode for GNU Emacs, gallina.el. This mode provides syntax highlighting and also a rudimentary indentation facility in the style of the Caml GNU Emacs mode.

Add the following lines to your .emacs file:

  (setq auto-mode-alist (cons '("\\.v$" . coq-mode) auto-mode-alist))
  (autoload 'coq-mode "gallina" "Major mode for editing Coq vernacular." t)

The Coq major mode is triggered by visiting a file with extension .v, or manually with the command M-x coq-mode. It gives you the correct syntax table for the Coq language, and also a rudimentary indentation facility:

An inferior mode to run Coq under Emacs, by Marco Maggesi, is also included in the distribution, in file coq-inferior.el. Instructions to use it are contained in this file.

15.6.2  Proof General

Proof General is a generic interface for proof assistants based on Emacs. The main idea is that the Coq commands you are editing are sent to a Coq toplevel running behind Emacs and the answers of the system automatically inserted into other Emacs buffers. Thus you don’t need to copy-paste the Coq material from your files to the Coq toplevel or conversely from the Coq toplevel to some files.

Proof General is developed and distributed independently of the system Coq. It is freely available at https://proofgeneral.github.io/.

15.7  Module specification

Given a Coq vernacular file, the gallina filter extracts its specification (inductive types declarations, definitions, type of lemmas and theorems), removing the proofs parts of the file. The Coq file file.v gives birth to the specification file file.g (where the suffix .g stands for Gallina).

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

15.8  Man pages

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