\[\begin{split}\newcommand{\as}{\kw{as}} \newcommand{\case}{\kw{case}} \newcommand{\cons}{\textsf{cons}} \newcommand{\consf}{\textsf{consf}} \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}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} \newcommand{\Indp}[4]{\kw{Ind}_{#4}[#1](#2:=#3)} \newcommand{\Indpstr}[5]{\kw{Ind}_{#4}[#1](#2:=#3)/{#5}} \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{\ModImp}[3]{{\kw{Mod}}({#1}:{#2}:={#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}\]

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 Coq source files, readable for a human and not only for the proof assistant;

  2. to help users navigate their own (or third-party) sources.

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 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 let id := fun [T : Type] (x : t) => x in id 0 by writing [let id := fun [T : Type] (x : t) => x in id 0]). Inside quotations, the code is pretty-printed the same way as in code parts.

Preformatted 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. Either the LaTeX or the HTML rule 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.

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 asterisks at the beginning of a line followed by a space and the title of the section. One asterisk is a section, two a subsection, etc.

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 enclosing 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:

  • $...LATEX stuff...$ inserts some LaTeX material in math mode. Simply discarded in HTML output.

  • %...LATEX stuff...% inserts some LaTeX material. Simply discarded in HTML output.

  • #...HTML stuff...# inserts some HTML material. Simply discarded in LaTeX output.

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)
>>

Verbatim material on a single line is also possible (assuming that >> is not part of the text to be presented as verbatim).

Example

Here is the corresponding caml expression: << fact (n-1) >>

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.

Lastly, it is possible to adopt a middle-ground approach when the desired output is HTML, where a given snippet of Coq material is hidden by default, but can be made visible with user interaction.

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

There is also an alternative syntax available.

(* begin details : Some summary describing the snippet *)
 *some Coq material*
(* end details *)

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 format. 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 using the 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 the current directory (option -d does not change the filename specified with the 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 filenames to be processed from the 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

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

--no-index

Do not output the index.

--binder-index

Include variable binders in the index. Not recommended with large source files, where binder information may dominate 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.

Hyperlink 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 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

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

-Q dir coqdir

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

Note

options -R and -Q only have effect on the files following them 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 first line 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 that control the parsing of comments:

--parse-comments

Parse 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

The default behavior is to assume ASCII 7 bit 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.

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.