Build dependency graphs between COQ objects
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Build dependency graphs between Coq objects, where Coq is the famous formal proof management system (see

Travis CI status on master branch: Build Status

What's inside ?

First of all, it is a small tool (a Coq plug-in) that extracts the dependencies between Coq objects, and produces a file (we suggest using the suffix .dpd) with this information.

The idea is that other small tools can be then developed to process the .dpd files. At the moment, there is:

  • dpd2dot that reads these .dpd files and produces a graph file using .dot format (cf. that makes possible to view them;
  • dpdusage: to find unused definitions.

Hope other tools later on to do more things. Feel free to contribute!

How to get it

You can:



  • The latest version runs with Coq 8.7.0
  • it has been tested with a version of Coq installed using opam and with Ocaml version 4.04.2
  • ocamlgraph (for dpd2dot tool) Any version should work since only the basic feature are used.

Compile from the pre-packaged source archive or the git repository

First download the archive, unpack it, and change directory to the coq-dpdgraph directory.

Depending on how you got hold of the archive, you may be in one of three situations:

1/ Makefile is present

You should type the following command.

$ make && make install

2/ configure is present, but no Makefile

You should type the following command.

$ ./configure && make && make install

3/ configure is not present, Makefile is not present

You should type the following command.

$ autoconf
$ configure && make && make install

install using opam

If you use opam, you can install coq-dpdgraph and ocamlgraph

$ opam repo add coq-released
$ opam install coq-dpdgraph


If you install the archive by cloning the git repository, you have a sub-directory containing test files. These can be tested using the following command.

$ make -s test

to check if everything is ok.

How to use it


  • to have compiled the tools (see above)
  • a compiled Coq file. You can for instance use tests/Test.v (a modified clone of Coq List.v) and compile it doing :
  $ coqc tests/Test.v

Generation of .dpd files

The available commands are :

  • Generate dependencies between a list of objects:

      Print FileDependGraph <module name list>.

    A module can be a file, or a sub-module in a file. Example :

      Print FileDependGraph M M2.A.B.

    Take all the objects of the specified modules and build the dependencies between them.

  • Generate the dependencies of one objects:

      Print DependGraph my_lemma.

    Analyse recursively the dependencies of my_lemma.

  • Change the name of the generated file (default is graph.dpd):

      Set DependGraph File "f.dpd".

    Useful when one needs to build several files in one session.

Advice: you need to use Require to load the module that you want to explore, but don't use any Import/Export command because the tool is then unable to properly group the nodes by modules.


$ ledit coqtop -R . dpdgraph -I tests/
Welcome to Coq 8.5 (April 2016)

Coq < Require dpdgraph.dpdgraph.
[Loading ML file dpdgraph.cmxs ... done]

Coq < Require List.
Coq < Print FileDependGraph List.
Print FileDependGraph List.
Fetching opaque proofs from disk for Coq.Lists.List
Info: output dependencies in file graph.dpd
Coq < Set DependGraph File "graph2.dpd".

dpd2dot: from a .dpd file to a .dot file

Graph generation

$ ./dpd2dot graph.dpd
Info: read file graph.dpd
Info: Graph output in

There are some options :

$ ./dpd2dot -help
Usage : ./dpd2dot [options]
  -o : name of output file (default: name of input file .dot)
  -with-defs : show everything (default)
  -without-defs : show only Prop objects
  -rm-trans : remove transitive dependencies (default)
  -keep-trans : keep transitive dependencies
  -debug : set debug mode
  -help  Display this list of options
  --help  Display this list of options

If the name of the output file finishes with .dot, then the name before the .dot suffix is used as the graph name in the dot syntax. There are two exceptions: graph and digraph will be replaced with escaped_graph and escaped_digraph respectively.

The only useful option at the moment is -without-defs that export only Prop objects to the graph (Axiom, Theorem, Lemma, etc).

Graph visualisation

You need :

You can also convert .dot file to .svg file using :

$ dot -Tsvg > file.svg

You can then use firefox or inskape to view the .svg graph.

The main advantage of using firefox is that the nodes are linked to the coqdoc pages if they have been generated in the same directory. But the navigation (zoom, moves) is very poor and slow.

Graph interpretation

The graph can be interpreted like this :

  • edge n1 --> n2 : n1 uses n2
  • node :
    • green : proved lemma
    • orange : axiom/admitted lemma
    • dark pink : Definition, etc
    • light pink : Parameter, etc
    • violet : inductive,
    • blue : constructor,
    • multi-circled : not used (no predecessor in the graph)
  • yellow box : module
  • objects that are not in a yellow box are Coq objects.

dpdusage: find unused definitions via .dpd file

You can use dpdusage command to find unused definitions. Example:

$ ./dpdusage tests/graph2.dpd
Info: read file tests/graph2.dpd
Permutation_app_swap	(0)

In the example above it reports that Permutation_app_swap was references 0 times. You can specify max number of references allowed (default 0) via -threshold command line option.

Development information

Generated .dpd format description

graph : obj_list
obj : node | edge

node : "N: " node_id node_name node_attributes ';'
node_id : [0-9]+
node_name : '"' string '"'
node_attributes :
   | empty
   | '[' node_attribute_list ']'
node_attribute_list :
   | empty
   | node_attribute ',' node_attribute_list
node_attribute :
   | kind=[cnst|inductive|construct]
   | prop=[yes|no]
   | path="m0.m1.m2"
   | body=[yes|no]

edge : "E: "  node_id node_id edge_attributes ';'
edge_attributes :
   | empty
   | '[' edge_attribute_list ']'
edge_attribute_list :
   | empty
   | edge_attribute ',' edge_attribute_list
edge_attribute :
   | weight=NUM

The parser accept .dpd files as described above, but also any attribute for nodes and edges having the form : prop=val or prop="string..." or prop=NUM so that the generated .dpd can have new attributes without having to change the other tools. Each tool can then pick the attributes that it is able to handle; they are not supposed to raise an error whenever there is an unknown attribute.

More information

Also see: