Coq plugin for parametricity
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The plugin is still in an experimental state. It is not very user friendly (lack of good error messages) and still contains bugs. But is useable enough to "translate" a large chunck of standard library.


The plugin currently works with Coq 8.5pl1. The easy (and long) way to test the plugin is to follow the following steps:

  • Retrieve the plugin and compile it:

      git clone
      cd paramcoq 
      sudo make install

To test the plugin:

    cd test-suite
    make ide

It will compile Parametricity.vo which loads the plugin. Then, it launches coq-ide with some simple examples.

Available commands

The default arity is 2. The default name is automatically generated when translating a constant (otherwise you need to provide it).

  • Parametricity [Recursive] ident [as name] [arity n].

Declare the translation named name from the translation of the constant or the inductive ident. You can use the recursive option to recursively translate all the constant and inductives which are used by ident.

  • Parametricity Translation term [as name] [arity n].

Define a new constant named name obtained by computing the parametricity translation of term.

  • Parametricity Module modulepath.

Recursively translate everything in a module.

  • Realizer constant or variable [as name] [arity n] := term.

Declare term to be the translation of a constant. Useful to translate terms containing section variables, or axioms.

Note that all that both translating a term or module may lead to proof obligations (for some fixpoints and opaque terms if you did not import ProofIrrelevence).

  • [Global | Local] Parametricity Tactic := t.

Use the tactic t to solve proof obligations generated by the Parametricity command.


Original authors:

External contributors (many thanks !):