Coq plugin for parametricity
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Build Status

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 is believed to work with Coq ≥ 8.7. One way to test the plugin is to follow the following steps:

  • Retrieve the plugin and compile it:

      git clone ...
      cd paramcoq
      git checkout master  # or v8.x depending on Coq version
      make install
  • To test the plugin:

      cd test-suite
      make ide

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

Available commands

The default arity is 2.

  • Parametricity ident as name [arity n].

Declare the translation named name from the translation of the constant or inductive ident.

  • Parametricity [Recursive] ident [arity n] [qualified].

The default name for the translation of the constant or inductive ident is automatically generated (from its unqualified name).
You can use the Recursive option to recursively translate all the constants and inductives which are used by ident.
You can use the qualified option to use a qualified default name for the translated constants and inductives. The default name then has the form Module_o_Submodule_o_ident if ident lies in the Module.Submodule namespace.

  • 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 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 !):


This software is distributed under the terms of the MIT License. See the file LICENSE for details.