Sigmaid: SIGMA-calculus In Dedukti

Table of Contents

1 What is Sigmaid?

Sigmaid (SIGMA-calculus In Dedukti) is type-checker for Abadi and Cardelli simply-typed ς-calculus1. It can be used to produce Dedukti2 and Coq3 files.

Sigmaid has a web page :

2 License

This software is governed by the CeCILL-B license under French law and abiding by the rules of distribution of free software. You can use, modify and/ or redistribute the software under the terms of the CeCILL-B license as circulated by CEA, CNRS and INRIA at the following URL "".

As a counterpart to the access to the source code and rights to copy, modify and redistribute granted by the license, users are provided only with a limited warranty and the software's author, the holder of the economic rights, and the successive licensors have only limited liability.

In this respect, the user's attention is drawn to the risks associated with loading, using, modifying and/or developing or reproducing the software by the user in light of its specific status of free software, that may mean that it is complicated to manipulate, and that also therefore means that it is reserved for developers and experienced professionals having in-depth computer knowledge. Users are therefore encouraged to load and test the software's suitability as regards their requirements in conditions enabling the security of their systems and/or data to be ensured and, more generally, to use and operate it in the same conditions as regards security.

The fact that you are presently reading this means that you have had knowledge of the CeCILL-B license and that you accept its terms.

3 Installation

3.1 Dependencies

Sigmaid has the same dependencies than Dedukti :

  • OCaml
  • Menhir
  • GNU Make

Sigmaid produces files for Dedukti and Coq.

3.2 Source code

Sigmaid source code is available on line:

  • using git
    git clone git://
  • as a tarball

3.3 Compilation

To compile, simply invoke


in Sigmaid's directory.

3.4 Installation

If you want Sigmaid to be installed system-wide, and if you have enough rights, invoke

make install

3.5 Check

Sigmaid comes with a small example file test.sigma. If you have Dedukti (v 2.2) installed, you can check this example with Dedukti using the command

make test.dko

If you have Coq installed, you can check this example with Coq using the command

make test.vo

You can do both with the command

make test

4 Further reading

Sigmaid is described in this article.

The Dedukti files presented there are:

  • corresponding to Section 4.1.1 (Domains),
  • corresponding to the other definitions and proofs of Section 4.1 (Encoding of types),
  • corresponding to Sections 4.2 (Encoding of terms) and 5.1 (Modified rewrite system)

The file coq_obj.v contains the definitions and proofs of the terminating encoding (Section 4) in Coq.

The inconsistency result of Section 4.3.4 is proved in coq_obj_inconsistency.v.

5 Author

Sigmaid is written by Raphaël Cauderlier.



Martin Abadi and Luca Cardelli, A Theory of Objects, Monographs in Computer Science, 1996