Equations - a function definition plugin.
Copyright 2009-2021 Matthieu Sozeau
Copyright 2015-2018 Cyprien Mangin
Distributed under the terms of the GNU Lesser General Public License Version 2.1 or later (see LICENSE for details).
Equations provides a notation for writing programs by dependent pattern-matching and (well-founded) recursion in Coq. It compiles everything down to eliminators for inductive types, equality and accessibility, providing a definitional extension to the Coq kernel.
Try it now in your browser with JSCoq!
A gallery of examples provides more consequent developments using Equations.
Two articles describing the system are available:
Equations Reloaded: High-Level Dependently-Typed Functional Programming and Proving in Coq. Matthieu Sozeau and Cyprien Mangin. 2019. Proc. ACM Program. Lang. 3, ICFP, Article 86 (August 2019), 29 pages. DOI. See Equations Reloaded for associated material, including a VM to run the examples.
Equations: A Dependent Pattern-Matching Compiler Matthieu Sozeau (2010) In: Kaufmann M., Paulson L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg.
We did a case study on a proof of normalization for an hereditary substitution procedure:
- Equations for Hereditary Substitution in Leivant's Predicative SystemF: A Case Study Cyprien Mangin and Matthieu Sozeau. In: Proceedings Tenth International Workshop on Logical Frameworks and Meta Languages: Theory and Practice. Volume 185 of EPTCS. May 2015 - LFMTP'15.
See releases for sources and official releases.
Install with OPAM
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-equations
To get the beta versions of Coq, activate the repository:
opam repo add coq-core-dev https://coq.inria.fr/opam/core-dev
To get the development version of Equations, activate the repository:
opam repo add coq-extra-dev https://coq.inria.fr/opam/extra-dev
Install from source
Alternatively, to compile Equations, simply run:
in the toplevel directory, with
ocamlc in your path.
Optionally, one can build the test-suite or examples:
make examples test-suite
Then add the paths to your
Add ML Path "/Users/mat/research/coq/equations/src". Add Rec LoadPath "/Users/mat/research/coq/equations/theories" as Equations.
Or install it:
As usual, you will need to run this command with the appropriate privileges
if the version of Coq you are using is installed system-wide, rather than
in your own directory. E.g. on Ubuntu, you would prefix the command with
sudo and then enter your user account password when prompted.
The HoTT variant of Equations works with the coq-hott library for Coq 8.13 and up.
opam, simply install first the
coq-hott library and
will install its HoTT variant. From source, first install
coq-hott and then use:
This will compile the
HoTT library variant in addition to the standard one.
make install, one can import the plugin in Coq, using:
From Equations Require Import HoTT.All.