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https://github.com/coq-community/trocq
A modular parametricity plugin for proof transfer in Coq [maintainers=@CohenCyril,@ecranceMERCE,@amahboubi]
https://github.com/coq-community/trocq
coq parametricity
Last synced: 4 months ago
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A modular parametricity plugin for proof transfer in Coq [maintainers=@CohenCyril,@ecranceMERCE,@amahboubi]
- Host: GitHub
- URL: https://github.com/coq-community/trocq
- Owner: coq-community
- License: lgpl-3.0
- Created: 2023-11-10T16:37:48.000Z (about 1 year ago)
- Default Branch: master
- Last Pushed: 2024-08-01T06:37:39.000Z (6 months ago)
- Last Synced: 2024-09-30T20:42:52.337Z (4 months ago)
- Topics: coq, parametricity
- Language: Coq
- Homepage: http://coq-community.org/trocq/
- Size: 1.85 MB
- Stars: 18
- Watchers: 4
- Forks: 2
- Open Issues: 20
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
Awesome Lists containing this project
README
# Trocq
[![Contributing][contributing-shield]][contributing-link]
[![Code of Conduct][conduct-shield]][conduct-link]
[![Zulip][zulip-shield]][zulip-link]
[![DOI][doi-shield]][doi-link]
[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg
[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md
[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg
[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md
[zulip-shield]: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg
[zulip-link]: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users
[doi-shield]: https://zenodo.org/badge/DOI/10.5281/zenodo.10492403.svg
[doi-link]: https://doi.org/10.5281/zenodo.10492403
Trocq is a modular parametricity plugin for Coq. It
can be used to achieve proof transfer by both translating a user goal into another, related,
variant, and computing a proof that proves the corresponding implication.
The plugin features a hierarchy of structures on relations, whose instances are computed from registered user-defined proof via parametricity. This hierarchy ranges from structure-less relations to an original formulation of type
equivalence. The resulting framework generalizes [raw parametricity](https://arxiv.org/abs/1209.6336),
[univalent parametricity](https://arxiv.org/abs/1209.6336) and
[CoqEAL](https://github.com/coq-community/coqeal), and includes them in a unified framework.
The plugin computes a parametricity translation "à la carte", by performing a fine-grained analysis of the requires properties for a given proof of relatedness. In particular, it is able to prove implications without resorting to full-blown type equivalence, allowing this way to perform
proof transfer without necessarily pulling in the univalence axiom.
The plugin is implemented in Coq-Elpi and the code of the parametricity translation is fairly close to a pen-and-paper sequent-style presentation.
## Meta
- Author(s):
- Cyril Cohen (initial)
- Enzo Crance (initial)
- Assia Mahboubi (initial)
- Coq-community maintainer(s):
- Cyril Cohen ([**@CohenCyril**](https://github.com/CohenCyril))
- Enzo Crance ([**@ecranceMERCE**](https://github.com/ecranceMERCE))
- Assia Mahboubi ([**@amahboubi**](https://github.com/amahboubi))
- License: [GNU Lesser General Public License v3.0](LICENSE)
- Compatible Coq versions: 8.17
- Additional dependencies:
- [Coq-Elpi custom version](https://github.com/ecranceMERCE/coq-elpi/tree/strat)
- [Coq-HoTT 8.17](https://github.com/HoTT/Coq-HoTT)
- Coq namespace: `Trocq`
- Related publication(s):
- [Trocq: Proof Transfer for Free, With or Without Univalence](https://hal.science/hal-04177913/document)
## Building and installation instructions
Trocq is a still a prototype. In particular, it depends on a [custom version](https://github.com/ecranceMERCE/coq-elpi/tree/strat) of Coq-Elpi.
It is not yet packaged in Opam or Nix.
There are however three ways to experiment with it,
all documented in the [INSTALL.md file](INSTALL.md).
## Documentation
See the [tutorial](artifact-doc/TUTORIAL.md) for concrete use cases.
In short, the plugin provides a tactic:
- `trocq` (without arguments) which attempts to run a translation on
a given goal, using the information provided by the user with the
commands described below.
And three commands:
- `Trocq Use t` to use a translation `t` during the subsequent calls to
the tactic `trocq`.
- `Trocq Register Univalence u` to declare a univalence axiom `u`.
- `Trocq Register Funext fe` to declare a function extensionality axiom `fe`.
## ESOP 2024 artifact documentation
The ESOP 2024 artifact documentation files can be found in the `artifact-doc` directory, except for `INSTALL.md` that can be found in the current directory.