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diff --git a/README.md b/README.md new file mode 100644 index 0000000..c70f1bf --- /dev/null +++ b/README.md @@ -0,0 +1,117 @@ +# AAC tactics + +[![Travis][travis-shield]][travis-link] +[![Contributing][contributing-shield]][contributing-link] +[![Code of Conduct][conduct-shield]][conduct-link] +[![Gitter][gitter-shield]][gitter-link] +[![DOI][doi-shield]][doi-link] + +[doi-shield]: https://zenodo.org/badge/DOI/10.1007/978-3-642-25379-9_14.svg +[doi-link]: https://doi.org/10.1007/978-3-642-25379-9_14 + +[travis-shield]: https://travis-ci.com/coq-community/aac-tactics.svg?branch=master +[travis-link]: https://travis-ci.com/coq-community/aac-tactics/builds + +[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 + +[gitter-shield]: https://img.shields.io/badge/chat-on%20gitter-%23c1272d.svg +[gitter-link]: https://gitter.im/coq-community/Lobby + +This Coq plugin provides tactics for rewriting universally quantified +equations, modulo associativity and commutativity of some operator. +The tactics can be applied for custom operators by registering the +operators and their properties as type class instances. Many common +operator instances, such as for Z binary arithmetic and booleans, are +provided with the plugin. + + +More details about the project can be found in the paper +[Tactics for Reasoning modulo AC in Coq](https://arxiv.org/abs/1106.4448). + +## Meta + +- Author(s): + - Thomas Braibant (initial) + - Damien Pous (initial) + - Fabian Kunze +- Coq-community maintainer(s): + - Fabian Kunze ([**@fakusb**](https://github.com/fakusb)) + - Karl Palmskog ([**@palmskog**](https://github.com/palmskog)) +- License: [GNU Lesser General Public License v3.0 or later](LICENSE) +- Compatible Coq versions: Coq 8.9 (use the corresponding branch or release for other Coq versions) +- Compatible OCaml versions: all versions supported by Coq +- Additional dependencies: none + +## Building and installation instructions + +The easiest way to install the latest released version is via +[OPAM](https://opam.ocaml.org/doc/Install.html): + +```shell +opam repo add coq-released https://coq.inria.fr/opam/released +opam install coq-aac-tactics +``` + +To instead build and install manually, do: + +``` shell +git clone https://github.com/coq-community/aac-tactics +cd aac-tactics +make # or make -j <number-of-cores-on-your-machine> +make install +``` + +After installation, the included modules are available under +the `AAC_tactics` namespace. + +## Documentation + +The following example shows an application of the tactics for reasoning over Z binary numbers: +```coq +Require Import AAC_tactics.AAC. +Require AAC_tactics.Instances. +Require Import ZArith. + +Section ZOpp. + Import Instances.Z. + Variables a b c : Z. + Hypothesis H: forall x, x + Z.opp x = 0. + + Goal a + b + c + Z.opp (c + a) = b. + aac_rewrite H. + aac_reflexivity. + Qed. +End ZOpp. +``` + +The file [Tutorial.v](theories/Tutorial.v) provides a succinct introduction +and more examples of how to use this plugin. + +The file [Instances.v](theories/Instances.v) defines several type class instances +for frequent use-cases of this plugin, that should allow you to use it off-the-shelf. +Namely, it contains instances for: + +- Peano naturals (`Import Instances.Peano.`) +- Z binary numbers (`Import Instances.Z.`) +- N binary numbers (`Import Instances.N.`) +- P binary numbers (`Import Instances.P.`) +- Rational numbers (`Import Instances.Q.`) +- Prop (`Import Instances.Prop_ops.`) +- Booleans (`Import Instances.Bool.`) +- Relations (`Import Instances.Relations.`) +- all of the above (`Import Instances.All.`) + +To understand the inner workings of the tactics, please refer to +the `.mli` files as the main source of information on each `.ml` file. + +## Acknowledgements + +The initial authors are grateful to Evelyne Contejean, Hugo Herbelin, +Assia Mahboubi, and Matthieu Sozeau for highly instructive discussions. +The plugin took inspiration from the plugin tutorial "constructors" by +Matthieu Sozeau, distributed under the LGPL 2.1. + |