https://github.com/bloomberg/game-trees
Functions and proofs about game trees in Rocq, implemented as rose trees.
https://github.com/bloomberg/game-trees
anamorphism game-theory game-trees rose-trees
Last synced: 11 months ago
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Functions and proofs about game trees in Rocq, implemented as rose trees.
- Host: GitHub
- URL: https://github.com/bloomberg/game-trees
- Owner: bloomberg
- License: apache-2.0
- Created: 2025-05-06T20:28:00.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2025-05-07T21:36:43.000Z (about 1 year ago)
- Last Synced: 2025-07-26T13:41:45.237Z (12 months ago)
- Topics: anamorphism, game-theory, game-trees, rose-trees
- Language: Coq
- Homepage:
- Size: 21.5 KB
- Stars: 9
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# game-trees
## Menu
- [Rationale](#rationale)
- [Quick start](#quick-start)
- [Building](#building)
- [Installation](#installation)
- [Contributions](#contributions)
- [License](#license)
- [Code of Conduct](#code-of-conduct)
## Rationale
This repository contains functions and proofs about game trees in [Rocq](https://rocq-prover.org/), implemented as [rose trees](https://en.wikipedia.org/wiki/Rose_tree). We provide two different flavors of game trees, inductive and coinductive game trees. Inductive game trees are finite by construction, but it is difficult to populate a tree from an initial value and a function that gives the next steps. We have to prove that the population (anamorphism or unfolding of a rose tree) terminates. Coinductive game trees can be infinite or finite. Populating a coinductive tree is easy since we do not have to prove termination, but we need bisimulation to reason about them.
## Quick start
In `GameTrees.Trees.Unfold`, we provide an `unfold_tree` function that populates an inductive tree in a provably terminating way, if you abide by certain restrictions about what the `next` function says the next steps will be. We prove that this function is *sound* and *complete*: a value is in the game tree if and only if there is a sequence of applications of `next` from the initial state that create that value.
In `GameTrees.Cotrees.Unfold`, we provide an `unfold_cotree` function that populates a possibly infinite tree. We prove that this function is also *sound* and *complete*.
To showcase our library, we provide an example: a tic-tac-toe game for which we unfold a proven-complete game tree and run minimax algorithm to implement an unbeatable AI.
## Building
You have to have the `rocq-released` registry of `opam`. You can obtain it by running `opam repo add rocq-released https://rocq-prover.org/opam/released` if you do not already have it.
To install the dependencies, run `opam install . --deps-only`. The project builds with Rocq 9.0.0 or higher.
To build the project use `make`. After that, you can optionally run the tic-tac-toe game with `make run`.
## Installation
To install the project use `opam install .`. You do not need the `make` step from the build instructions for this.
## Contributions
We :heart: contributions.
Have you had a good experience with this project? Why not share some love and contribute code, or just let us know about any issues you had with it?
We welcome issue reports [here](../../issues); be sure to choose the proper issue template for your issue, so that we can be sure you're providing the necessary information.
Before sending a [Pull Request](../../pulls), please make sure you read our
[Contribution Guidelines](https://github.com/bloomberg/.github/blob/master/CONTRIBUTING.md).
## License
Please read the [LICENSE](LICENSE) file.
## Code of Conduct
This project has adopted a [Code of Conduct](https://github.com/bloomberg/.github/blob/master/CODE_OF_CONDUCT.md).
If you have any concerns about the Code, or behavior which you have experienced in the project, please
contact us at opensource@bloomberg.net.