# Arboretum.hs

*A Haskell library for symbolic computation in algebras of trees and forests.*

**Arboretum** is a Haskell library for algebraic computations involving trees and forests, designed to support research in areas such as numerical analysis, rough path theory, regularity structures, and non-associative algebra.

This package provides a flexible and extensible framework for working with algebras of graphs, including the implementation of decorated trees, aromatic forests, and operations such as grafting and substitution. It also supports symbolic computation in graded vector spaces. In addition, the package can generate LaTeX code and corresponding PDF output to visualize decorated aromatic forests and other elements of vector spaces, facilitating the interpretation of computation results.

The manual can be found in the **manual** directory.

## Features

- Abstract framework for defining algebras of graphs and forests
- Support for graded vector spaces
- Pre-Lie and pre-Lie-Rinehart algebra operations
- Implementation of decorated aromatic trees and forests
- Symbolic operations including grafting and substitution
- PDF export for graphical representation of tree structures

## Motivation

Many modern mathematical frameworks use trees and forests as a foundational combinatorial structure. From the Butcher group in numerical analysis to the branched rough paths and regularity structures in stochastic analysis, trees encode the composition of operations, hierarchical dependencies, and renormalization procedures. Arboretum offers a unified platform for prototyping and computing in these contexts.

## Getting Started

### Installation using Stack

    git clone https://github.com/ebronasco/arboretum.hs.git
    cd arboretum.hs
    stack build

### Documentation and Example Usage

Check the manual in the **manual** directory.

## References

- Eugen BRONASCO (2025) *Algebraic structures and numerical methods for invariant measure sampling of Langevin dynamics*. Doctoral Thesis.
- Eugen BRONASCO, Jean-Luc FALCONE, Gilles VILMART (in preparation) *Arboretum.hs: Symbolic manipulation for algebras of graphs*.

## Contributing

Contributions are welcome! Please:

1. Fork the repository  
2. Create a new branch  
3. Commit your changes  
4. Open a pull request  

## License

This project is licensed under the **BSD 3-Clause "New" or "Revised" License**. See the `LICENSE` file for details.

## Development

- **Autoformatting**:  
  `fourmolu -i <file-name>`  
  Configuration is specified in `fourmolu.yaml`.

- **Linting**:  
  `hlint <file-name>`

- **Documentation**:  
  Generated with `haddock`.

- **Testing**:  
  Uses `doctest` and `QuickCheck`.