Arboretum.hs: Symbolic manipulation for algebras of graphs
2026-04-28 • Symbolic Computation
Symbolic Computation
AI summaryⓘ
The authors created Arboretum.hs, a software package in the Haskell programming language, to work with mathematical structures called trees and graphs. Because Haskell is declarative and functional, their code closely matches the math definitions, making it easier to understand. Arboretum.hs helps researchers try out new algebraic operations and can produce nice visualizations using LaTeX. Compared to similar tools written in languages like Julia or Python, this package is more flexible and safer thanks to Haskell's features. Overall, it supports both practical computations and further mathematical research in algebraic combinatorics.
Haskelltreesgraphsalgebraic combinatoricsfunctional programmingLaTeXButcher seriessymbolic computationnumerical integratorsimperative programming
Authors
Eugen Bronasco, Jean-Luc Falcone, Gilles Vilmart
Abstract
We design the Arboretum.hs package for symbolic computations with algebras of trees and more general graphs in Haskell. Thanks to the declarative nature of functional programming, the package's implementation closely follows mathematical definitions, making the code intuitive and transparent for users working with algebraic and combinatorial structures. To assist with current mathematical research, Arboretum.hs supports experimentation by facilitating the introduction of new algebraic operations, as well as providing functionality for rendering trees and forests through LaTeX integration. Compared to recent imperative implementations in languages such as Julia or Python, Arboretum.hs offers greater flexibility for manipulating and extending tree-based structures. Its use of Haskell enables safe programming and strong compile-time guarantees, serving both as a practical computational tool and a foundation for further research in algebraic combinatorics, beyond the setting of trees usually considered in the implementation of Butcher series, which are a fundamental tool for the analysis of numerical integrators.