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.

翻译：我们设计了Arboretum.hs软件包，用于在Haskell中对树代数及更一般图结构进行符号计算。得益于函数式编程的声明式特性，该软件包的实现紧密遵循数学定义，使从事代数与组合结构研究的用户能够直观理解代码。为辅助当前数学研究，Arboretum.hs通过简化新代数运算的引入机制支持实验性探索，并提供通过LaTeX集成渲染树与森林的功能。相较于近期Julia或Python等语言中的命令式实现，Arboretum.hs在操作与扩展树结构方面展现出更高的灵活性。其基于Haskell的实现保障了安全编程与强编译期保证，既可作为实用计算工具，亦能为代数组合学领域的后续研究奠定基础——其应用范围超越通常用于Butcher序列（求解数值积分器的基本工具）实现的树结构场景。