Arboretum.hs: Symbolic manipulation for algebras of graphs

TL;DR

Arboretum.hs is a Haskell package enabling symbolic algebraic computations on trees and graphs, emphasizing mathematical clarity, extensibility, and integration with LaTeX for research in algebraic combinatorics.

Contribution

It introduces a Haskell-based framework that closely follows mathematical definitions, offering enhanced flexibility and safety over imperative implementations for algebraic graph manipulations.

Findings

Supports experimentation with new algebraic operations

Provides LaTeX rendering for trees and forests

Offers greater flexibility than imperative languages

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.