The Power-Set Construction for Tree Algebras

TL;DR

This paper investigates the algebraic properties of power-set operations on classes of trees, establishing a distributive law for linear trees and proving its non-existence for non-linear trees.

Contribution

It introduces a distributive law between the tree monad and the upwards-closed power-set monad for linear trees, and shows such a law cannot exist for non-linear trees.

Findings

Distributive law exists for linear trees

No such law exists for non-linear trees

Advances understanding of tree algebra structures

Abstract

We study power-set operations on classes of trees and tree algebras. Our main result consists of a distributive law between the tree monad and the upwards-closed power-set monad, in the case where all trees are assumed to be linear. For non-linear ones, we prove that such a distributive law does not exist.