LTree in PureScript: A Detailed Overview

In this article, we will explore the LTree data structure and its implementation in PureScript.

What is an LTree?

An LTree, also known as Leaf Tree, is a special type of binary tree in which all the values are stored only in the leaf nodes. Non-leaf nodes (also known as internal nodes) do not hold any data but serve the purpose of maintaining the tree’s structure.

data LTree a = Leaf a | Node (LTree a) (LTree a)

PureScript Implementation

Building an LTree

In PureScript, an LTree is defined using a data declaration, indicating it as a data type with a type parameter ‘a’. An LTree of type ‘a’ is either a Leaf containing a value of type ‘a’, or a Node containing two subtrees of type ‘a’.

Operations on LTree

In-Order Traversal

The inorder function is used for the in-order traversal of an LTree.

In-order traversal is a method of visiting all the nodes of a tree in a specific order: left child, parent, and then right child.

inorder:: forall a. LTree a -> Array a
inorder (Leaf x) = [x]
inorder (Node l r) = inorder l <> inorder r 

When applied to an Leaf, the inorder function simply returns an array with a single element, the value of the Leaf.

When applied to a Node, the inorder function performs an in-order traversal of the tree. It first traverses the left subtree, then the right subtree, and concatenates the results.

Conclusion

The LTree is a simple yet powerful data structure that exemplifies the principle of separation of concerns: the leaf nodes are responsible for storing data, while the internal nodes are responsible for defining the tree’s structure. The LTree data structure and its corresponding operations are efficiently and elegantly implemented in PureScript, showcasing the language’s strong support for algebraic data types and higher-order functions.