functional programming - What is the Zipper data structure and should I be using it?

Question

The question is simple: I cannot understand the Zipper data structure.

My question is related to its uses with a Tree.

I want to understand how can I change the tree node using zipper. And how not to copy the whole tree (or the most part of it).

Please, clarify if I'm wrong with zipper. Maybe it cannot help with the tree update?
Or, maybe, it is possible to update the tree and I just cannot see the way?

Answer 1

Let's start with the Zipper-analog for lists. If you'd like to modify the nth element of a list, it takes O(n) because you have to copy the n-1 first elements. Instead, you can keep the list as a structure ((first n-1 elements reversed) nth element (remaining elements)). For example, the list (1 2 3 4 5 6) modifiable at 3 would be represented as ((2 1) 3 (4 5 6)). Now, you can easily change the 3 to something else. You can also easily move the focus left ((1) 2 (3 4 5 6)) and right ((3 2 1) 4 (5 6)).

A zipper is the same idea applied to trees. You represent a certain focus in the tree plus a context (up to parents, down to children) which gives you the whole tree in a form where it's easily modifiable at the focus and it's easy to move the focus up and down.