I can see how this is useful if you’re repeatedly updating the same part of a tree. I can’t quite see how to use this approach for random edits. Seems like you’re back at recreating all the nodes back up to the root every time?

Zippers are part of Clojure API (clojure.zip). They take a bit of work to get used to, but once you get it they are an amazing way of making "transactional" "changes" to immutable data structures.

I've built quite a lot of functionality on top of Clojure's version of this. For deeply nested stuff it's great, necessary even. But for shallow sequences where you're mostly doing complex logic looking back and forth, I genuinely think you're better off building some sort of parser combinator solution where you can more naturally match multiple conditions over long ranges, and alter the output as you send it out, transducer-style. You're also much more likely to end up with good performance compared to the constant recursive navigation you do with zippers.

i was messing around on hackerrank a few years ago and one of the problems involved implementing Huet's zipper tree, which I did in haskell. it was quite fun

https://github.com/xdavidliu/fun-problems/blob/main/zipper-t...

There's a neat paper where they implement basic blocks (in a control flow graph) as zippers (https://www.cs.tufts.edu/~nr/pubs/zipcfg.pdf). The neat part is that - due to how the host language works (mutation having the cost of invoking the write barrier) - their measurements show that the zipper version is more performant than the mutable version.

I've used the zipper concept with lists for making impossible states impossible [0] in the context of Rust programs. The rich enum type in Rust creates opportunities to avoid bugs by baking small state machines into the code everywhere, like loading data in the linked example.

A concrete example is for managing the active item in a list. Instead of storing the active item as an index into the vector like this:

  struct List<T> {
    items: Vec<T>,
    active: usize,
  }

...which two the glaring impossible states. The vector can be empty, or the index can be outside the vector. Each time the active item is desired, we must check the index against the current state of the list.

Instead, we can use the zipper concept so we always have a concrete active item:

  struct List<T> {
    prev: Vec<T>,
    active: T,
    next: Vec<T>,
  }

Switching to a different active item requires some logic internal to the data structure, but accessing the active item always results in a concrete instance with no additional checks required.

[0]: https://sporto.github.io/elm-patterns/basic/impossible-state...

  struct List<T, A> {
    prev: Vec<T>,
    active: A,
    next: Vec<T>,
  }

  self.prev.iter()
    .chain(iter::once(self.active))
    .chain(self.next)

Zippers are the derivative of lists. You can go beyond lists, too.

https://journals.sagepub.com/doi/abs/10.3233/FUN-2005-651-20...

Here[1] is a nice breakdown of Zippers in Clojure. I am not the author of the post but I found it very helpful when I wanted to learn more about Zippers in Clojure. There are some nice illustrations as well.

- https://grishaev.me/en/clojure-zippers/

Archived version with the images still there...

https://web.archive.org/web/20160328032556/http://www.goodma...