How do I code a tree of objects in Haskell with pointers to parent and children?

Question

I\'ve got the following problem: I have a tree of objects of different classes where an action in the child class invalidates the parent. In imperative languages, it is trivial

Answer 1

Modifying a tree which might require frequent excursions up the path to the root and back seems like the perfect job for a variant of the Zipper data structure with "scars", in the terminology of the original paper by Huet; the code samples from the paper also suggest a name of "memorising zipper". Of course, with some care, a regular zipper could also be used, but the augmented version might be more convenient and/or efficient to use.

The basic idea is the same as that behind a regular zipper, which already allows one to move up and down a tree in a purely functional manner (without any explicit back-pointers), but a "go up" operation followed by a "go down" operation becomes a no-op, leaving the focus at the original node (whereas with the regular zipper it would move it to the leftmost sibling of the original node).

Here's a link to the paper: Gérard Huet, Functional Pearl: The Zipper. It's just six pages, but the ideas contained therein are of great usefulness to any functional programmer.