zipper package:zippers is:module

This module provides a Zipper with fairly strong type checking guarantees. The code here is inspired by Brandon Simmons' zippo package, but uses a different approach to represent the Zipper that makes the whole thing look like his breadcrumb trail, and can move side-to-side through traversals. Some examples types:

• Top :>> a represents a trivial Zipper with its focus at the root.
• Top :>> Tree a :>> a represents a Zipper that starts with a Tree and descends in a single step to values of type a.
• Top :>> Tree a :>> Tree a :>> Tree a represents a Zipper into a Tree with an intermediate bookmarked Tree, focusing in yet another Tree.

Since individual levels of a Zipper are managed by an arbitrary IndexedTraversal, you can move left and right through the IndexedTraversal selecting neighboring elements.

>>> zipper ("hello","world") & downward _1 & fromWithin traverse & focus .~ 'J' & rightmost & focus .~ 'y' & rezip
("Jelly","world")

This is particularly powerful when compiled with plate, uniplate or biplate for walking down into self-similar children in syntax trees and other structures. Given keys in ascending order you can jump directly to a given key with moveTo. When used with traversals for balanced tree-like structures such as an IntMap or Map, searching for a key with moveTo can be done in logarithmic time.