Say we have a zipper containing [0, 1, 2, 3, 4, 5], and we're focusing on the 3. In code this will look like:
([2, 1, 0], 3, [4, 5])
To focus on the next element, we put the currently focused element on the first list, and pull the head off the second list:
([3, 2, 1, 0], 4, [5])
([1, 0], 2, [3, 4, 5])
3
/ \
2 4
| |
1 5
|
0
This works nicely as an immutable datastructure, since the tails of both lists can be shared (i.e. we don't need to copy the whole list, just the wrap/unwrap an element on to the head)
Zippers were first applied to lists, but have since been generalised:
- To trees: focusing on one node, and being able to move the focus up, to the left-child, or to the right child
- To having more than one focus
- To datastructures more generally, by treating them as 'derivatives' (as in calculus)
https://en.wikipedia.org/wiki/Zipper_(data_structure)
As an example, the XMonad window manager uses a zipper to keep track of the currently-focused window.
I've also used Zippers for window management, e.g. having a list of Displays, with one of them focused (accepting keyboard input); each Display containing a list of Workspaces, with one of them focused (currently shown); and each Workspace containing a list of Windows, with one of them focused (the active window). Keyboard shortcuts could shift between the previous/next Window, Workspace, or Display.