tree-zipper
Navigate immutable trees with a zipper cursor. Use when implementing tree traversal, editing tree structures functionally, or tracking focus through breadcrumbs.
What this skill does
## When to use A tree zipper is a cursor for immutable trees. State = (focus, trail). ## Rules - focus is the current subtree - trail is a list of "breadcrumbs" describing the path from root to focus - Each crumb remembers the parent's value plus the siblings NOT taken - down_left/down_right push a crumb and make the chosen child the new focus - up pops the top crumb, rebuilds the parent, and makes that parent the new focus - set_value replaces the focused subtree's value - to_tree walks all the way up to rebuild the whole tree - Key invariant: you can ALWAYS reconstruct the full original tree from (focus, trail) - Equality of two zippers = equality of the fully-reconstructed trees, NOT of the raw (focus, trail) pairs - NEVER compare raw (focus, trail) pairs for equality ## Operations down_left, down_right, up, set_value, to_tree. ## Example Navigate: `z.down_left()` pushes a crumb (parent value + right siblings), sets focus to left child. `z.up()` pops crumb, rebuilds parent. `z.to_tree()` walks all the way up. Compare zippers by `to_tree()` equality, never raw (focus, trail).
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