# Tree Zipper

> Navigate immutable trees with a zipper cursor. Use when implementing tree traversal, editing tree structures functionally, or tracking focus through breadcrumbs.

- Skill: `knoopx/tree-zipper` (Agent Skill)
- Install (CLI): `npx skillmds@latest add knoopx/tree-zipper`
- Raw SKILL.md: https://api.skillmd.com/api/skills/knoopx/tree-zipper/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: knoopx (https://skillmd.com/u/knoopx)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/knoopx/tree-zipper

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## 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).