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Efficient "positions" for lists and text - enabling rich documents and collaboration


Many apps use a list whose values can change index over time: characters in a text document, items in a todo list, rows in a spreadsheet, etc. Instead of thinking of this list as an array, it's often easier to think of it as an ordered map (position -> value), where a value's position doesn't change over time. So if you insert a new entry (position, value) into the map, the other entries stay the same, even though their indices change:


Index    | 0       1       2
Position | pos123  posLMN  posXYZ
Value    | 'C'     'a'     't'

After calling list.set(posABC, 'h') where pos123 < posABC < posLMN:

Index    | 0       1       2       3
Position | pos123  posABC  posLMN  posXYZ
Value    | 'C'     'h'     'a'     't'

This library provides positions (types Position/AbsPosition) and corresponding list-as-ordered-map data structures (classes List/Text/Outline/AbsList). Multiple lists can use the same positions (with the same sort order), including lists on different devices - so you can use this library to implement collaborative lists & text, on top of a variety of network architectures.

Example Use Cases

  1. In a text document with annotations (comments/highlights), store the text using our Text class (a list of characters), and indicate each annotation's range using start and end Positions instead of regular array indices. That way, when the user inserts text in front of an annotation, the annotation stays "in the same place".
  2. In a todo-list app built on top of a database, store each todo-item's Position as part of its database entry, and sort the items using a List at render time. Using positions lets you insert a new todo-item in the middle of the list (by assigning it a position in that spot) or move a todo-item around (by changing its position). This works even for a collaborative todo-list built on top of a cloud database.
  3. In a text editor with an edit history, store the history of (position, char) pairs that were inserted or deleted. By correlating these positions with the text's current (position -> char) map, you can see where text came from ("git blame") and compute exact diffs between historical states. You can even revert edits in the history, or "cherry-pick" edits across history branches.
  4. To make a collaborative text editor, you just need a way to collaborate on the map (position -> char). This is easy to DIY, and more flexible than using an Operational Transformation or CRDT library. For example:
    • When a user types char at index, call [pos] = list.insertAt(index, char) to insert the char into their local list at a new Position pos. Then broadcast (pos, char) to all collaborators. Recipients call list.set(pos, char) on their own lists.
    • Or, send each (position, char) pair to a central server. The server can choose to accept, reject, or modify the change before forwarding it to other users - e.g., enforcing per-paragraph permissions.
    • Or, store the (position -> char) map in a cloud database that syncs for you. You can do this efficiently by understanding the structure of Positions. (See our demos for collaborative rich-text editors on top of various cloud databases.)


Performance Our list data structures have a small memory footprint, fast edits, and small saved states. See our benchmark results for a 260k operation text-editing trace.

Collaboration Lists on different devices can share the same positions. Even in the face of concurrent edits, positions are always globally unique, and you can insert a new position anywhere in a list. To make this possible, the library essentially implements a list CRDT (Fugue), but without the restrictions that come with CRDTs - ultimately, each List is a local data structure that you can edit at will.

Non-interleaving In collaborative scenarios, if two users concurrently insert a (forward or backward) sequence at the same place, their sequences will not be interleaved. For example, in a collaborative text editor, if Alice types "Hello" while Bob types "World" at the same place, then the resulting order will be "HelloWorld" or "WorldHello", not "HWeolrllod".

Escape hatches You can make use of the library without storing all of your data in one of our data structures. In particular, you can ask for a lexicographically-ordered version of a position to use independently of this library, or store list values in your own data structure instead of our default List class.

Related Work

  • Fractional indexing, a related but less general idea.
  • Blog post describing the Fugue list CRDT and how it relates to the "list position" abstraction. This library implements an optimized version of that post's tree implementation (List/Position) and an analog of its string implementation (AbsList/AbsPosition).
  • Paper with more details about Fugue - in particular, its non-interleaving guarantees.
  • Rope, a data structure for efficient text editing that our List class uses as inspiration.


Install with npm:

npm i --save list-positions

AbsList and AbsPosition

An easy way to get started with the library is using the AbsList<T> class. It is a list-as-ordered map with value type T and positions (keys) of type AbsPosition.

Example code:

import { AbsList, AbsPosition } from "list-positions";

// Make an empty AbsList.
const list = new AbsList();

// Insert some values into the list.
list.insertAt(0, "x");
list.insertAt(1, "a", "b", "c");
list.insertAt(3, "y");
console.log([...list.values()]); // Prints ['x', 'a', 'b', 'y', 'c']

// Other ways to manipulate an AbsList:
list.setAt(1, "A");
console.log([...list.values()]); // Prints ['A', 'b', 'y', 'c']

// 2nd way to insert values: insert after an existing position,
// e.g., the current cursor.
const cursorPos = list.cursorAt(3);
const newPos = list.insert(cursorPos, "z");
console.log([...list.values()]); // Prints ['A', 'b', 'y', 'z', 'c'];

// Map-like API:
list.set(newPos, "Z");

AbsPositions are easy to use because they are self-contained: you can use AbsPositions in an AbsList without any prior setup. In other words, their sort order is "absolute", not "relative" to some separate metadata.

The downside of AbsPositions is metadata overhead - their JSON encodings have variable size and can become long in certain scenarios (an average of 187 characters in our benchmarks).

Using AbsList is more efficient than storing all of the literal pairs (absPosition, value) in your own data structure. If you do need to use your own data structure (e.g., a DB table with one pair per row), it should be practical for short lists of perhaps <1,000 values - e.g., the items in a todo list, or the scenarios where Figma uses fractional indexing.

List, Position, and Order

The library's main class is List<T>. It is a list-as-ordered-map with value type T and positions (keys) of type Position.

Example code:

import { List, MIN_POSITION, Order, Position } from "list-positions";

// Make an empty Order and an empty List on top of it.
const order = new Order();
const list = new List(order);

// Insert some values into the list.
list.insertAt(0, "x");
list.insertAt(1, "a", "b", "c");
list.insertAt(3, "y");
console.log([...list.values()]); // Prints ['x', 'a', 'b', 'y', 'c']

// Other ways to manipulate a List:
list.setAt(1, "A");
console.log([...list.values()]); // Prints ['A', 'b', 'y', 'c']

// 2nd way to insert values: insert after an existing position,
// e.g., the current cursor.
const cursorPos: Position = list.cursorAt(3);
const [newPos] = list.insert(cursorPos, "z");
console.log([...list.values()]); // Prints ['A', 'b', 'y', 'z', 'c'];

// Map-like API:
list.set(newPos, "Z");

// You can create and compare Positions directly in the Order,
// without affecting its Lists.
const [otherPos] = order.createPositions(MIN_POSITION, list.positionAt(0), 1);
console.log(, otherPos) < 0); // Prints true
console.log(, list.positionAt(0)) < 0); // Prints true

// Optionally, set the value at otherPos sometime later.
// This "inserts" the value at the appropriate index for otherPos.
list.set(otherPos, "w");
console.log([...list.values()]); // Prints ['w', 'A', 'b', 'y', 'c'];

Unlike AbsPositions, Positions aren't directly comparable. Instead, their sort order depends on some separate metadata, described in Managing Metadata below. The upside is that Positions have nearly constant JSON size, so they are more efficient to share and store than AbsPositions (which embed all of their dependent metadata).

Positions are JSON objects with the following format:

type Position = {
  bunchID: string;
  innerIndex: number;

The bunchID identifies a bunch of Positions that share metadata (for efficiency). Each bunch has Positions with innerIndex 0, 1, 2, ...; these were originally inserted contiguously (e.g., by a user typing left-to-right) but might not be contiguous anymore. Regardless, bunches makes it easy to store a List's map (Position -> value) compactly:

// As a double map:
  [bunchID: string]: {
    [innerIndex: number]: T;

// As a sparse array for each bunch's Positions:
  [bunchID: string]: (T | null)[];

// Using our internal sparse array format:
type ListSavedState<T> = {
  // The sparse array alternates between "runs" of present and deleted
  // values. Each even index is an array of present values; each odd
  // index is a count of deleted values.
  // E.g. [["a", "b"], 3, ["c"]] means ["a", "b", null, null, null, "c"].
  [bunchID: string]: (T[] | number)[];


  • A Position's innerIndex is unrelated to its current list index. Indeed, Positions are immutable, but their list index can change over time.

  • Do not create a never-seen-before Position from a bunchID and innerIndex unless you know what you're doing. Instead, use a method like List.insertAt, List.insert, or Order.createPositions to obtain new Positions. (Reconstructing previously-created Positions is fine, e.g., deserializing a Position received from a collaborator.)

  • AbsPositions have a similar format to Positions:

    type AbsPosition = {
      // Analogous to bunchID, but also includes all of the bunch's dependent metadata.
      bunchMeta: AbsBunchMeta;
      innerIndex: number;
    type AbsBunchMeta = {
      // Opaque JSON struct...

    Thus you can store a map (AbsPosition -> value) compactly, using representations like those above. For example:

    type AbsListSavedState<T> = Array<{
      // One bunch's metadata.
      bunchMeta: AbsBunchMeta;
      // The bunch's values, in ListSavedState's sparse array format.
      values: (T[] | number)[];

Managing Metadata

Each Position depends on some metadata, which is stored separately. (In contrast, an AbsPosition embeds all of its metadata - this is why AbsPositions have a variable size.) To use the same Positions with different instances of the List class (possibly on different devices), you must first transfer this metadata between the Lists.

Specifically, a List's bunches form a tree. Each bunch, except for the special root with bunchID "ROOT", has a BunchMeta that describes its location in the tree:

type BunchMeta = {
  /** The bunch's ID, which is the same as its Positions' bunchID. */
  bunchID: string;
  /** The parent bunch's ID. */
  parentID: string;
  /** A nonnegative integer used by the tree. */
  offset: number;

A List's tree of bunches is stored by a separate class Order, accessible from the List's order property. Multiple List instances can share the same Order via a constructor option. But when Lists have different Order instances, before using a Position from one List in the other (e.g., calling list.set or list.indexOfPosition), you must call list.order.addMetas with:

  • The Position's bunch's BunchMeta.
  • That bunch's parent's BunchMeta.
  • The parent's parent's BunchMeta, etc., up the tree until reaching the root (exclusive). Together, these are the Position's dependencies.

Here are some scenarios, in order of difficulty.

Single List If you only ever use Positions with the List instance that created them (via list.insert, list.insertAt, or list.order.createPositions), you don't need to manage metadata at all.

Single session, multiple Lists Suppose you have multiple Lists in the same session (JavaScript runtime). E.g., a rich-text document might be represented as a List of characters and a List of formatting info. Then it suffices for those Lists to share an Order instance: const list2 = new List(list1.order).

Single user, multiple sessions Consider a single-user app that saves and loads a List to disk. Then you must also save and load the List's Order:

function save<T>(list: List<T>): string {
  // Save the List's state *and* its Order's state (an array of BunchMetas).
  return JSON.stringify({

function load<T>(savedState: string): List<T> {
  const list = new List<T>();
  const { orderSave, listSave } = JSON.parse(savedState);
  // Load the Order's state first, to add the saved BunchMetas.

Multiple users Suppose you have multiple users and a single list order, e.g., a collaborative text editor. Any time a user creates a new Position by calling list.insertAt, list.insert, or list.order.createPositions, they might create a new bunch. Other users must learn of the new bunch's BunchMeta before they can use the new Position.

One option is to always send AbsPositions over the network instead of Positions. Use list.order.abs and list.order.unabs to translate between the two. This is almost as simple as using AbsList and AbsPosition, but with the same cost in metadata overhead - in our collaborative list benchmarks, it has about 2.5x larger network messages than the second option below. However, the messages are still small in absolute terms (216 bytes/op).

A second option is to distribute a new BunchMeta immediately when it is created, before/together with its new Position. For example:

// When a user types "x" at index 7:
const [position, newMeta] = list.insertAt(7, "x");
if (newMeta !== null) {
  // Distribute the new bunch's BunchMeta.
  broadcast(JSON.stringify({ type: "meta", meta: newMeta }));
} // Else position reused an old bunch - no new metadata.
// Now you can distribute position:
broadcast(JSON.stringify({ type: "set", position, value: "x" }));

// Alt: Use an Order.onNewMeta callback.
// list.order.onNewMeta = (newMeta) => { /* Broadcast newMeta... */ }

// When a user receives a message:
function onMessage(message: string) {
  const parsed = JSON.parse(message);
  switch (parsed.type) {
    case "meta":
    case "set":
      list.set(parsed.position, parsed.value);
    // ...

This works best if your network has ordering guarantees that ensure you won't accidentally receive a Position before a BunchMeta that was sent earlier (e.g., causal-order delivery).

Errors you might get if you mis-manage metadata:

  • "Position references missing bunchID: {...}. You must call Order.addMetas before referencing a bunch."
  • "Received BunchMeta {...}, but we have not yet received a BunchMeta for its parent node."

Other Data Structures

The library provides additional data structures that are like List<T> but optimized for specific scenarios. See Classes below.


The library's internals are conceptually simple. By understanding them, you can unlock additional features and optimizations, or implement compatible libraries in other languages. See Internals.


This section gives a high-level overview of the library's exports. The implementations have complete docs, which should show up in your IDE's tooltips.



A list of values of type T, represented as an ordered map with Position keys.

List's API is a hybrid between Array<T> and Map<Position, T>. Use insertAt or insert to insert new values into the list in the style of Array.splice.


A total order on Positions, independent of any specific assignment of values.

An Order manages metadata (bunches) for any number of Lists, Texts, Outlines, and AbsLists. You can also use an Order to create Positions independent of a List (createPositions), convert between Positions and AbsPositions (abs and unabs), and directly view the tree of bunches (getBunch, getBunchFor).


A list of characters, represented as an ordered map with Position keys.

Text is functionally equivalent to a List<string> with single-char values, but it uses strings internally and in bulk methods, instead of arrays of single chars. This reduces memory usage and the size of saved states.


An Outline is like a List but without values. Instead, you tell the Outline which Positions are currently present, then use it to convert between Positions and their current indices.

Outline is useful when you are already storing a list's values in a different sequence data structure: a traditional array, a rich-text editor's internal state, a server-side search library, etc. Then you don't need to waste memory & storage space storing the values again in a List, but you might still need to:

  • Look up the current index of a cursor or annotation that uses Positions.

  • Add a (position, value) pair to the list that was received from a remote collaborator:

    const index = outline.indexOfPosition(position);
    /* Splice value into your other sequence data structure at index; */
  • Convert the other sequence's changes into (position, value) pair updates:

    // When the other sequence inserts `value` at `index`:
    const position = outline.insertAt(index);
    /* Broadcast/store the newly-set pair (position, value); */

Like List, Outline requires you to manage metadata.


A list of values of type T, represented as an ordered map with AbsPosition keys.

AbsList's API is a hybrid between Array<T> and Map<AbsPosition, T>. Use insertAt or insert to insert new values into the list in the style of Array.splice.

Unordered Collections

The library also comes with unordered collections:

  • PositionMap<T>: A map from Positions to values of type T, like List<T> but without ordering info.
  • PositionCharMap: A map from Positions to characters, like Text but without ordering info.
  • PositionSet: A set of Positions, like Outline but without ordering info.

These collections do not support in-order or indexed access, but they also do not require managing metadata, and they are slightly more efficient.

For example, you can use a PositionSet to track the set of deleted Positions in a CRDT. See the ListCrdt implementation in @list-positions/crdts for sample code.


All types are JSON serializable.

Representations of positions:

  • Position, used in List and Outline.
  • AbsPosition, used in AbsList.


  • BunchMeta, used in Order.
  • AbsBunchMeta, used by each AbsPosition to store all of its dependent metadata.

Saved states: Each class lets you save and load its internal states in JSON format. You can treat these saved states as opaque blobs, or read their docs to understand their formats.

  • ListSavedState<T>
  • OrderSavedState
  • TextSavedState
  • OutlineSavedState
  • AbsListSavedState<T>


Min and Max Positions

The constants MIN_POSITION and MAX_POSITION are defined to be the minimum and maximum Positions in any Order. They are the only Positions with bunchID: "ROOT". You'll mostly use these to create positions at the beginning or end of a list: e.g., order.createPositions(p, MAX_POSITION, 1) will create a position after p.

You can also use MIN_POSITION and MAX_POSITION as List keys, like any other Position. Note: Attempting to insert before MIN_POSITION or after MAX_POSITION will throw an error.

For AbsPositions, use AbsPositions.MIN_POSITION and AbsPositions.MAX_POSITION.


A cursor points to a spot in the list between two values - e.g., a cursor in a text document.

Internally, a cursor is represented as the Position (or AbsPosition, for AbsList) of the value to its left, or MIN_POSITION if it is at the start of the list. If that position becomes not-present in the list, the cursor's literal value remains the same, but its current index shifts to the left. (To bind to the Position on the right instead, pass bind = "right" to the cursor methods.)

Convert indices to cursors and back using methods cursorAt and indexOfCursor, on classes List, Text, Outline, and AbsList. These are wrappers around positionAt and indexOfPosition that get the edge cases correct.

Lexicographic Strings

The function lexicographicString(pos: AbsPosition): string returns a string with the property: The lexicographic order on strings matches the list order on positions. These are useful as an escape hatch for interacting with external systems (e.g., ORDER BY in a database), but they should be used sparingly for efficiency reasons.

If you plan to use lexicographic strings exclusively, consider using the position-strings package instead, which is optimized for that use case (smaller JS bundle & more compact strings). Note: Its strings are not compatible with this library's.


Utilities for manipulating AbsPositions.

For example, AbsPositions.encodeMetas and AbsPositions.decodeMetas let you convert between a bunch's dependencies (an array of BunchMetas) and an AbsBunchMeta, which encodes those dependencies more compactly than the literal array.


Utitilies for generating bunchIDs.

When a method like List.insertAt creates a new Position (or AbsPosition), it may create a new bunch internally. This bunch is assigned a new bunchID which should be globally unique - or at least, unique among all bunches that this bunch will ever appear alongside (i.e., in the same Order).

By default, the library uses dot IDs with a random alphanumeric replicaID, via BunchIDs.usingReplicaID(). You can supply a specific replicaID in Order's constructor. E.g., to get reproducible bunchIDs in a test environment:

import { maybeRandomString } from "maybe-random-string";
import seedrandom from "seedrandom";

const prng = seedrandom("42");
const order = new Order({ replicaID: maybeRandomString({ prng }) });
const list = new List(order);
// Test list...

More generally, you can supply an arbitrary newBunchID function in Order's constructor.

Interface BunchNode

An Order's internal tree node corresponding to a bunch of Positions.

You can access a bunch's BunchNode to retrieve its dependent metadata, using the meta() and dependencies() methods. For advanced usage, BunchNode also gives low-level access to an Order's internal tree.

Obtain BunchNodes using Order.getNode or Order.getNodeFor.

Misc Functions

  • expandPositions(startPos: Position, sameBunchCount: number): Position[] Returns an array of Positions that start at startPos and have sequentially increasing innerIndex.
  • positionEquals(a: Position, b: Position): boolean Equality function for Positions.
  • compareSiblingNodes(a: BunchNode, b: BunchNode): number Compare function for BunchNodes with the same parent, giving their order in the internal tree.


The benchmarks/ folder contains benchmarks using List/Text/Outline/AbsList directly (for local usage or client-server collaboration) and using CRDTs built on top of the library.

Each benchmark applies the automerge-perf 260k edit text trace and measures various stats, modeled on crdt-benchmarks' B4 experiment.

Results for an op-based/state-based text CRDT built on top of a Text + PositionSet, on my laptop:

  • Sender time (ms): 655
  • Avg update size (bytes): 92.7
  • Receiver time (ms): 369
  • Save time (ms): 11
  • Save size (bytes): 599817
  • Load time (ms): 10
  • Save time GZIP'd (ms): 42
  • Save size GZIP'd (bytes): 87006
  • Load time GZIP'd (ms): 30
  • Mem used estimate (MB): 1.8

For more results, see

Performance Considerations

For questions about performance, optimizations, or specific use cases, feel free to open an issue.

Here are some general performance considerations:

  1. The library is optimized for forward (left-to-right) insertions. If you primarily insert backward (right-to-left) or at random, you will see worse efficiency - especially storage overhead. (Internally, only forward insertions reuse bunches, so other patterns lead to fewer Positions per bunch.)

  2. AbsPositions and Positions are interchangeable, via the Order.abs and Order.unabs methods. So you could always start off using the simpler-but-larger AbsPositions, then do a data migration to switch to Positions if performance demands it.

  3. The saved states are designed for simplicity, not size. This is why GZIP shrinks them a lot (at the cost of longer save and load times). You can improve on the default performance in various ways: binary encodings, deduplicating replicaIDs, etc. Before putting too much effort into this, though, keep in mind that human-written text is small. E.g., the 600 KB uncompressed CRDT save size above is the size of one image file, even though it represents a 15-page LaTeX paper with 6x overhead.

  4. For smaller AbsPositions, saved states, and lexicographic strings, you can reduce the size of replicaIDs from their default of 21 chars. E.g., even in a popular document with 10,000 replicaIDs, 8 random alphanumeric chars still guarantee a < 1-in-5,000,000 chance of accidental replicaID reuse (cf. birthday problem):

    import { maybeRandomString } from "maybe-random-string";
    const order = new Order({ replicaID: maybeRandomString({ length: 8 }) });
  5. For very large lists, you can choose to call List.set on only the Position-value pairs that are currently scrolled into view. This reduces memory and potentially network usage.

  6. The Text and Outline classes have smaller memory usage and saved state sizes than List, so prefer those in situations where they are sufficient.

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