# CRDT Design for Music Notation Grid

## Overview

This document captures the design considerations for implementing a CRDT-based state management system for a music notation grid that supports rhythmic subdivisions (e.g., triplets, quintuplets).

**Last Updated:** 2025-11-12

## Domain Context

- **Grid Structure:** Rows of cells representing rhythmic divisions
- **Base Unit:** Cells represent musical durations (e.g., quarter notes)
- **Subdivisions:** Replacing N cells with M cells of different duration (e.g., 4 eighth notes → 3 eighth note triplets)
- **Critical Constraint:** Total rhythmic duration of each row must remain constant (width preservation)

## Why Not Use Automerge/JSON CRDT?

### Problems with Generic JSON CRDTs

1. **Invariant Enforcement:** Automerge doesn't know about width constraints
   - Concurrent edits might violate total duration
   - No way to "reject" a CRDT merge after the fact
   - Can't undo without breaking causality

2. **Wrong Abstraction Level:**
   - Automerge provides list/map primitives
   - We need rhythmic subdivision semantics
   - Like using text CRDT for spreadsheet formulas

3. **Validation After Merge:**
   ```typescript
   const doc = Automerge.merge(docA, docB);
   if (!isValidWidth(doc.grid.rows[0])) {
     // Now what? Can't reject, can't undo easily
   }
   ```

## Recommended Approach: Operation-Based CRDT

### Core Principles

1. **Cell IDs instead of indices** - stable references across replicas
2. **Subdivide = delete + insert** - clear semantics that preserve duration
3. **Conflict detection** - width violations shown to users, not silently resolved
4. **Operation-level commutativity** - same result regardless of operation order

### Type Definitions

```typescript
export type CellId = string; // UUID

export type Cell = Immutable<{
  id: CellId;

  // Fractional index for positioning (like Figma, Linear)
  position: string;  // e.g., "a0", "a0.5", "a1"

  // Rhythmic duration this cell represents (e.g., 0.25 = quarter note)
  duration: number;

  // Reference to parent if this is a subdivision
  parentCellId: CellId | null;

  // CRDT metadata
  createdBy: string;  // OpId
  timestamp: HLCTimestamp;
  deleted: boolean;  // Tombstone for deletions
}>;

export type CreateGrid = Immutable<{
  type: "createGrid";
  opId: string;
  timestamp: HLCTimestamp;
  gridId: string;
  rows: number;
  baseCellsPerRow: number;

  // Pre-generated cell IDs for initial cells
  initialCellIds: CellId[][];  // [row][col]
}>;

export type Subdivide = Immutable<{
  type: "subdivide";
  opId: string;
  timestamp: HLCTimestamp;
  gridId: string;
  rowIndex: number;

  // Cells to mark as deleted (tombstone)
  deletedCellIds: CellId[];

  // New cells to insert
  newCells: Array<{
    id: CellId;
    position: string;  // Fractional index between neighbors
    duration: number;  // Must sum to deleted cells' total duration
  }>;
}>;
```

### Key Design Decisions

#### 1. Fractional Positioning

Uses fractional indexing (similar to Figma's approach) to allow insertion between any two cells without reindexing.

```typescript
// Example positions:
"a0"     // First cell
"a0.5"   // Inserted between first and second
"a1"     // Second cell
"a1.25"  // Inserted between second and third
```

#### 2. Tombstones for Deletions

Cells are never truly deleted, just marked with `deleted: true`. This ensures:
- Idempotent operations (deleting twice is safe)
- Causal consistency (can tell what existed when)
- Conflict detection (know if concurrent ops targeted same cells)

#### 3. Duration Preservation by Construction

Each `Subdivide` operation ensures:
```typescript
const deletedDuration = deletedCellIds.reduce(
  (sum, id) => sum + getCellById(id).duration,
  0
);

const insertedDuration = newCells.reduce(
  (sum, cell) => sum + cell.duration,
  0
);

// Must be equal (enforced when creating operation)
assert(deletedDuration === insertedDuration);
```

## Conflict Resolution Options

### Option 1: Last-Writer-Wins Per Cell

```typescript
function applySubdivide(cells: Cell[], op: Subdivide): Cell[] {
  const targetCellsExist = op.deletedCellIds.every(id =>
    cells.find(c => c.id === id && !c.deleted)
  );

  if (!targetCellsExist) {
    // Target cells already deleted by concurrent op
    // This op becomes no-op (idempotent)
    return cells;
  }

  // Apply deletion + insertion
  // ...
}
```

**Pros:**
- Simple, deterministic
- Guaranteed commutative (same result regardless of order)

**Cons:**
- Silently drops one user's edit
- No way to recover lost intent

### Option 2: Hierarchical Cell Model

Subdivisions create nested structure:

```typescript
export type Cell = Immutable<{
  id: CellId;
  duration: number;

  // If subdivided, contains child cells
  children: Cell[] | null;

  // For CRDT: track modifications
  createdBy: string;
  subdivideOps: Set<string>;
}>;
```

**Pros:**
- Preserves both users' intent
- Can show both subdivisions in UI

**Cons:**
- Complex merge logic
- Unclear what "subdivide an already-subdivided cell" means
- May require user resolution anyway

### Option 3: Conflict Detection + User Resolution (RECOMMENDED)

Allow concurrent operations to apply, but detect conflicts:

```typescript
function validateRowWidth(row: Row): ValidationResult {
  const activeCells = row.cells.filter(c => !c.deleted);
  const totalDuration = activeCells.reduce((sum, c) => sum + c.duration, 0);
  const expected = getExpectedDuration(row);

  if (totalDuration !== expected) {
    return {
      valid: false,
      conflictingOps: findConflictingOps(row),
      affectedCells: findAffectedCells(row),
      suggestedResolution: {
        // Provide options to user
      }
    };
  }

  return { valid: true };
}
```

**Pros:**
- No silent data loss
- Users understand what happened
- Can choose best resolution per case

**Cons:**
- Requires UI for conflict resolution
- Temporary invalid states exist
- More complex UX

## Open Questions

1. **Which conflict resolution method to use?**
   - Pure LWW?
   - Conflict detection + user resolution?
   - Hybrid approach?

2. **Fractional indexing implementation:**
   - Use existing library or custom?
   - How to handle position exhaustion?

3. **Operation validation:**
   - Client-side only or server-side too?
   - How to handle invalid operations from old clients?

4. **Snapshot strategy:**
   - When to create snapshots for performance?
   - How to compact operation history?

## Next Steps

- [ ] Decide on conflict resolution strategy
- [ ] Implement basic Cell ID system
- [ ] Replace index-based operations with ID-based
- [ ] Add operation IDs and timestamps (HLC)
- [ ] Implement fractional positioning
- [ ] Test commutativity with randomized operation order
- [ ] Design conflict UI (if using Option 3)

## References

- [Automerge Documentation](https://automerge.org/)
- [Yjs CRDT](https://docs.yjs.dev/)
- [Figma's Fractional Indexing](https://www.figma.com/blog/realtime-editing-of-ordered-sequences/)
- [Hybrid Logical Clocks Paper](https://jaredforsyth.com/posts/hybrid-logical-clocks/)

## Related Code

- Current implementation: `src/doc/index.ts`
- Grid realization logic: `src/doc/index.ts:87-125`