Implementing a Conflict-Free Replicated Data Type (CRDT) for Text Editing in Go

The challenge is to implement a specific type of Conflict-Free Replicated Data Type (CRDT) designed for collaborative text editing. CRDTs are data structures that allow multiple users to concurrently edit shared data without requiring central coordination, ensuring eventual consistency. This implementation will focus on a Grow-Only Counter (G-Counter) to represent character insertions and a Last-Write-Wins (LWW) register for character deletions.

Problem Description

You are tasked with building a Go implementation of a CRDT that can handle concurrent text insertions and deletions across multiple replicas. The goal is to create a data structure that, when synchronized between replicas, will converge to the same final state, even if operations are applied in different orders.

Key Requirements:

1. G-Counter (Grow-Only Counter): Implement a G-Counter to track character insertions. A G-Counter is a data type that only allows increment operations. Each replica maintains its own counter, and the global value is the maximum of all replica counters. For our text CRDT, this will represent the unique identifier for each character inserted.
2. LWW Register (Last-Write-Wins): Implement a Last-Write-Wins (LWW) register for handling character deletions. An LWW register stores a value and a timestamp. When updating, if the new timestamp is greater than the current one, the value is updated. For deletions, we'll store a "deleted" marker and the timestamp of the deletion.
3. Text CRDT Structure: Design a data structure that represents the text and can store the history of operations. This structure should allow for inserting characters at specific positions and deleting characters at specific positions.
4. Operation Merging: Implement a mechanism to merge operations from different replicas. This involves correctly applying insertions and deletions according to their unique identifiers and timestamps.
5. Text Reconstruction: Provide a method to reconstruct the current state of the text from the CRDT.

Expected Behavior:

• When a character is inserted, it should be assigned a unique identifier (using the G-Counter) and appended to the internal representation of the text.
• When a character is deleted, the corresponding entry in the internal representation should be marked as deleted, along with the timestamp of the deletion (using the LWW register concept).
• When operations from another replica are merged, the CRDT should correctly integrate these operations, ensuring that the final text state is consistent across all replicas.
• The text reconstruction should accurately reflect the current state, excluding deleted characters.

Edge Cases:

• Concurrent insertions at the same logical position (handled by unique IDs).
• Concurrent deletions of the same character.
• Insertion followed by deletion of the same character.
• Deletion followed by insertion of the same character.
• Empty text.
• Large number of operations.

Examples

Example 1: Basic Insertion and Reconstruction

Let's consider a single replica.

Input:

• Initialize an empty TextCRDT for replica "A".
• Insert "H" at position 0.
• Insert "e" at position 1.
• Insert "l" at position 2.
• Insert "l" at position 3.
• Insert "o" at position 4.

Output:

Text: "Hello"

Explanation: The operations are applied sequentially. The G-Counter assigns unique IDs to each character, and the text is built up.

Example 2: Concurrent Insertions and Merging

Replica "A" and Replica "B" start with an empty TextCRDT.

Replica "A" operations:

1. Insert "W" at position 0.
2. Insert "r" at position 1.

Replica "B" operations:

1. Insert "o" at position 0.
2. Insert "l" at position 1.
3. Insert "d" at position 2.

After Replica "A" performs its operations, its internal state might look something like: [{id:1, char:'W', deleted:false}, {id:2, char:'r', deleted:false}]

After Replica "B" performs its operations, its internal state might look something like: [{id:3, char:'o', deleted:false}, {id:4, char:'l', deleted:false}, {id:5, char:'d', deleted:false}]

Now, Replica "A" receives operations from Replica "B" and merges them. Replica "B" receives operations from Replica "A" and merges them.

Assume Replica "A" merges Replica "B"'s operations. The G-Counter will continue to increment globally. The order of insertion matters for the logical position.

If we consider a simplified sequence of operations and merging:

Replica A:

1. Insert 'H' at 0
2. Insert 'i' at 1

Replica B:

1. Insert 'G' at 0
2. Insert 'o' at 1

Scenario:

1. Replica A: Inserts 'H' at 0. Internal state: [{id: 1, char: 'H', deleted: false}]. G-Counter: 1.
2. Replica B: Inserts 'G' at 0. Internal state: [{id: 2, char: 'G', deleted: false}]. G-Counter: 2.
3. Replica A: Inserts 'i' at logical position 1 (after 'H'). Internal state: [{id: 1, char: 'H', deleted: false}, {id: 3, char: 'i', deleted: false}]. G-Counter: 3.
4. Replica B: Inserts 'o' at logical position 1 (after 'G'). Internal state: [{id: 2, char: 'G', deleted: false}, {id: 4, char: 'o', deleted: false}]. G-Counter: 4.

Now, Replica A merges operations from B. The operation {id: 2, char: 'G', deleted: false} needs to be inserted. Based on its unique ID and relative position to other known IDs, it should be placed at logical position 0. Replica A after merge: [{id: 2, char: 'G', deleted: false}, {id: 1, char: 'H', deleted: false}, {id: 3, char: 'i', deleted: false}]. G-Counter: 4.

Replica B merges operations from A. The operations {id: 1, char: 'H', deleted: false} and {id: 3, char: 'i', deleted: false} are merged. Replica B after merge: [{id: 2, char: 'G', deleted: false}, {id: 1, char: 'H', deleted: false}, {id: 3, char: 'i', deleted: false}]. G-Counter: 4.

Output (from either replica after full merge):

Text: "HGi"

(Note: The exact text output depends on how logical positions are resolved during insertion based on unique IDs. A common approach is to use a sequence of characters where insertion position is determined by the "rank" of the character in the sorted list of all active characters.)

Example 3: Deletion and Reconstruction

Starting with the text "Hello" (from Example 1). Assume Replica "A" has this text.

Input:

• Delete character at index 1 (which is 'e'). Timestamp: 100.
• Insert "a" at index 1. Timestamp: 150.

Output:

Text: "Hallo"

Explanation: The character 'e' at index 1 is marked as deleted with timestamp 100. Then, the character 'a' is inserted at logical position 1 (which is now after 'H' and before the original 'l's) with timestamp 150. The reconstruction will omit the deleted character 'e'.

Constraints

• Each replica will have a unique identifier (e.g., a string or integer).
• Timestamps for LWW operations will be integers.
• The G-Counter will generate unique, strictly increasing integer IDs.
• The number of replicas can be large.
• The total number of operations can be very large.
• The implementation should be reasonably efficient for common operations (insert, delete, merge).

Notes

• Consider how to represent the "internal state" of the text. A common approach for text CRDTs is to store a sequence of character "tombstones" (representing deleted characters) and active characters, each with a unique identifier.
• Think about how to determine the logical insertion position for new characters, especially when merging operations from different replicas. This often involves comparing the unique identifiers of existing characters.
• For LWW, the "value" being stored will be the fact that a character at a specific ID has been deleted, along with the timestamp of that deletion.
• The core challenge lies in correctly merging operations to ensure eventual consistency.
• You might need to design data structures for the G-Counter and the CRDT elements themselves.