Operational Transform

Prerequisites

What it is

Operational transform is a technique for collaborative editing where concurrent operations are transformed against each other before being applied.

Why it matters

If two users edit the same document at once, raw operations can target stale positions. OT adjusts those positions so each user’s intent survives.

How it works

Clients send operations such as insert or delete. A server orders them, transforms operations against concurrent changes, and broadcasts the transformed versions back to clients.

The core is the transform function. When two operations were based on the same document state, the server adjusts the second one so it applies correctly to the document after the first one was applied:

# Transform insert(A) against insert(B) that was applied first.
# If B inserted text before A's position, shift A's position right.

function transform_insert_insert(opA, opB):
    if opA.position > opB.position:
        return Insert(opA.position + len(opB.text), opA.text)
    elif opA.position == opB.position:
        # tie-break by client ID for determinism
        if opA.client_id > opB.client_id:
            return Insert(opA.position + len(opB.text), opA.text)
    return opA   # A is before B, no shift needed

# User A inserts "hello" at pos 0
# User B inserts "!" at pos 0 (concurrent)
# Server applies A first, then transforms B:
#   transform_insert_insert(Insert(0,"!"), Insert(0,"hello"))
#   → Insert(5, "!")   →  document becomes "hello!"

The same idea extends to delete operations and combinations of insert/delete. The hard part is ensuring transform functions are correct for every pair — a single edge case can corrupt the document.