[_urga]

See: https://en.wikipedia.org/wiki/Operational_transformation#Cri...

"Due to the need to consider complicated case coverage, formal proofs are very complicated and error-prone, even for OT algorithms that only treat two characterwise primitives (insert and delete)" - Du Li & Rui Li - "An Admissibility-Based Operational Transformation Framework for Collaborative Editing Systems"

There's also an interesting comment there from the author of ShareJS, I think that might be you?

The other critical difference between CRDTs and OT is that CRDTs work offline, in a distributed setting, whereas OT cannot. OT requires a central online server to coordinate, which as far as I understand is the cause of the classic UI freeze in Google Docs whenever the network goes.

[josephg]

Yes thats me! For what its worth, I no longer believe that wave would take 2 years to implement now - mostly because of advances in web frameworks and web browsers. When wave was written we didn't have websockets, IE9 was quite a new browser. We've come a really long way in the last few years.

Working offline and working in a distributed setting are two different properties.

OT can work very well offline - the client and server just buffer ops and you do reconciliation. Some OT algorithms experience O(n*m) performance when the client comes back online (n client ops, m server ops), though the constant is quite low, you can make the client do the work. But you can do better - a better designed text reconciliation system can do O(nlog(n) + mlog(m)) if I remember correctly - which is quite usable in real systems and very competitive with CRDTs.)

P2P is much harder. I've got a sketch for a system that would use OT in a P2P setting, but in many ways its a poor man's CRDT. That said, the downside of CRDTs is that they grow unbounded as you make more modifications. Which would work great for documents that are written then discarded (like a HN thread). But it would work much less well for long lived, frequently written documents (like a server status dashboard). You can fix that using fancy coordination algorithms, but if you're going down that path you're back to sketching out an overcomplicated OT system.

There's lots of fun space to explore there - but not enough actual useful systems being made for production use.

[nornagon]

Designer & author of the JSON OT algorithm that underlies ShareJS/ShareDB here. I do not have a formal proof for any of the properties of the algorithm, but we have extensively fuzzed it and are confident in its correctness. I believe a proof of correctness is possible, merely tedious.

[dangoor]

FWIW, Google Docs can be used offline (both in its Chrome-based and native-app-based incarnations).