Exploring the NaiadClock TLA+ model in TLA-Web

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I have been impressed by the usability of TLA-Web from Will Schultz. Recently I have been using it for my TLA+ modeling of MongoDB catalog protocols internally, and found it very useful to explore and understand behavior. This got me thinking that TLA-Web would be really useful when exploring and understanding an unfamiliar spec I picked up on the web.

To test my hunch, I browsed through the TLA+ spec examples here,  and I came across this spec about the Naiad Clock. Since I had read DBSP paper recently, this was all the more interesting to me. I had written about Naiad in 2014, and about dataflow systems more broadly in 2017.


Getting to the ASCII version of the spec

Unfortunately, I would not be able to play with the spec, because it only came in paper form: "The Naiad Clock Protocol: Specification, Model Checking, and Correctness Proof."  The spec was available only as 13 pages of latex symbols in the Appendix A of this paper. I did briefly consider manually transforming this to the ASCII version by spending 2-3 hours, but then I remembered I am lazy, ADHD, and hahaha it is so funny that I even considered I could do this. Then I had a thought. What if I give this pdf to ChatGPT and asked back the ASCII version. Lo and behold that worked almost flawless, and in less than a minute's work!

I was so impressed that I tweeted about what a marvel this is. This could be a great way to salvage some TLA+ specs that only appear in latex formatted pdf publications. 



There was only one place that didn't parse, and ChatGPT was confused about prec versus preceq. This is understandable because this is a rare symbol; I haven't seen those used in a tla spec before. The interesting thing is that, it didn't even matter. I found that the prec definitions where superfluous. I could have just used leq[a][b] instead, which I ended up doing.


The spec

After I got to a compiling spec in a couple of minutes, I started looking for simplifications and improvements. I ended up making several of these over the next hour. For example, I parametrized the next actions to make the spec more readable. Parametrized next actions also enable us to select which parametrized version of the action to choose for the next action in TLA-Web and makes interactive exploration/simulation possible, as we discuss soon. 

In the spec, there are a lot of definitions early on about Delta vectors. It is better to skim over those, as the interesting part of the spec starts with variable definitions towards the end. The protocol has the flavor of incrementalized computation as I describe below. 

Where is the clock? There is no clock, this is more of a distributed convergent progress tracker maintained across the processes. As the paper says: "The Naiad Clock Protocol oversees the progress of a computation running within Naiad."

Here is the ASCII version I ended up producing. I hope this helps someone else when modeling a similar protocol. The model checking takes a  long time, even with small value choices for the parameters, e.g.,  Point = {p1,p2, p3} and Proc = {a,b}.

In a Naiad computation, each record is associated with a point in "virtual time," which represents its stage in the computation. These points form a partially ordered set. Operations transform input records from one set of points into output records at another set. The Procs {a,b} are just stateless compute nodes that perform that processing/operation.

This is a lot to take in. The spec also looks daunting, but TLA-Web makes exploring this specification easier and understandable, and that is what I'll describe next.


TLA-Web

After loading spec in TLA-Web, we get to choose an initial spec. To keep things interesting I choose a partial ordering of the points such that p3>p2 and p3>p1 and p1 and p2 are not ordered. So we have a DAG. This initial state might be hard to find because there are so many initial states allowed by the spec. So, if you click this link, these all comes preselected/loaded, and you can get to explore the computation by clicking on the enabled actions on the left panel.



On the right panel for state visualization, try this. Click on (un)explode and choose explode "points". This groups variables that are point-indexed together for better visualization. As an alternative process centered view, you can try exploding "Procs" and following the computation from that lens as well. 

As I mentioned above, "points" are important. Records go up through the points DAG. The processors {a,b} are just stateless compute nodes that help with that processing. The processors also exchange messages to inform each other and catchup on the current progress of records in the DAG. You can track the progress in the temp and nrec variables that are  point-indexed.  

When clicking an enabled NextPerformOperation in the left pane, notice that you get options. In some of the options, a p1 or p2 consumption may lead to a p3 increase, a new record created for processing at p3. That makes things interesting. 

An action chosen for processor a to process the record at p1 may create a record for p3. This action creates a local diff at temp[a] but that hasn't been shared with processor b. Temp is basically the delta vector to update the current state. temp[a] and temp[b] that keeps delta updates.  

After all NextPerformOperations are performed, and after you select all send updates receive updates to make these crdts converge, you have quiescence as in this computation trace. 


Epilogue 

This was fun. As I predicted, TLA-Web proved really useful when exploring and understanding a new spec I picked up on the web. I don't think I would have gotten a good sense of what the spec was doing without playing with it using TLA-Web. 



Will keeps adding features on TLA-Web, even though he does this as a hobby project. He just added animation support to TLA-Web, checkout the Cabbage Goat Wolf puzzle and select the animation tab on the right. There are other examples on the repo. This kind of visualization/exploration tools is a huge boon for the TLA+ ecosystem. Will is on a roll, he just finished his PhD, and joined me and Jesse at the distributed systems team at MongoDB Research today. Welcome Will!


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