Can LLMs model real-world systems in TLA+?

https://www.sigops.org/2026/can-llms-model-real-world-systems-in-tla/

by mad • 3 months ago

123 33 3 months ago

dgacmu• 3 months ago

This post reads like an accidental advertisement for approaches like Verus [1], which couple the implementation and verification so you can't end up with a model that diverges from the actual implementation. I'm personally much more optimistic about the verus approach, but I freely admit that's my builder bias speaking.

[1] https://github.com/verus-lang/verus

tmaly• 3 months ago

I remember NVIDA sponsored a TLA+ challenge last year https://foundation.tlapl.us/challenge/index.html

uptodatenews• 3 months ago

Whoa didn't even know cool

asxndu• 3 months ago

... we asked Claude to write a TLA+ specification (spec) for Etcd’s Raft implementation. It passed syntax checks, ran through the TLC model checker, and at first glance looked like a polished formal model.

This is a mistaken use of TLA+!

Leslie Lamport insists that he invented it to be a way of creating "blueprints" for systems.

- You are supposed to go from TLA+ Spec to System (codebase or hardware).

- Not codebase to TLA+ like the author has done.

Otherwise, you may simply model an existing bug properly and the pass all the checks based of its implementation.

He (Leslie Lamport) insists that the value AI can provide is in compiling TLA+ specs to a code base.

tombert2• 3 months ago

Claude has certainly been getting better with TLA+. It's not perfect yet but for laughs I got it to model the rules of Monopoly last night [1]. I haven't done any exhaustive checking on it yet, but it certainly looks passable.

It is pretty impressive at how good it's gotten at this, in a relatively short amount of time no less. I still usually write my specs by hand, but who knows how much longer I'll be doing that.

[1] https://pdfhost.io/v/KU2j37YKrP_Monopoly

ofrzeta• 2 months ago

It looks quite complicated and I have no idea what it is doing. Obviously, since I don't know about TLA+. But what about someone who knows TLA+? It still seems hard to make sure it is valid. And it's just for a relatively simple game.

_doctor_love3• 2 months ago

There is a nice guide to TLA+ from Hillel Wayne here: https://learntla.com/

PlusCal is recommended as the gentler on-ramp to TLA+ for first learning.

comex• 2 months ago

Well, for one thing:

Decline to buy: property stays with bank (auction abstracted out)

Ignoring an entire game mechanic is really stretching the definition of “abstracted out”…

Also, at the bottom it defines a “Liveness: someone eventually wins” property which I believe cannot be proven. Monopoly doesn’t have any rules forcing the game to end eventually. There is only a probabilistic guarantee, and even that only applies if the players are trying to win; if the players are conspiring to prevent the game from ending then they’re unlikely to fail.

_flux• 2 months ago

I've played a bit with having a Claude generate a TLA+ model, I review it, Claude reviews it, and then Claude checks for alignment with the actual system. The code in the system can be annotated with comments to link back to the model, and vice versa, to make human and AI review easier.

I think it's highly promising. I might even call it a success. For example, I was able to express a bug in the system and Claude was able to find me a property that would reveal that in the model; and then revise the model to eliminate that bug, and then revise the code accordinly.

Additionally (with OpenAI) I have a small guest management system I had the LLM generate a TLA+ model about the API which endpoints a client can request from it, and which tokens it learns from it (there are session ids, event ids, guest ids and invitation ids that interact in interesting ways, as guests are not required to have an invitation to the system, and they can have only magic-link protected account, resulting in different visibility on the contact details of others), and what data it can or cannot access with those tokens.

I still haven't manually verified, but it seems rather promising as well.

NooneAtAll32• 2 months ago

I haven't done any exhaustive checking on it yet, but it certainly looks passable.

isn't that exactly the kind of fails LLMs do the most? first-glance-passable nonsense?

randusername• 2 months ago

What's the advantage of provable correctness if it's apparently not easy to prove even for people who understand TLA+? I'm not trying to be a party pooper, just curious.

Isn't logical incorrectness less of a problem in software than failures of imagination or conscientiousness in modeling the domain?

tclancy• 2 months ago

My thought (as someone interested in formal verification but unable to grok the math) is it exists as a canary in any sufficiently-complex codebase I let AI create. Even if it's wrong, knowing that something "we" changed breaks an agreement things currently assume is valuable.

iFire2• 2 months ago

I don't use tla+ to model real-world systems anymore, Claude is able to model systems in Lean 4 and the binary executable can handle real input or I can directly generate c / rust on proofs with numeric types that have ring structure (integers, rationals, bits).

https://github.com/lambdaclass/truth_research_zk

thomasahle• 2 months ago

I'm currently choosing between the right formalization for a big hardware project.

I'm considering between SVA, TLA+ and Lean. With the former being more domain specific and the later more general.

Do you think we'll move towards "Lean for everything" or do domain specific formalisms still make sense?

NooneAtAll32• 2 months ago

what's SVA?

kown7• 2 months ago

Have you considered P? It feels like a good abstraction for engineers as it's "proper" code.

https://github.com/p-org/P

dmos62• 2 months ago

Do you find Lean 4 sufficient for highly async systems?

iFire2• 2 months ago

I haven't made money on yet, but I'm trying to model a webtransport (http/3, quic) system for massive multiplay vr games.

See https://aws.amazon.com/builders-library/challenges-with-dist... for how async related to distributed systems.

pron• 2 months ago

The point of TLA+ is easily readable specs with refinements. That's why it was designed in a novel way rather than in the older executable-with-more-complex-logic style that Lean (and other maths/spec languages) offer. I'm not saying you should prefer TLA+'s approach, but that's what it's meant to accomplish and LLMs don't change that.

atomicnature• 2 months ago

Just a question to people who may know better than me about this.

I thought the whole point of trying to write out TLA+ is so that you get a better idea of what you want and put it into formal language?

I get that an LLM can assist/help with expressing what we want in formal language a bit, but if one automates all this there is no human intent/design anymore.

If the LLM generates both the design (TLA+) and writes an arbitrary program that satisfies said design -- what exactly have we proved?

What assurance do humans get since human doesn't know or cannot specify what they want.

majormajor• 2 months ago

An LLM-generated TLA+ model can be verified for certain things in a way that LLM-generated code can't. It's infamously hard to exhaustively unit-test concurrency.

Whether or not you're modeling the right things or verifying the right things, of course... that's always left as an exercise for the user. ;)

(How to prove the implementation code is guaranteed to match the spec is a trick I haven't seen generalized yet, either, too.)

kiwicopple• 2 months ago

It's infamously hard to exhaustively unit-test concurrency.

a useful example from last week where TLA+ found a bug in pg_rewind:

https://multigres.com/blog/2026/05/04/tla-pg-rewind

pzoln• 2 months ago

Sorry, must be a very naive question, but what if you give LLM just a source code (maybe even obfuscate the names like Raft and Etcd) and ask it to create a TLA+ spec of that?

_doctor_love3• 2 months ago

This is already being done by some folks, reverse-engineering existing source into a TLA+ spec. Like other commenters have mentioned, the challenge is in ensuring that the spec and code match each other.

simplegeek• 2 months ago

I feel LLMs are indeed getting better at writing models. But, in my experience, they struggle to come up with correct safety and liveness properties unless you closely work with them. And of these two, they struggle the most with correct liveness properties.

Also for some problems I observe that models produced by LLMs often cause state space explosion. For simpler models they can fix this when you guide them though.

I’m sure LLMs will get even better.

That said, I take slightly different approach. Lamport said “If you're thinking without writing, you only think you're thinking.” So taking that advice I always try to write the first draft with hand and once I have the final shape in place I then turn to an LLM for further exploration and experimentation if I have to.

alhazrod• 2 months ago

Hopefully some people find this interesting too:

TLAiBench[0]: A dataset and benchmark suite for evaluating Large Language Models (LLMs) on TLA+ formal specification tasks, featuring logic puzzles and real-world scenarios.

[0] https://github.com/tlaplus/TLAiBench

gr71• 2 months ago

is the training data for these testcases in benchmark not already there ? how do llms perform in novel complex systems spec design ?

radarkilat• 2 months ago

hmm

Kab1r• 2 months ago

I've been building a TLA style Temporal Logic library for Verus (using LLMs). My experience so far is that LLMs are surprisingly useful at generating the mechanical proof scaffolding (when they're not occasionally trying to cheat with `assume(false)` statements), but they are not a substitute for knowing what property you actually want.

Can LLMs model real-world systems in TLA+?

Related Stories