A verified program assumes a correct compiler, a correct OS, and hardware that never flips a bit. Formal methods don't remove assumptions. They make you write them down, and they can stitch those layers together too, proving each one keeps the promises the next relies on.
In 2009 I spent months convincing HOL4 that Γ(n+1) = n!, one tactic at a time. It took 3 years to land in the Journal of Automated Reasoning.
17 years later, AI is formally verifying real software at scale. Huge respect to everyone who kept proving by hand all these years so we could see this go mainstream.
New on our Frontier Red Team blog: using Claude to formally verify software at large scale.
Formal verification can prove that code is free of certain bugs, but historically it has only been feasible for small codebases (or required a lot of expert time).
With AI models, however, this is beginning to change. In collaboration with @theoremlabs, we used Claude to prove security properties in over one hundred real-world open-source libraries over the span of a few weeks.
Read our research in full here: anthropic.com/research/forma…
A robot earns its place when people stop noticing it. Reliability is the real product, and everything else is a prototype.
Two jobs for every robotics founder:
Avoid pseudo-safety specialists. They sell checklists, not judgment, and they're why people think safety is paperwork.
Ignore the AI slop on compliance and safety cases.
Safety isn't irrelevant. It's been badly represented.
People have said for years that end to end autonomy will not work. FSD and Robotaxi already answer that. The next decade is fleets that learn a city overnight and robots that take the same stack off the road and into the world. The spec catches up to the system, not the other way around. @teslasi
Great example of proactive safety xitter.cf/aelluswamy/status/2104…
Formal methods deserves a comeback, but the fog is killing it. Nobody can answer: where, when, what it buys over testing, how proving differs. Stop the cannon-for-a-bee instinct. Clear the fog, or the comeback never lands.
As a formal methods guy, I would like to see the properties/statements for both lean and TLA+
Overall great to see formal
I used Opus 5.5 to formally verify the Claude Agent SDK using Lean. A couple short prompts = 16 PRs fixing various bugs and race conditions. Video attached.
TLA+ also works well. I sometimes combine Lean and TLA+ to look for issues around data flow, concurrency, and state mgmt.
I don't know either language well, but Claude is excellent at both. This approach is super useful for formally modeling your code and finding bugs that a human probably wouldn't have spotted.
Is formal verification the future of coding (or at least, bug finding)?
Humanoid robotics is harder than autonomous driving, not easier. Most companies won’t solve either.
One will solve both - Tesla
@teslasi @Tesla_Optimus @Tesla
Decomposing autonomous driving into sense → perceive → plan doesn't make it safer. It makes it easier to audit, which isn't the same thing.
Safety is a system-level property. You can have modules that each pass their own tests and still get failures at the interfaces, where the real bugs live.
Decomposition works great for hardware and for vertical software stacks, where interfaces are well-defined and boundaries are natural. Decomposing the driving task doesn't give you that. It just gives you lossy abstractions at every handoff.
Worth remembering: the human brain isn't cleanly modular either. Perception and planning are deeply entangled, not a pipeline. Maybe the right question isn't "modular vs end-to-end" but "how do we verify systems whose safety lives in the interactions, not the parts
Funny to see topics we were working on 11 years ago suddenly become some of the hottest topics in AI: learning-assisted automated reasoning, theorem proving, and formalizing physics.
Sometimes research just needs a decade for the world to catch up😀
Heads up, robotics: car autonomy is on track to be solved and the sensor wars are coming for you sooner than you think. Same people, same slides. The plastic bag drifting across the freeway is now a small object on your kitchen floor matching the floor color and it puts your robot on its back.
I am not talking about Lidar.
In near future, we won’t need countless apps. One master app will adapt its interface to you, whether for personal use or engineering. Same data, endless experiences.
Umair S retweeted
FSD doesn’t need to squint its 👁️ when facing the ☀️.
Wow. FSD and I were staring straight into the sun near Pagosa Springs, CO. FSD started to slow down. I initially started to override it, but remembered that FSD is usually right so I let it slow. Boy was it right. I would've hit this deer. @aelluswamy @teslasi