HN staff: someone posted before me. Could we change the title to
"Bend - a language that blocks AI mistakes via proof and runs on GPUs"?
Everyone: feel free to ask any question, but I'd be highly appreciative if you could be a bit civilized and respectful this time. I've worked on this for 1 year, nearly 16h/day, 7 days a week, and I'm giving it for free. You need not to use it. So, I'd be thankful if you could point occasional failures politely rather than throwing me in a lava pit.
Amazing work, one question regarding the guide, it states:
> That same file is the CPU program and the GPU kernel: clang builds it for the host, Metal or CUDA builds it for the device, so a `!` runs the exact same code on either chip.
What exactly is this saying? The guide doesn't really explicitly define `!`, and it's unclear from this sentence whether it's saying that, "clang builds it for the host and Metal, and CUDA builds it for the device", or if it's saying, "clang builds it for the host, Metal, and CUDA, and builds it for the device", or something else entirely.
It just means that Bend compiles to a single .c file, and that file compiles to either Metal or CUDA, via macros, depending on your target. This shouldn't be relevant to most users. It is just a way I found to keep the file small and reuse as much code as possible, rather than rewriting the runtime 3 times (once for C, once for Metal, once for CUDA).
Don't know whether this is a common outcome, but I tried the "remove the walls" example, and the result was... scary. It completely changed the game so that movement is now diagonal, and made the arbitrary decision that up/down move you on the positive diagonal, and left/right move you on the negative diagonal.
The problem, of course, is that having only the one single "you can't win" law is severely underspecified, but the solution was too clever by half, and highlights the problem with this approach — every program will be under-specified, because, at some point, writing the laws becomes a bigger problem than writing the code itself.
This becomes a real issue because the combination of underspecified but rigid laws pushes the aI towards this sort of "creative" solution that matches the letter but not spirit of the law. In this case, the issue was obvious, but I seriously worry about what sort of shenanigans will occur in less obvious cases.
I like the idea of a language intended from the start to be proved and it seems very compelling given coding agents. It's a good idea that others don't see coming -- so expect it to be frequently misunderstood and even verbally abused!
Could you recommed literature (preferrably a single book) that does not require prior knowledge and allows to fully understand the logical foundation of it?
(Why it is done the way it is, what problems are solved by affinity, why closure can be called at most once, how a function that never returns can prove anything, and everything else)
I'm confused - could you explain how the board/flag animation relates to Bend's compile time checking? Is it actually a direct demonstration of Bend running a check?
The check is happening in between the animations. When the AI edits the code, Bend will check if all laws still hold, mathematically so. If not, the AI repeats, until that's the case. So, the animations just show what happens to the app with and without Bend's involvement.
> In the post-AGI economy, humans will eventually stop writing and reading code, but we still need an ambiguity-free way to tell the AIs building the world around us what we want done.
Why? Won't an AI that can correctly write any program (and make any change) also be smart enough to know what exactly we want better than we can explain, at least ahead-of-time?
> With proofs, we can verify that the AI implemented our prompts correctly.
How? Either we're able to understand all the theorems, which takes a lot of work, or we need to trust the AI, in which case the verification method can be a hidden implementation detail. Normally, when using formal methods, we choose to focus on certain important properties and verify only those.
I like the law idea, but what i found they end up doing is they just modify the law itself to fit the new feature they are working on, which defeats the point.
Which means some laws needs to be frozen. But not all laws, otherwise you can't add or modify anything. So the judgement is still on the human part, and we're back to meatbags being the bottleneck.
I've seen some success adding these proof-like checks to CI every time agents do something irrational. I definitely think it should be part of every codebase.
Would the author have specified on the page that it's a fast new language with a new take on proof and so on, without mentioning ai and that alone would have caught my attention. It seems like if there isn't the word ai people are not interested anymore, we used to care many of us used to care
I read the readme and the guide file. There is just one thing I can comment: might as well solve the NP hard problems. I think you can do it easily, author. As you can already solved harder problems than those with your language.
Jokes aside, I think the idea is that the law is simple to code, the proof that it holds is where the agent is responsible. This probably becomes less true though as you try to express more complicated laws.
Unless the proofs themselves are defined with natural language, I don't see them being adopted by humans. It takes a high cognitive load to read let alone write a proof.
Agree, but natural languages have ambiguity, the AI output should really include the assumptions and we seriously need to replace the word "prompt" with "conversation".
Victor Taelin's work (HVM) got me interested in interaction combinators as a compilation target. I'm now working on an implementation as part of my Uni research. Cool to see Bend 2.0 release!
Then you might be interested in Marc Thatcher's recent PhD thesis dedicated to interaction nets [1]. A great exposition of interaction nets through multiplicative linear logic's proof nets, and several novel contributions like productivity analysis for interaction nets.
...did they just squash the repo to 1 commit for v2.0.4? Why? Yall should know that in this age of AI trust is the real currency... and nuking your history is one hell of a way to raise eyebrows.
> Enjoy bug-free, fast vibe-coded apps! Hints: ask it to write laws for whatever should never break, and to parallelize everything you want running fast. Bend is
young: if anything goes wrong, ask it to open an issue.
Emphasis mine. I don't want to be snarky but like... come on.
There is just a lot of private data and even proprietary code (like SupGen) in the commit story, so I just squashed it. I didn't think that'd be an issue? Why?
This reads very vibecoded, but putting that aside...
1. How does this benefit from GPU parallelism? I don't know much about implementing proof assistant, as I am just a user, but its my understanding that these tasks aren't amenable to running on a GPU.
2. The comparison to Lean/Agda/Isabelle/etc have no meaning without understanding what programs are being used for comparison. I also so far have no reason to believe large-scale verified programs would ever adapt to Bend. For instance, I have a large software verification project written in Cubical Agda
https://github.com/um-catlab/cubical-categorical-logic
it's not clear to me how one would even begin to port this over to Bend, especially given the dependence on cubical
3. Single commit history is hella sus
4. Bend uses "an affine dependent type theory". Substructural dependent type systems are an active area of research. If this weren't slop, I'd expect such a system to be worthy of publication at a top programming languages conference. It sounds quite unlikely that a random vibecoded project with a Fable-written paper has worked out all of the kinks
I'm glad you're having fun vibecoding, and I like that you're interested in this area of research/engineering, but you are wildly overstating what you have here and sound sus af
Yes, there's a lot of vibe-coding in many places, but the critical parts (compiler, runtime, kernel) are human designed, and the kernel has been extensively audited by human. All of it is my own design and architecture, and I'm a human, I think. We'll prune AI slop over time. The project is big, and we're a small team.
1. The paper explains it well (sadly it is written by Claude for now, but it is accurate):
In short, we implemented a complete allocator, garbage-collector, closure evaluator and functional evaluator, on the GPU (with zero interaction net overhead this time). We then use a very simple (for now) scheduler that spreads binary recursive calls as to saturate all CPU or GPU cores, depending on where it is running. This is the simplest thing that works fast. In the future, we want to have a more flexible task stealing queue, but contention destroys GPU performance, so, that's the best thing that works, for now.
2. Benchmarks aside, large scale verified programs would run much faster on Bend for a simple reason: Bend is fully explicit. It has no tactics, and it does zero compile-time search. As always: the less a computer does, the faster it runs. This is a tradeoff. In exchange, Bend code is substantially more verbose than Lean, and it is more laborious to write Bend proofs. I argue this is the right tradeoff, because AI write proofs, and AI time is cheap, while bugs take human time, which is expensive.
3. Sorry I'm not proud of the commit history
4. I don't think it is worthy publication because the core idea is simple. We just use QTT-like linear types to fully prohibit runtime closures. So, paradoxes like Russel's and Girard's are blocked. In exchange, functions like List.map are not expressive (without templates). So it is not a research breakthrough. I just made a conscious trade here, which makes Bend way closer to C or Rust, than to Haskell or Lean.
5. Will patch.
Great questions actually, and surprisingly respectful. I appreciate it a lot.
1. thanks, I'll try to take a look later at this. Most of my skepticism was rooted in a personal-hell I endured when trying to parallelize SAT-solving with GPUs...which didn't go well because its hard to share across workers effectively.
Another thing to note, I'd frown upon using Claude-written works for communication between humans. If the ideas are yours then it should be feasible to write the paper. Many people will take "Claude wrote this paper" as a big sign telling them to ignore it
2. With no offense, but until it is demonstrated that this is useful for larger verified software projects I will be intensely skeptical; and, I'd advise not making claims like this until you have empirical evidence
4. Assuming this all holds air and isn't AI-bs (I'll make no claims in either direction), then yeah I'd say its valid research. To be clear with what you're claiming here, you're giving the impression that you have a GPU-accelerated proof assistant that is 2 orders of magnitude faster than Lean. If true, then that's a big and interesting contribution
Best of luck with everything. I certainly understand the frustration with how slow proof assistants can be, and I hope that we as a community can significantly speed them up
You expect an arxiv only paper to be cited? Do you even know fuck all about scientific research? Do you think someone can slap "Foundations of" in an arxiv title and we are mandated to cite it?
Yes, I'd expect a 2 year old preprint from a rising research in this utlra-niche field to likely be discussed when someone is claiming to have a sweeping solution on exactly the same research question
Maybe not necessarily so, but while looking through the paper's bibliography I get the sense that these were AI-gathered references because there seems to be gaps in the current literature on this topic
Maybe in our brave new world only the "laws" will matter and the implementation language is irrelevant to humans. In the mean time I have some questions about the "guide", which claims to define the entire language:
- There are no infinite loops, and recursion is kind of softly bounded to 2^48-1. This sounds grrrreat for games. I guess they have to stop working after a while? (What would be wrong with addressing this conceptually like Lean does? Have a way to annotate a term as possibly non-terminating?)
- We seem to have Data and Type and Kind, and they don't mean what they conventionally do. '-' means "used 0 types". And the example is:
def length(a, -A: Kind(a), xs: List<a, A>) -> Nat:
match xs:
case Nil{}:
0n
case Con{h, t}:
1n+length(a, A, t)
But wait! A is used albeit not at runtime. Is it possible that this actually intends "A may be used any number of times and is itself the name of a - type"? Shouldn't that be spelled "A: Kind(a) & -" or similar? Why does the kind even matter for this example?
- I don't understand the Array example:
import Base
def main() -> Array<U32> & U32:
a = [0 : U32*8n] # new array with 8 copies of 0
a[5] <- 42 # performs an in-place rewrite
a[5] # reads index 5
What is the return type of this function? It looks like it returns U32. So what's "Array<U32> & U32"?
- I don't even understand the Array explanation:
> The slot count after * is a power of two; [0 : U32^3n] names the depth instead.
Okay, the 8 in *8n above is indeed a power of two. Does the language require it? Does it actually mean 2^8? What is the "depth" of an array? Does this language not have non-power-of-two-sized arrays?
Nothing wrong with addressing it conceptually! We will, in the upcoming versions, probably via codata / coroutines. For V1, I'm keeping the language set smell. When it is stable, we'll add more features. Lean had 10+ years to mature; Bend is on day 1.
`-` means "erased argument". You can use an erased argument as many times as you want, in erased positions. That's also how QTT works (Idris2 is based on it). This example is there precisely to introduce Kinds, which are universes indexed on quantities.
- Kind(&2) is inhabited by clonable values.
- Kind(&1) is inhabited by linear values.
- Kind(&0) is like Rocq's Prop.
`A & B` is just sugar for the pair type former (which is sugar for a sigma).
So why does the length function take the ‘a’ parameter (the type of the elements?) and its Kind? Wouldn’t the type imply the kind? Why does the kind matter? Is the - a constraint on the kind? How would the program be different without the -?
When you say “pair type former” do you mean that Array<U32> & U32 is what Rust would call (Array<U32>, U32)? If so, why does that example function actually return a value of this type? It sure looks like it returns plain U32.
Sick of seeing "vibecoded!!" in the comments. It is an AI-oriented tool. Do you expect the author to write everything by hand? Do you think a couple of Claudeisms in the docs means the entire thing is unsupervised slop?
HN staff: someone posted before me. Could we change the title to "Bend - a language that blocks AI mistakes via proof and runs on GPUs"?
Everyone: feel free to ask any question, but I'd be highly appreciative if you could be a bit civilized and respectful this time. I've worked on this for 1 year, nearly 16h/day, 7 days a week, and I'm giving it for free. You need not to use it. So, I'd be thankful if you could point occasional failures politely rather than throwing me in a lava pit.
Thank you!
> That same file is the CPU program and the GPU kernel: clang builds it for the host, Metal or CUDA builds it for the device, so a `!` runs the exact same code on either chip.
What exactly is this saying? The guide doesn't really explicitly define `!`, and it's unclear from this sentence whether it's saying that, "clang builds it for the host and Metal, and CUDA builds it for the device", or if it's saying, "clang builds it for the host, Metal, and CUDA, and builds it for the device", or something else entirely.
It just means that Bend compiles to a single .c file, and that file compiles to either Metal or CUDA, via macros, depending on your target. This shouldn't be relevant to most users. It is just a way I found to keep the file small and reuse as much code as possible, rather than rewriting the runtime 3 times (once for C, once for Metal, once for CUDA).
The problem, of course, is that having only the one single "you can't win" law is severely underspecified, but the solution was too clever by half, and highlights the problem with this approach — every program will be under-specified, because, at some point, writing the laws becomes a bigger problem than writing the code itself.
This becomes a real issue because the combination of underspecified but rigid laws pushes the aI towards this sort of "creative" solution that matches the letter but not spirit of the law. In this case, the issue was obvious, but I seriously worry about what sort of shenanigans will occur in less obvious cases.
(Why it is done the way it is, what problems are solved by affinity, why closure can be called at most once, how a function that never returns can prove anything, and everything else)
I'm confused - could you explain how the board/flag animation relates to Bend's compile time checking? Is it actually a direct demonstration of Bend running a check?
Why? Won't an AI that can correctly write any program (and make any change) also be smart enough to know what exactly we want better than we can explain, at least ahead-of-time?
> With proofs, we can verify that the AI implemented our prompts correctly.
How? Either we're able to understand all the theorems, which takes a lot of work, or we need to trust the AI, in which case the verification method can be a hidden implementation detail. Normally, when using formal methods, we choose to focus on certain important properties and verify only those.
I like the law idea, but what i found they end up doing is they just modify the law itself to fit the new feature they are working on, which defeats the point.
Which means some laws needs to be frozen. But not all laws, otherwise you can't add or modify anything. So the judgement is still on the human part, and we're back to meatbags being the bottleneck.
I've seen some success adding these proof-like checks to CI every time agents do something irrational. I definitely think it should be part of every codebase.
There's also https://code-contracts.cc/ which co-locates code and proofs together.
Question, does the parallelism work on M-Series GPU? The page says CUDA parallelism but shows Mac performance numbers.
[1] https://hdl.handle.net/10779/uos.32024301
...did they just squash the repo to 1 commit for v2.0.4? Why? Yall should know that in this age of AI trust is the real currency... and nuking your history is one hell of a way to raise eyebrows.
> Enjoy bug-free, fast vibe-coded apps! Hints: ask it to write laws for whatever should never break, and to parallelize everything you want running fast. Bend is young: if anything goes wrong, ask it to open an issue.
Emphasis mine. I don't want to be snarky but like... come on.
One time they force pushed and erased everything except a 2-line README... on purpose.
Pre-obliteration version: https://github.com/bendlang/bend/tree/814453670d0e0d6777c131...
Hmmm... needs `sudo`.
is this a problem to you? why
...so now their work has been reduced to nothing?
I will later. From what I can tell it looks nice. I like the syntax. I don’t know of the claims but willing to give it a shot.
The GPU story would it work on my Mac or is it not GPU agnostic?
1. How does this benefit from GPU parallelism? I don't know much about implementing proof assistant, as I am just a user, but its my understanding that these tasks aren't amenable to running on a GPU.
2. The comparison to Lean/Agda/Isabelle/etc have no meaning without understanding what programs are being used for comparison. I also so far have no reason to believe large-scale verified programs would ever adapt to Bend. For instance, I have a large software verification project written in Cubical Agda https://github.com/um-catlab/cubical-categorical-logic it's not clear to me how one would even begin to port this over to Bend, especially given the dependence on cubical
3. Single commit history is hella sus
4. Bend uses "an affine dependent type theory". Substructural dependent type systems are an active area of research. If this weren't slop, I'd expect such a system to be worthy of publication at a top programming languages conference. It sounds quite unlikely that a random vibecoded project with a Fable-written paper has worked out all of the kinks
5. I would've at least expected this paper to be cited https://arxiv.org/abs/2401.15258 but it is noticeably absent
I'm glad you're having fun vibecoding, and I like that you're interested in this area of research/engineering, but you are wildly overstating what you have here and sound sus af
1. The paper explains it well (sadly it is written by Claude for now, but it is accurate):
https://github.com/bendlang/bend/blob/main/paper/BendRT.pdf
In short, we implemented a complete allocator, garbage-collector, closure evaluator and functional evaluator, on the GPU (with zero interaction net overhead this time). We then use a very simple (for now) scheduler that spreads binary recursive calls as to saturate all CPU or GPU cores, depending on where it is running. This is the simplest thing that works fast. In the future, we want to have a more flexible task stealing queue, but contention destroys GPU performance, so, that's the best thing that works, for now.
2. Benchmarks aside, large scale verified programs would run much faster on Bend for a simple reason: Bend is fully explicit. It has no tactics, and it does zero compile-time search. As always: the less a computer does, the faster it runs. This is a tradeoff. In exchange, Bend code is substantially more verbose than Lean, and it is more laborious to write Bend proofs. I argue this is the right tradeoff, because AI write proofs, and AI time is cheap, while bugs take human time, which is expensive.
3. Sorry I'm not proud of the commit history
4. I don't think it is worthy publication because the core idea is simple. We just use QTT-like linear types to fully prohibit runtime closures. So, paradoxes like Russel's and Girard's are blocked. In exchange, functions like List.map are not expressive (without templates). So it is not a research breakthrough. I just made a conscious trade here, which makes Bend way closer to C or Rust, than to Haskell or Lean.
5. Will patch.
Great questions actually, and surprisingly respectful. I appreciate it a lot.
2. With no offense, but until it is demonstrated that this is useful for larger verified software projects I will be intensely skeptical; and, I'd advise not making claims like this until you have empirical evidence
4. Assuming this all holds air and isn't AI-bs (I'll make no claims in either direction), then yeah I'd say its valid research. To be clear with what you're claiming here, you're giving the impression that you have a GPU-accelerated proof assistant that is 2 orders of magnitude faster than Lean. If true, then that's a big and interesting contribution
Best of luck with everything. I certainly understand the frustration with how slow proof assistants can be, and I hope that we as a community can significantly speed them up
Maybe not necessarily so, but while looking through the paper's bibliography I get the sense that these were AI-gathered references because there seems to be gaps in the current literature on this topic
https://github.com/bendlang/bend/blob/main/guide/GUIDE.md
Let's see:
- There are no infinite loops, and recursion is kind of softly bounded to 2^48-1. This sounds grrrreat for games. I guess they have to stop working after a while? (What would be wrong with addressing this conceptually like Lean does? Have a way to annotate a term as possibly non-terminating?)
- We seem to have Data and Type and Kind, and they don't mean what they conventionally do. '-' means "used 0 types". And the example is:
But wait! A is used albeit not at runtime. Is it possible that this actually intends "A may be used any number of times and is itself the name of a - type"? Shouldn't that be spelled "A: Kind(a) & -" or similar? Why does the kind even matter for this example?- I don't understand the Array example:
What is the return type of this function? It looks like it returns U32. So what's "Array<U32> & U32"?- I don't even understand the Array explanation:
> The slot count after * is a power of two; [0 : U32^3n] names the depth instead.
Okay, the 8 in *8n above is indeed a power of two. Does the language require it? Does it actually mean 2^8? What is the "depth" of an array? Does this language not have non-power-of-two-sized arrays?
At this point I stopped reading.
`-` means "erased argument". You can use an erased argument as many times as you want, in erased positions. That's also how QTT works (Idris2 is based on it). This example is there precisely to introduce Kinds, which are universes indexed on quantities.
- Kind(&2) is inhabited by clonable values. - Kind(&1) is inhabited by linear values. - Kind(&0) is like Rocq's Prop.
`A & B` is just sugar for the pair type former (which is sugar for a sigma).
Thanks for your questions and patience!
When you say “pair type former” do you mean that Array<U32> & U32 is what Rust would call (Array<U32>, U32)? If so, why does that example function actually return a value of this type? It sure looks like it returns plain U32.
Why would anyone want to work with such a dystopian setup? Prove your code directly in Lean or Coq or leave it.
it is not a pretty file and it has a lot of gambiarra and AI slop for now
if you want to read something worthy, read the kernel (bend.ts)
It's too difficult and doesn't scale well to many real world programs - how do you formally verify Facebook?
We'll probably be stuck with normal testing and at least skimming code for a while.
https://aws.amazon.com/blogs/compute/aws-nitro-isolation-eng...
And for the PQ parts of Apple's crypto libraries, from May:
https://security.apple.com/blog/formal-verification-corecryp...
Similar from Microsoft, from July:
https://www.microsoft.com/en-us/research/blog/verifying-rust...