Woxi: Wolfram Mathematica Reimplementation in Rust | Hacker News Reader

Woxi: Wolfram Mathematica Reimplementation in Rust

github.com

350 pointsadamnemecek137 comments

My Bona fides: I've written my own Mathematica clone at least twice, maybe three times. Each time I get it parsing expressions and doing basic math, getting to basic calculus. Then I look up the sheer cliff face in front of me and think better of the whole thing.

There is an architectural flaw in Woxi that will sink it hard. Looking through the codebase things like polynomials are implemented in the rust code, not in woxilang. This will kill you long term.

The right approach is to have a tiny core interpreter, maybe go to JIT at some point if you can figure that out. Then implement all the functionality in woxilang itself. That means addition and subtraction, calculus, etc are term rewriting rules written in woxilang, not rust code.

This frees you up in the interpreter. Any improvements you make there will immediately show up over the entire language. It's also a better language to implement symbolic math in than rust.

It also means contributors only need to know one language: woxilang. No need to split between rust and woxilang.

Mh, I thought about this a little and came actually to exactly the opposite conclusion: Implement as much as possible in Rust to get the fastest code possible. Do you have any more insights why this should not be possible / unsustainable?

You have two distinct products 1) An interpreter 2) a math language. Don't write your math in some funny imperative computer language.

Keep the interpreters surface area as small as possible. Do some work to make sure you can accelerate numeric, and JIT/compile functions down to something as close to native as you can.

Wolfram, and Taliesin Beynon have both said Wolfram were working internally to get a JIT working in the interpreter loop. Keep the core small, and do that now while it's easy.

Also, it's just easier to write in Mathematica. It's probably 10x smaller than the rust code:

    f[x_Integer]:=13*x;
    f::help:="Multiplies x by 13, in case you needed an easy function for that."

EDIT: Another important thing to note is the people who really deeply know specific subjects in math won't be the best, or even good rust programmers. So letting them program in woxilang will give the an opportunity to contribute which they wouldn't have had otherwise.

I'm not a PL expert but isn't building a decent JIT a massive undertaking? I guess you're saying that the JIT itself would be what makes a project like this worth using in the first place?

It's like most things in software, if you constrain the problem enough, focus on the problems you actually have and make some smart choices early on, it can be a very modest lift on the order of a week or two for a 90% solution, but on the other end of the spectrum, it's a lifetime of work for a team of hundreds...

Symbolic manipulation?

Switching out to an interpreted language has got to be anathema to a rewrite-it-in-Rust project

implementing addition in woxilang itself?? this gotta be terribly slow. am i missing something?

You are missing the term "JIT", which would enable a host of runtime optimizations which include generating calls to some static piece of native code which performs addition.

But surely you can have a "fast path" that is implemented in the host language, right?

I am confused for the same reason you are. Isn't the rust code just "pre-jitted" code essentially? i.e. hand optimized. You are going to want to hand-optimize some functions in cases where the jit cannot do a good job in its current form. You probably also want a benchmarking system where you compare the jitted code to the hand optimized code, to prove to yourself that the hand optimized code is still worth keeping, after any automatic jit improvements you make. And if you don't want the runtime overhead of the jit then you can pre-jit certain functions and distribute them as part of the binary's executable code

Mathematica has symbolic and infinite-precision addition, so you can't automatically take advantage of obvious compiled code.

What? Arbitrary precision arithmetic implemented in a compiled language will be faster than the alternative. This is no great mystery. The same is true of essentially all low-level symbolic or numerical math algorithms. You need to get to a fairly high level before this stops being true.

Of course. The point is whether you interpret a call to arbitrary_precision_add or compile the call doesn't matter much.

I noticed the same thing, having also written an interpreter for the Wolfram language that focused on the core rule/rewriting/pattern language. At its heart it’s more or less a Lisp-like language where the core can be quite small and a lot of the functionality built via pattern matching and rewriting atop that. Aside from the sheer scale of WL, I ended up setting aside my experiments replicating it when I did performance comparisons and realized how challenging it would be to not just match WL in functionality but performance.

Woxi reminds me of some experiments I did to see how far vibe coding could get me on similar math and symbolic reasoning tools. It seems like unless you explicitly and very actively force a design with a small core, the models tend towards building out a lot of complex, hard-coded logic that ultimately is hard to tune, maintain, or reason about in terms of correctness.

Interesting exercise with woxi in terms of what vibe coding can produce. Not sure about the WL implementation though.

(For context, I write compiler/interpreter tools for a living - have been for a couple decades)

I’ve personally had luck at correcting the complex one-off logic the agents produce with the right prompting.

and when I say prompting, I just mean code review feedback. All of this is engineering management. I review code. I’ll point out architectural flaws if they matter and I use judgement to determine if they matter. Code debt is a choice, and you can afford it in some situations but not others. We don’t nit over style because we have a linter. Better documentation results in better contribution quality. etc.

Agent coordination? Gastown? All I hear is organizational design and cybernetics

Sorry, perhaps, a dumb question:

Is it not that Mathematica, and most of the Wolfram innovation, is about a smart way of applying some rule-based inference. I think of it as parametrized PROLOG rules, with large lib. So term rewriting all the way to the end, correct me if I'm wrong.

Where does the mini-core+JIT come into this?

Thanks for taking time to answer.

The interpreter / JIT is the one actually applying the rules.

So it is the tokenizer, and rule expansion, that gets JIT'd, right? I mean - there's no some secondary process running on top of the rule expansion?

I love Rust for mathematical and scientific tasks (I am building the structural bio crate infrastructure), and I love Mathematica and have a personal sub. I should be the audience, but... What makes Mathematica great, IMO, is the polish and overall experience created by consistent work with applications in mind over decades. So, I look at this project with skepticism regarding its utility.

Yeah, the Mathematica language is the least interesting aspect of the Mathematica system. Closely followed by the interactive notebooks.

I disagree, the language itself is one of the more elegant parts of the system, and enables a lot of the rest of the elegance.

From a purely programming language theory, it's pretty unique.

I once tried to find a language that had all the same properties, and I failed. The Factor language is probably the closest. But they are still pretty different.

The relevant programming paradigm is string/term rewriting, which is featured in other programming languages such as Pure. It seems to have few direct applications outside of symbolic computing itself, compilers and related fields such as PL theory. (Formal calculi and languages are often specified in PL theory as rewrite rules, even though the practical implementation may ultimately differ.)

Indeed, I think I messed up the language name too.

It was Kernel that was most similar with the fexpr capability.

Pure is a good example too.

https://web.cs.wpi.edu/~jshutt/kernel.html

First I believe there is no such thing as the Mathematica language, it's Wolframscript which is useful in a bunch of different applications. And second, if you don't have access to a $1000 / yr wolfram subscription, this would be the next best thing.

They rebranded it to Wolfram Language a few years ago (which I actually appreciate, as it is so much more than just "math" by now!)

https://writings.stephenwolfram.com/2013/02/what-should-we-c...

The notebooks were THE thing of Mathematica, at least to me. 12 years ago, as I was finishing my PhD in quantum optics, I wanted to migrate to the stack used in industry - and picked Python. Also, that way I was an early adopter of Jupyter Notebook, as it captured what was need + was open.

Now Mathematica notebooks (still remember, it is .nb) do not have the novelty factor. But they were the first to set a trend, which we now take for granted.

That said, I rarely use notebooks anymore. In the coding time, it is much easier to create scripts and ask to create a visualization in HTML.

> Closely followed by the interactive notebooks.

Mathematica's notebooks are the only environment where I can do some computation to arrive at a symbolic expression. Copy the expression from the output cell into a new input cell. Then manipulate it by hand into the form I want. Then continue processing it further.

Also, symbolic expressions can be written nicely with actual superscripts and subscripts, and with non-latin characters.

One of the best features of Mathematica system.

Have a look at TeXmacs! (https://texmacs.org)

(AFAIK, you can run Mathematica sessions in TeXmacs, get proper typesetting, and can copy/paste expressions for simplification by hand or using other CAS sessions in the same TeXmacs document).

Sure, but you've got to start somewhere! And with the amount of progress I was able to make in just a few weeks, I'm very optimistic that the polish will come sooner rather than later.

Based on the list of contributors to your project, I am not sure this starting location is optimally suited to the task of building a foundation for polished, reliable, expandable software.

The sneering on HN really has no end. This is a good project! I for one am very excited to see an interpreter born out of rust.

It’s so obnoxious

It's a defense mechanism. I was guilty as charge as well initially. Suddenly most of your l33t skillz are trivialized and surpassed by an inhumane actor. It's a tough pill to swallow.

It's having ~ 5000 tests already. Used correctly, AI agents can help you improve the quality of the code!

Do you see why this perspective is a red flag on its own?

No I don’t, review your code

If I go by the contributor numbers on Github, I see Claude has committed something on the order of 300,000 lines of code. I don't think it's reasonable to review that much code, even in weeks worth of time.

I haven’t needed to do such a thing in a while, but my “rule” for explaining how unreasonable is to say “if I only glanced at each line of code for 1 second, without bothering to understand the details, it would take me 3 and a half full 24hr days non stop to simply look at”. So it’s definitely more than 1 work week because presumably other stuff is going to need to get done in that time too. Actually understanding it is going to be at least a multiple of that, and probably the multiple is ~30x.

I certainly don't. If a software developer has found a way to use these tools that works well for them and produces good results, that's a good thing.

I have no dog in this fight, but simply claiming a count of tests get you anything is like saying your code coverage is 100% - it sounds really good until you think about what 5000 unreviewed tests actually... do.

God help us.

In that case I kindly refer you to the matter of Arkell v. Pressdam.

i'm curious if you intend to reimplement highly optimized numerical algorithms, symbolic algorithms, and so on, accumulated and tuned in mathematica since its 1988 release?

it's a huuuuuuuuge amount of technology in the standard library of mathematica, beyond the surface syntax and rewrite system, i mean.

Similarly I'm not sure Octave ever really got that polish to compete with MATLAB.

SPSS is hilariously painful to use. Still it's only losing ground ever so slowly. PSPP remains almost unheard of among SPSS core users.

I am not sure Octave ever had to put on that much polish. It just had to be decent enough to save $$$$ vs a Matlab license. If it can drop-in run the code that has been keeping the lab going for decades, good enough.

MathWorks offers a huge list of "toolboxes", domain specific extensions that cover a lot of features in each domain. Replacing Matlab isn't about the core language alone.

Which often means that e.g. loading an image for displaying it increases cost by a few thousands

The price tags are wild for sure. But the sheer number of supported features is what makes them attractive. Cloning that completely is practically infeasable.

If you were using everything in the toolboxes, it would be absolutely worth it. As it is, you often need an additional toolbox for basic functionality and pay for everything in it.

> It just had to be decent enough to save $$$$ vs a Matlab license

And it failed at this.

I did my PhD with Octave. Sure, I did not have this nice convex optimization toolbox. But I had everything else I needed and did not need to wait because people arrived earlier in the lab and grabbed all floating licenses of, for instance, the communications toolbox.

However, I switched to Python during the last years.

Half-assed reimplementations of existing software (often in the name of "memory safety") is what the Rust community is best known for.

I find rust to be the best language and tool set in most categories. I still agree with this characterization.

Mathematica is proprietary software. Any reimplementation is better than nothing at all, at least for people that don't run proprietary software

Useless thing is not less useless by the virtue of being FOSS. That's something FOSS folks have yet to understand.

All the best to the author, they definitely have fun doing this, but I've seen enough of such attempts. Having agents doesn't make much difference.

The difference is huge - It burns money quicker and nobody understands the code

People said the same thing about Linux in the 90s

Very nice, now explain what makes this fact relevant.

What's wrong with Maxima?

Maxima is a CAS. Mathematica is a complete programming environment with an insanely featureful standard library.

People who don't run proprietary software also don't get tech support :) wolfram's support team is very good

Thanks for the sensible chuckle.

Hi, I'm the main developer. We're steadily getting closer to the next release which will support most features of Mathematica 1.0 plus some of the most popular newer functions (> 900 overall!). AMA!

What percentage of the overall code was written primarily by agents?

https://github.com/ad-si/Woxi/graphs/contributors

How does it compare to mathics?

How close is it to being able to run rubi: https://rulebasedintegration.org/?

You can find the whole integration routine here https://github.com/ad-si/Woxi/blob/36343ab2cbc97e5081f7c811e.... It's essentially a test mock-up (not even trying partial fraction decomposition for rational functions).

    // ∫ tan(x) dx = -ln|cos(x)| - not implemented (requires Log)

This really doesn't bode well... I'm no expert in CASes, but everything I've looked at seems very naive. Vibe coding a Mathematica replacement makes zero sense to me.

Reported a few issues, e.g. https://github.com/ad-si/Woxi/issues/16

Thank you for sharing this on HN.

It's a worthwhile effort. If successful, Woxi can enable a large mass of scientists and engineers who don't have access to Mathematica to run legacy code written for it. Also, Woxi would give those scientists and engineers who regularly use Mathematica a non-proprietary, less restrictive alternative, which many of them would welcome.

How does Woxi compare to other "clean-room implementations"[a] of the same language?

[a] Please check with a lawyer to make sure you won't run into legal or copyright issues.

Interesting, thanks for sharing. Naive question as I'm not familiar with Mathematica much (but aware of it and Wolfram Alpha and related tools), how does it compare to e.g. Jupyter or Julia or maybe another language (with its framework) that might be even closer?

I think Wolfram Language is just so much more ergonomic. No need to import dependencies - everything's included and consistent, very readable - yet compact - syntax, less gotchas than Python, R, etc., sensible default, …

Ymmv, but I've found that you sure do need to import things eventually, and it's not so ergonomic because most projects just end up as mega-notebooks.

Just like Python or any other language that looks easy for the learning examples, there are still hairy bits, they're just better hidden. The difference is that the debuggers for Python are far better.

Mathematica is great for quick stuff, but once you hit a particular level complexity it goes crazy. In this regard I find it similar to Bash.

I'd add the pattern matching syntax. it's so natural for a mathematician.

Why would I use this and not Wolfram Script?

Better license? Allowed for commercial operations?

Exactly! And:

- Faster startup time because of no license check

- Can run multiple instances of Woxi at the same time

- Embeddable via WASM

- Configurable via compile time flags (which features should be included)

- …

License is a big deal, and not just for cost and openness, but also for practical use in pages like docker, ci/cd pipeline, cloud deployments, or other places licenses need to be dynamic.

How is the popularity/rank in functions.csv determined?

That's actually a value that Wolfram determines themselves. Here is the documentation for it: https://reference.wolfram.com/language/ref/WolframLanguageDa...

Here is e.g. all the values for the Plus[] function:

$ wolframscript -code 'WolframLanguageData["Plus", "Ranks"]' {All -> 6, StackExchange -> 8, TypicalNotebookInputs -> 5, TypicalProductionCode -> 6, WolframAlphaCodebase -> 6, WolframDemonstrations -> 4, WolframDocumentation -> 4}

There's a mystique around Mathematica's math engine. Is this groundless, or will you eventually run into problems getting correct, identical answers -- especially for answers that Mathematic derives symbolically? The capabilities and results of the computer algebra systems that I've used varied widely.

Hard to tell honestly. So far there was always some surprisingly straight forward solution If had any problems with the math engine. There is actually a lot of public research how equations can be solved/simplified with computer algorithms. So I'm optimistic. I also stumbled upon a few cases where Mathematica itself didn't quite do things correctly itself (rounding errors, missing simplifications, etc.). So maybe it's actually a little overhyped …

I also found problems with integrating some obscure functions a few years black, though IIRC the issue was remedies by using the amazing Rubi package:

https://rulebasedintegration.org/

Scmutils from MIT does a very good -- arguably better -- job for correctness. No symbolic integration by ideology and not identical. Sussman and Terman. Amazing attention to detailand correctness. Claude could probably bridge Scheme to Wolfram.

I'm not sure how important but- for-bug identical output really is.

Mathematica gets incorrect answers quite frequently.

Have you considered using quickcheck/random/property-based testing with LLM code generation to automate function implementation?

Yeah, I've already looked into it, but decided to keep developing it "example driven" for now. Aka I'm playing around with it, and whenever I find something that's broken I keep a note of it and then I pick those notes one by one and implement them. Once the most common things are implemented I will start writing property tests to catch all the edge cases of each feature.

I'm saying you can go even further and automate the entire thing using LLMs/agents, it is pretty much the ideal use case: you have a black-box reference implementation to test against; descriptive documentation for what the functions should do; some explicitly supplied examples in the documentation; and the ability to automatically create an arbitrary number of tests.

So not only do you have a closed loop system that has objective/automatic pass-fail criteria you also don't even have to supply the instructions about what the function is supposed to do or the test cases!

Obviously this isn't going to be 100% reliable (especially for edge cases) but you should be able to get an enormous speed up. And in many cases you should be able to supply the edge case tests and have the LLM fix it.

(Codex is still free for the next few days if you want to try their "High"/"Extra high" thinking models)

You accidentally raise an interesting point: good, thorough public documentation, once considered a great selling point for your system, now invites automated reimplementation by competition. It would be a shame to see public docs vanish because it turns out they are literally machine readable specs.

LSP?

Not yet, but on the roadmap!

What is your plan for long term support?

This is cool! I've always wanted a polished kernel on the terminal. I spent a lot of time a few years ago writing my own Wolfram Kernel. It was a blast to understand how a pattern matching (symbolic) language is implemented.

https://github.com/anandijain/cas8.rs

For folks who are considering passing, note that there is a "Jupyter Lite" mode in addition to "Woxi Studio" --- seems very promising and the former addressed my first concern out-the-gate.

I regularly use Mathematica for working with symbolic expressions (for its DSolve and transfer function stuff) and it is way more maintainable and elegant to have fractions, symbols and powers rendered in math mode instead of having to deal with a text only representation. Are there any front ends (either custom or somehow extending jupyter) for this project which recreate this experience?

Maybe http://texmacs.org would fit here!

Glad to see Rust project under AGPL-3.0. I wish to see more Rust projects under (A)GPL, because (A)GPL is rare in the Rust community for some reason.

Have you considered doing property tests with Mathematica as an oracle?

An ai based development workflow with a concrete oracle works very well. You still need the research and planing to solve things in a scalable way, but it solves the "are the tests correct" issue.

What we've done is pull out failing property tests as a unit tests, makes regression testing during the agentic coding loop much more efficient.

Have you gotten any nastygrams from Wolfram about this? They're pretty protective of their IP. Not saying I think that it's some violation of it, but I could see them being alarmed.

Is the syntax for symbolic computation already near optimal or should something be rethought and redone?

AGPL licensed. An interesting choice. Author really doesn’t want Wolfram to use it??

Why should I want them to use it?

Well it would get vastly more popular if it was officially endorsed. Do you want lots of people using it?

Why is that important?

Because you get changes upstreamed.

Most humans like external validation. Having other people use what they've built is a common metric of validation in open source software. Economically, these metrics can be used as credentials for things like job applications or consideration in joining groups.

> The initial focus is to implement a subset of the Wolfram Language so that it can be used for CLI scripting and notebooks.

If you have Mathematica installed you can write CLI scripts and notebooks.

I wonder if it would make a good Zeppelin interpreter. https://zeppelin.apache.org/

Oh cool, haven't heard of this before. Could be a good fit - I'll have to try it out some day!

Wow! Do my eyes deceive me? What kind of ‘sunset’ are we talking of here?!

How did claude code became contributor?

Many Wolfram language algorithms are proprietary right?

vibe coded?

Such a massive undertaking would be almost impossible without AI agents, so yeah, they help me. But with around 5000 tests, they are actually helping to improve the software quality!

are all the tests hand written or are some agent-contributed? curious

What’s the difference if you review the code getting merged?

Reviewing the correctness of code is a lot harder than writing correct code, in my experience. Especially when the code given looks correct on an initial glance, and leads you into faulty assumptions you would not have made otherwise.

I'm not claiming AI-written and human-reviewed code is necessarily bad, just that the claim that reviewing code is equivalent to writing it yourself does not match my experience at all.

Plus if you look at the commit cadence there is a lot of commits like 5-10 minutes a part in places that add new functionality (which I realize doesn't mean they were "written" in that time)

I find people do argue a lot about "if it is reviewed it is the same" which might be easy when you start but I think the allure of just glancing going "it makes sense" and hammering on is super high and hard to resist.

We are still early into the use of these tools so perhaps best practices will need to be adjusted with these tools in mind. At the moment it seems to be a bit of a crap shoot to me.

eh with plenty of tests that I can easily read and are well documented I haven't actually ever found this to be a problem in practice

i mean idk that's sorta like asking what's the difference of having tests if you review the code getting merged

The difference is we can't tell if you reviewed the code.

To be fair, we also couldn’t tell for sure if they hand-wrote the code.

If they hand wrote the code we know they at least looked at it once.

Since we can’t know whether they really hand-wrote the code, we also wouldn’t know whether they looked at it.

Err yeah that's the point.

You wrote: “If they hand wrote the code we know they at least looked at it once.”

But that’s not true, because even if they did indeed hand-write the code, we as third parties wouldn’t have any reliable proof of that, and therefore still couldn’t draw the conclusion that they looked at the code.

Them claiming to have hand-written the code isn’t any better than them claiming to have thoroughly reviewed the code. We can’t know in either case.

> Them claiming to have hand-written the code isn’t any better than them claiming to have thoroughly reviewed the code. We can’t know in either case.

It is better, because most people aren't out-right liars. If he said "I hand-wrote the code", sure it doesn't prove it, but I would believe him. When he says "I thoroughly reviewed the code"... yeah maybe. That's the sort of thing people do lie about (even to themselves).

you never can, thats the responsibility of the engineers to not lie. You can tell if there are sufficient tests and if they passed

Code review basically never actually means thinking through all the code again as if you wrote it

Did you actually review 313,397 LOC written by claude? And you wrote the tests? That's honestly very impressive if yes.

Great! Math tools for everyone.

what's stopping some Mathematica employee from taking the source code and having an agent port it. Or even reconstruction from the manual. Who owns an algorithm?

Will everything get copied eventually?

According to https://en.wikipedia.org/wiki/Lotus_Development_Corp._v._Bor...., a software clone does not infringe software copyright. So yeah, I'd guess sooner or later everything is going be cloned …

> what's stopping some employee from something like Mathematica from taking the source code and having an agent port it to open source

Laws against theft. Also the same reason employees don't release the code on pastebin or something.

> Who owns an algorithm?

The org or person who was granted the software patent. https://en.wikipedia.org/wiki/Software_patent

> Will everything get copied eventually?

If we're lucky. More likely everything bitrots as technical capabilities are lost. Slowly at first, then quickly.

https://en.wikipedia.org/wiki/Illegal_number

honestly one of my favorite Wikipedia articles. It's silly, but it is a logical conclusion to the existence of secret information.

45 5F E1 04 22 CA 29 C4 93 3F 95 05 2B 79 2A B1

REDACTED

45 5F E1 04 22 CA 29 C4 93 3F 95 05 2B 79 2A B3

Which patent are you referring to?

Any patent. The question was who owns a (arbitrary) algorithm. The elaborated answer is that nobody “owns” an algorithm (i.e. has intellectual property rights to it) without a patent: in USA and many other jurisdictions, patents are the IP tool relating to algorithms.

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