It's truely great if Litex does compile to existing formal languages. The only problem is that we can not find a good way to compile our verification process, which does not require users to give names to facts they are using and thus very different from how Lean works, to Lean (set theory example is just the first one of a series of comparisons). Besides, it's even harder to compile future functionaliteies, like printing out results of each statement of litex in a human readable way, to lean. So since litex is still a young language and we are using our limited resources to try new ideas and crack here and there, for the time being we believe it's not a good time to migrate our code in such a great scale. Thank you. Merry Christmas.
[Litex](https://litexlang.com) is a simple open-source computer language for mathematical proofs. Anyone can have a rough understanding of Litex in 2 hours.
Although it is not yet ready for production use, it is already powerful enough to formalize set theory and basic logic, which is enough for most daily mathematical proofs. Visit [Set Theory Examples](https://litexlang.com/doc/How_Litex_Works/Litex_vs_Lean_Set_...) for more examples.
Thank you auggierose. Your comment is by far the best description of the stage of Litex is now: very flawed, but very different from other formal languages. I guess it is because Litex is closer to reasoning (or math in general) rather than to programming.
The first line is essential, because Litex does not implement transitivity of >= in its kernel and one has to formalize it:
know @larger_equal_is_transitive(x, y, z R):
x >= y
y >= z
```
If litex's strategy is "you describe the steps you want to take, and litex will automatically figure out why they're correct", how are you supposed to do any nontrivial proofs?
```
HAHA, what i am saying here is, each statement you write, is automatically checked by Litex, using its known specific facts and universal facts. Since any math proof, no matter complex or simple, can be divided into many small steps and each small step can be verified in that way, I guess it is fair to say "automatically figure out why they're correct" to a non-mathematicl person when introducing Litex.
Thank you thau! Your example is pretty interesting! I avoid using any advanved Mathlib tactic to make the comparison fairer. We are comparing Lean and Litex under conditions where they don’t rely too much on external packages, which makes the comparison a bit fairer. (since Lean does have a very rich set of libraries, but building libraries is itself a challenge. Litex really needs to learn from Lean on how to build a successful library!).)(afterall, Litex can also abstract all proofs here and give it a name linear_combination, right?)
I feel really lucky that Litex has drawn so much attention from you guys! I always like the geek culture of HN, and have absolutely no idea why such a random guy from a random background can rush into the top 10 on Hacker News.
Litex gets its name from Lisp and LaTeX. I want to make Litex as elegant and deep as Lisp, and at the same time as pragmatic as LaTeX.
Many people have raised questions and suggestions about Litex, and I’m truly grateful. Since I’m developing the Litex core on my own, a lot of the documentation is still incomplete — I’ll try my best to improve it soon! All of your suggestions are really helpful. Thank you so much!
Litex is a simple, intuitive, and open-source formal language for coding reasoning (Star the repo! https://github.com/litexlang/golitex). It ensures every step of your reasoning is correct, and is actually the first reasoning formal language (or formal language for short) that can be learned by anyone in 1–2 hours, even without math or programming background.
Making Litex intuitive to both human and AI is the mission of Litex. That is how Litex scales formal reasoning: making it accessible to more people, applicable to more complex problems, and usable by large-scale AI systems.
The comparision between Litex and Lean is on our website(https://litexlang.com). There is also a straightforward tutorial about it on our web that you do not want to miss.
Contact me if you are interested! Really hope we can scale formal reasoning in AI era together!