[litexlang]

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!

[thaumasiotes]

> Even Kids can formalize the multivariate equation in Litex in 2 minutes, while it [takes] an experienced expert hours of work in Lean 4.

Well, I propose an alternative proof in lean4:

    import Mathlib.Tactic
    
    example (x y : ℝ)
      (h₁ : 2 * x + 3 * y = 10)
      (h₂ : 4 * x + 5 * y = 14)
      : x = -4 ∧ y = 6 := by
        have hy : y = 6 := by
          linear_combination 2 * h₁ - h₂
        have hx : x = -4 := by
          -- you'd think h₁ - 3 * hy would work, but it won't
          linear_combination 1/2 * h₁ - 3/2 * hy
        exact ⟨hx, hy⟩

---

One thing I like about the lean proof, as opposed to the litex proof, is that it specifies why the steps are correct. 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?

[litexlang]

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?)

[c0balt]

> how are you supposed to do any nontrivial proofs?

One should also take a look at Isabelle/HOLs AFP here. You can get very far with Metis et al but it is very inefficient computationally.

Especially when proofs get larger and/or layer on abstractions (proving something nontrivial likely involves building on existing algorithms etc.) the ability to make proofs efficient to verify is important.

[litexlang]

``` 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.

[JonChesterfield]

The website tells me it's simple over and over but not what it is. What're the semantics? Which mathematical system is this? What can it prove?

[litexlang]

Thank you Jon, I will put the semantics and the mathematical system behind online soon! Just give me some time!