Litex: Formal math for everyone – set theory examples with Lean comparison

Litex: Formal math for everyone – set theory examples with Lean comparison(litexlang.com)

30 points by litexlang 255 days ago | 11 comments

litexlang 255 days ago |

[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.

Star the repo [here](https://github.com/litexlang/golitex) to support Litex, and join our [Zulip community](https://litex.zulipchat.com/join/c4e7foogy6paz2sghjnbujov/) to give us feedback and suggestions!

lupire 249 days ago |

Something that always bugged me about Lean is how unreadable and unwritable.

Math uses extremely heavy notation to make statements concise. It's hard to learn the notation without a visual reference guide, sync the symbols don't have guessable names, but once you know what the symbols mean, it's readable.

Java is incredibly verbose but you can make out what it's saying word by word

Lean is line noise. It's like assembly language for math, which is great, but not what humans should be using day to day.

This Litex does a nice job of being concerned about humans reading and writing the code.

jojomodding 248 days ago | |

Do you have an example Lean statement you struggle with? I would have posed that they're "just" using standard math notation that should be explained in the relevant textbook for the math you're trying to formalize, but perhaps they are indeed cooking...

tucnak 249 days ago |

The code bits are criminally unreadable in dark mode—white outlines over light gray background...

litexlang 249 days ago | |

Thanks! It seems the font color defers in different systems (I did not find this behavior on my machine). So I changed the font color to pink :)

Happy Christmas

observationist 249 days ago | |

Almost looks like the highlight and default colors got swapped - ctrl+a to read looks ok, but oof.

markusde 249 days ago |

One thing I never understood about this: why does this not just compile to Lean so they're compatible with each other? Having a good interface is admirable, but the difference between set and type based foundations seems not very important and porting any enough math to sustain Litex seems like a huge undertaking.

litexlang 248 days ago | |

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.

markusde 247 days ago | | |

To be honest I'm not convinced by the technical downsides you mentioned here BUT I can see why you wouldn't want to spend time on this if it takes away from language development. Thanks!

igornotarobot 249 days ago |

Litex is probably closer to TLA+ than to Lean. Both draw inspiration from untyped set theory and LaTeX.

gravifer 248 days ago |

I would have to port this Chinese thread to HN

[如何评价 Litex 语言？ - 知乎](https://www.zhihu.com/question/1965786839827854197)