mm0

Metamath's Python verifier - its trusted kernel - is just 700 lines of Python short: https://github.com/david-a-wheeler/mmverify.py/blob/master/m... Metamath Zero's Haskell implementation 700, and the C implementation 1000 lines (or 1800 overall) https://github.com/digama0/mm0 How do other proof systems compare? Some bug counts: https://tristan.st/blog/in_search_of_falsehood

There's some interesting work going on with this with Metamath Zero[0], where he's working on verifying everything down to the compiler, to make sure the compiler always emits correct code. His language, Metamath C, also allows for refinement types, which means you can prove certain properties. It's still in its infancy, but I've been watching it from the sidelines for a bit now. Though in terms of practicality, Graydon Hoare has mentioned in the past that he isn't a big fan of complex systems, and so it's better to have a simple type system that covers 95% of the cases, and an escape hatch when it doesn't. I think that's still a fair assessment, but I've fallen down the proof rabbit hole so I am curious to see how far it could be pushed. [0] https://github.com/digama0/mm0

Have you looked at Metamath Zero[1] before? You mentioned using sorts which is what reminded me of it. Just thought I'd point to some additional interesting work :) [1] https://github.com/digama0/mm0

I feel the same. When I first heard about metamath I was blown away at how I could drill down to the base axioms (I had only tried Lean before). Lean also feels too magical for my taste, and I dislike that I don't have a good mental model of its execution under the hood. I care a lot about execution speed as well, and Lean... isn't always fast. It's another reason metamath's design really speaks to me. You might find metamath0 interesting, its kernel design has a similar focus on simplicity while cleaning up a lot of metamath's cruft: https://github.com/digama0/mm0 EDIT: and feel free to ask any questions about mm0, I don't know a ton about it yet but I have researched it a good deal. I'm hoping to use it more this fall when I take a class on first order logic and set theory!