I knew someone would call me out on that. I used the wrong word; what I meant was "expressed in a way that would satisfy" which implies proof within the symbolic order being used. I don't claim to be a mathematician or philosopher.

Language models aren't world models for the same reason languages aren't world models.

Symbols, by definition, only represent a thing. They are not the same as the thing. The map is not the territory, the description is not the described, you can't get wet in the word "water".

They only have meaning to sentient beings, and that meaning is heavily subjective and contextual.

But there appear to be some who think that we can grasp truth through mechanical symbol manipulation. Perhaps we just need to add a few million more symbols, they think.

If we accept the incompleteness theorem, then there are true propositions that even a super-intelligent AGI would not be able to express, because all it can do is output a series of placeholders. Not to mention the obvious fallacy of knowing super-intelligence when we see it. Can you write a test suite for it?

The borrow checker just verifies that you're handling the concept of ownership of memory correctly.

The actual management of memory- allocating, reclaiming, etc - are all handled automagically for you.

I assume you wouldn't want to be replaced by an LLM.

I take it you didn’t read the whole thing, as the next example is NonEmptyList, which is a good compelling example. It’s also not hard to think of other examples from my own work: I can imagine a URL type that only exposes constructors to create well-formed URLs. Etc etc.

Really good examples will be rather domain-specific, so it’s perfectly understandable why Alexis would trust her readers to be able to imagine uses that suit their needs.

Tao is a) unusually intelligent and b) an expert in his field. Most people are neither very intelligent nor have expert knowledge in any academic subject. So Tao is pretty much the least representative LLM user possible.