alt Hacker NewsI don't know much about Lean, but I attended an introductory talk at some point and I was particularly bothered by these partial function definitions. The example was sqrt, which would give 0 on the negatives.
Now, of course, if you're careful with the definitions you use, there is no problem. But in the (increasingly relevant) context of automatic theorem proving with LLMs, this seems to defeat the 'groundtruthness' of Lean!
How do you make sure that the LLM doesn't reward hack a proof using these workarounds?
I don't understand why they would make such footgun functions either, especially because (IIUC, and I probably don't) in a way the whole point of Lean's dependent type system is to be able to express arbitrary constraints on the inputs of these functions so that they can be total -- e.g., to be able to define a subtraction function on the nonnegative integers that takes one integer and one {integer that is less than or equal to the first integer}. And to even call this function, you (or perhaps Lean itself) would need to first prove that its second argument is less than or equal to its first.