alt Hacker NewsIn HOL Light? Just so you can run the proof objects through another prover like Isabelle. Wasn't that your original ambition?
As you know, Rocq and Lean folk want more than just that from their proof objects. They want proofs to contain executable code, often of the very programs they were verifying, and so treat their proof assistants like programming languages with verifiers attached. So you get complex recursion and inductive definitions baked into the kernel. Whether this is a good idea or not is obviously pretty disputed among us, though I'm mostly with you and Larry :)
> So you get complex recursion and inductive definitions baked into the kernel.
It is a pragmatic choice, just like a type system is. I think both of these choices are outdated now that formalisation is fast. What you really want is a simple semantics (what is the semantics of Lean again...?), and build on top of that by verified kernel extensions. Program extraction via proof objects doesn't really work, I don't think anyone does that for real. What you do is you write your program in your term language, and export the meaning of that term as a program. Isabelle does that, too, and you don't need proof objects for that.
In my current version of Practal (Practal Zero) I have a switch for keeping proof objects around as well, in case I want to maybe transform proofs in some reuse scenario. Not sure if I will actually use that, ever, because it would be slow, too. Also, I would rather prove that a certain transformation is correct, and then add this as a kernel extension.