alt Hacker NewsA proof object in dependent type theory is just the term that inhabits a type. So are you saying the Lean implementation can construct proofs without constructing such a term?
A proof object in dependent type theory is just the term that inhabits a type. So are you saying the Lean implementation can construct proofs without constructing such a term?
No, I'm saying it is checked and then discarded. (Or at least, discarded by the kernel. Presumably it ends up somewhere in the frontend's tactic cache.) That matches perfectly the metaphor, "rubs out earlier parts of proofs to make space for later ones".
The shared misconception seems to be in believing that because _conceptually_ the theory implemented by Lean builds up a massive proof term, that _operationally_ the Lean kernel must also be doing that. This does not follow. (Even the concept is not quite right since Lean4 is not perfectly referentially transparent in the presence of quotients.)