Homotopy Type Theory Electronic Seminar Talks, 2025-02-06
https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html
This talk will present Lean4Lean, a project to construct a verified checker for the Lean theorem prover in the style of MetaCoq. It consists of a new “external verifier” for Lean, written in Lean. It is the first complete verifier for Lean 4 other than the reference implementation in C++ used by Lean itself, and the new verifier is competitive with the original, running between 20% and 50% slower and usable to verify all of Lean’s mathlib library, forming an additional step in Lean’s aim to self-host the full elaborator and compiler. The second part of the project concerns the type theory itself, and establishing its properties (in spite of several known negative results about the behavior of the type system), with the ultimate goal of being able to show that the verifier is correct to a specification of the type theory, and that the type theory is consistent relative to ZFC with countably many inaccessible cardinals. This work is still ongoing but we plan to use this project to help justify any future changes to the kernel and type theory and ensure unsoundness does not sneak in through either the abstract theory or implementation bugs.