HoTTLean is a project that aims to

  • Create a proof assistant for a fragment of HoTT (homtopy type theory) called HoTT0 within Lean as a domain specific language, using its meta-programming facilities.
  • Formalize the semantics of HoTT0 using natural model semantics using category theory in the Lean mathemtaics library Mathlib.
  • Foramlize the groupoid model of HoTT as an instance of natural model semantics.
  • Automate the interpretation so that axiomatic HoTT0 proofs can be “compiled” into proofs about Mathlib’s groupoids.

The github repository is available here.