I don't know anything about homotopy types, but I think that they are trying to build a system in which automated proofs can be computed more easily. So the app

I don't know anything about homotopy types, but I think that they are trying to build a system in which automated proofs can be computed more easily. So the appeal is for applying computer methods for proofs. Also it tries to use the language of homotopy to suggest that some ideas category theory and homotopy theory can be translated to see if they give a new perspective of old problems. I don't know if the road to computer proofs via homotopy types is going to give fruits or not, but I think it should be tested in that field: creating computer proofs for theorems. https://math.stackexchange.com/questions/1158383/examples-of-the-benefits-of-homotopy-type-theory-for-computer-aided-proofs https://math.stackexchange.com/questions/1158383/examples-of...