I don't think there are any great advantages for computational viability. He is introducing a new category-theoretic language, but in the end the same computat

I don't think there are any great advantages for computational viability. He is introducing a new category-theoretic language, but in the end the same computations have to be done. In his language, there is no "tape" because instead there is "continuation passing" which plays exactly the same role. I guess he hopes to construct the continuation-passing form at compile time, which limits the application to cases where the tape would be small anyway. He hints that his approach should allow more parallelization but I don't see it. In practice the people trying to build AD engines are paying attention to the actual computation being done, and understand what can be parallelized. A more abstract understanding of the problem is little help there I think.