Is there an interest for adding Automatic Differentiation?

[adtzlr]

I wonder if the addition of (optional) Automatic Differentiation (foward mode, up to second order derivatives) would be of interest?
I could think of adding it (in the long term, not just tomorrow...) in a similar way as it is available in Torch or how I have done it in tensortrax (Python packages).

This could be a first proposal, inspired by PyTorch:

      type(TensorHyperDual2)  :: F
      
      F%ab(1:3,1:3) = some_data(1:3,1:3)
      F = requires_grad(F)

      C = transpose(F)*F
      W = C10 * (tr(C) - 3)
      
      ! let the magic happen...
      S = 2. * grad(W, C)

Please let me know your opinions, wishes, etc.