[melvinzzz]

Here the way autodiff for a simple 1-D concatenation is computed. First we write the concat itself:

  function (A[SA], B[SB]) -> (O) {
    O[i : SA + SB] = +(A[i] + B[i - SA]);
  }

Note, that SA and SB are the sizes of the two tensors, and due to the way that edge case handling works, either A or B is out of bounds and thus equivalent to zero for each index i of O. Now in the case of +/+ accumulation/combination, the autodiff writes the derivative of each input as the sum over only the output (rather than multiplied by the other inputs as in the +/* case). This gives us:

  dA[i : SA] = +(dO[i]); 
  dB[i - SA : SB] = +(dO[i]); 

A further reduce/defract slightly changes this to:

  dA[i : SA] = +(dO[i]); 
  dB[i : SB] = +(dO[i + SA]); 

which basically extracts the proper portion of the derivative of dO into dA and dB respectively.