The K "over" adverb (/) is like a conventional reduce/accumulate/fold. The K "scan" adverb (\) produces a list of the intermediate results. Having both is extremely handy.

If the verb argument of over/scan takes a single argument (rather than two), the adverbs will iterate to a fixed point. As before, "/" will return the final result and "\" returns all the intermediates.

For example:

      +/1 2 3
    6
    
      +\1 2 3
    1 3 6
    
      *:/,,,0
    0
    
      *:\,,,0
    (,,,0
     ,,0
     ,0
     0)

Oh wait, so you're not preserving the subsequence, you just preserving the sum. So it's a standard scan. So my original translation is correct, my subsequence preserving version is doing a bit more than this by preserving the subarray as well as the sum.

Ah, if we have to preserve the sequence:

((⊃∘⍒0⌷⍉)⌷⊢)(+\,∘⍪,\)