An algorithm to compact arrays (python). I figured it out but I can't explain why it works.

compact.py

def compact(a_list): 
    # strategy - find the first empty and nonempty items
    empty, nonempty = 0, 0
    while empty < len(a_list) and nonempty < len(a_list):
        # ok, so in principle this works really well... why?
        # what happens is that nonempty looks for the earliest nonempty
        # element and empty looks for the earliest empty element
        if a_list[nonempty] is None: 
            nonempty += 1
        elif not a_list[empty] is None:
            empty += 1
        # if both a nonempty and an empty element are found, switch them
        # but only if the empty was found 'earlier' than the nonempty position
        elif empty < nonempty:
            a_list[empty] = a_list[nonempty]
            a_list[nonempty] = None
            empty += 1
        else:
            nonempty += 1 
    return a_list[:empty]