I think this even works

Recursion?

def recurse(input_file):
    """Takes a file and recursively evaluates lines to get an answer."""
    children, value = split_line(input_file.read())
    # All operations we implement are binary, we should either have zero
    # children or two.  Anything else is an error.
    if children == 0:
        return float(value)
    elif children == 2:
        return operate(value,
                       recurse(input_file.read()),
                       recurse(input_file.read()))