the more detailed description you wrote starts getting a little off-topic

Fair enough, and the link to the reference manual makes up for trimming it.

[for exists on arrays]

The tests apply, even though the results can be surprising, mostly due to the fact that Perl's arrays have a contiguous range of index values. I suspect that exists $array[$i] is equivalent to $i <= $#array. If not, then that is really surprising and probably better left "under the rug". :-)