First it is one liner. Second you can add logic you want under these parentheses map{....}@yourarray. But on your one liner with grep you are just doing a print "do something ...".

Please excuse the long delay of my reply.

I will respond to your specific points, but what prompts my reply now is my post regarding a syntactic idiom I've recently seen that perplexes me even more than the use of map under discussion here; more on that programming pearl below.

First it is one liner.

But Perl has a format-free syntax: any program can be written in one line — at least, up to the limit of the size of the compiler line input buffer. (Update: In fact, I think every modern computer language, even the P-word one, is or can be made format-free.)

... you can add logic you want under these parentheses ... on your one liner with grep you are just doing a print ...

But one can add limitless logic within the statement block (the parentheses) of a for-loop:

for (@tt) {
    if ($_ != 0) {
        do_something_with_non_zero_iterator_variable($_);
        do_something_else_with_it($_);
        }
    do_even_more_stuff($_);
    etc();
    }
[download]

One could even use a meaningfully-named aliasing iterator variable:
    for my $tt_thingy (@tt) { ... }
One could even write it on a single line (please forgive any wraparound):
    for (@tt) { if ($_ != 0) { do_something_with_non_zero_iterator_variable($_); do_something_else_with_it($_); } do_even_more_stuff($_); etc(); }
So why use a map function? The only motive I can see is that one need never write a Perl-style for-loop again, but what's the advantage of that?

But as I say, the immediate prompt for this reply is the post mentioned above. As you see, this discusses the use of grep in a fashion identical to the use of map we've been talking about. Per your example code, one might write
    grep { if ($_!=0) { print "I did something when it is not zero\n"; } } @tt;
This is semantically exactly equal to the corresponding map statement and to the equivalent for-loop. While the use of map in the circumstances we've been discussing perplexes me, I'm absolutely gobsmacked by this usage of grep. Can you offer any insight into the rationale at work here? I'd be very grateful for any idea about this.

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