This code is a little unusual. The do {} is a runtime construct to allow you to put statements where an expression is expected. It has scope, but is not actually block (iirc) in that you can't use next to exit out of it.

D:\dev>perl -e"do { next };"
Can't "next" outside a loop block at -e line 1.

D:\dev>perl -e"{ next };"
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The named sub there is a closure, but only in a trivial sense, and you'll probably more likely see people talk about "static" vars in this situation. For instance I would expect to see that code written something like:

BEGIN {
    my $count=0; # static
    sub counter {$count++}
}

for (0..9) {
    print counter();
}
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Without the do on there the block is really a block (albeit a magic one), and its clear the $count=0 is only going to be executed once, and its going to occur before counter() is ever used, that is immediately after the block is compiled (because of the BEGIN).

If you want to make a counter factory then you get into more interesting forms of closures:

sub make_counter {
  my $start=shift||0;
  return sub {$start++};
}
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