I have this clever idea to have the function use its own name as the slot for the return value.

sub regex {
    my $in = shift;

    # Assign something to $ret in a code assertion
    my $function = (caller 0)[3];
    no strict 'refs';
    $$function = '';
    $in =~ m/^(a)(?{ $$function = 1})/;

    return $$function;
}

while(<DATA>) {
    print regex($_) . ".";
}

__DATA__
a
b
a
abcd
bcda
[download]

I think that's a bit too clever. What if there is a global variable named $regex? You've just clobbered it. I think creating a local alias is probably better.

use strict;
use warnings;
sub regex {
    my $in = shift;
    my $ret = '';

    # Assign something to $ret in a code assertion
    local *alias = \$ret; 
    $in =~ m/^(a)(?{ $alias = 1})/;

    return $ret;
}

while(<DATA>) {
    print regex($_) . ".";
}
print "\n";

__DATA__
a
b
a
abcd
bcda
[download]

-sauoq
"My two cents aren't worth a dime.";