package base;
use overload
    '""'     => sub { shift->as_string },
#    '""'     => \&as_string,
    fallback => 1;

sub as_string { "this is a base class" }

package child;
@ISA = qw(base);
sub as_string { "this is a child class" }

package main;

$obj = bless {}, "child";

print "\$obj=$obj\n";
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Try both versions. Do you see the difference? The original version calls the as_string method of the object (which may be either an instance of the base class or a child) while the second calls always the as_string subroutine in the base class.