Perl array vs list

The square brackets are used to create an anonymous array. When evaluated, it returns a reference to this array, not the actual array values.

Parentheses have no such hidden property, but simply override precedence inside expressions, much like in math. For example:

my @array = 1,2,3;

Is actually evaluated like this:

my @array = 1;
2,3; # causes the warning "Useless use of constant in void context"

because the = operator has higher precedence than the commas. So to get around that, we use parentheses when assigning arrays, like so:

my @array = (1,2,3);

Your example:

my @array = [1,2,3];

is somewhat like saying this:

my @tmp = (1,2,3);
my @array = \@tmp;

Where the \ is used to create a reference to the @tmp array.

Lists in Perl are not data structures, they are positions in the source code, determined by the context around them. Lists are basically the transient structures that Perl uses to move data around. You interact with them with all of Perl's syntax, but you can not work with them as a data type. The data type that is closest to a list is an array.

my @var    =    (1, 2, 3);  # parens needed for precedence, they do not create a list
   ^ an array    ^ a list

say 1, 2, 3;
    ^ a list

say @var;
    ^ a list (of one array, which will expand into 3 values before `say` is called)

When you write [1, 2, 3] what you are doing is creating a scalar array reference. That array reference is initialized with the list 1, 2, 3, and it is the same as creating a named array and taking a reference to it:

[1, 2, 3]   ~~   do {my @x = (1, 2, 3); \@x}

Since the [...] construct creates a scalar, you should hold it in a scalar:

my $array = [1, 2, 3];                                            

for my $elem (@$array) {   # lexical loop variable
    print $elem."\n";
}

Since you want to operate on the whole array, and not just the reference, you place a @ in front of the $array which dereferences the stored array reference.

The square brackets create an anonymous array, populate the array with the contents of the brackets, and return a reference to that array. In other words,

[ "1", "2", "3" ]

is basically the same as

do { my @anon = ("1", "2", "3"); \@anon }

So the code should look like

my $array_ref = [ "1", "2", "3" ];

for (@$array_ref) {  # Short for @{ $array_ref }
    print "$_\n";
}

or

my @array_of_refs = ([ "1", "2", "3" ]);

for my $array_ref (@array_of_refs) {
    for (@$array_ref) {
        print "$_\n";
    }
}