You want to identify if two filenames in a list correspond to the same file on disk (because of hard and soft links, two filenames can refer to a single file). You might do this to make sure that you don't change a file you've already worked with.
Maintain a hash, keyed by the device and inode number of the files you've seen. The values are the names of the files:
%seen = ();
sub do_my_thing {
    my $filename = shift;
    my ($dev, $ino) = stat $filename;
    unless ($seen{$dev, $ino}++) {
        # do something with $filename because we haven't
        # seen it before
    }
}A key in %seen is made by combining the device number ($dev) and inode number ($ino) of each file. Files that are the same will have the same device and inode numbers, so they will have the same key.
If you want to maintain a list of all files of the same name, instead of counting the number of times seen, save the name of the file in an anonymous array.
foreach $filename (@files) {
    ($dev, $ino) = stat $filename;
    push( @{ $seen{$dev,$ino} }, $filename);
}
foreach $devino (sort keys %seen) {
    ($dev, $ino) = split(/$;/o, $devino);
    if (@{$seen{$devino}} > 1) {
        # @{$seen{$devino}} is a list of filenames for the same file
    }
}The $; variable contains the separator string using the old multidimensional associative array emulation syntax, $hash{$x,$y,$z}. It's still a one-dimensional hash, but it has composite keys. The key is really join($; => $x, $y, $z). The split separates them again. Although you'd normally just use a real multilevel hash directly, here there's no need, and it's cheaper not to.
The $; variable in perlvar (1), and in the "Special Variables" section of Chapter 2 of Programming Perl; the stat function in perlfunc (1) and in Chapter 3 of Programming Perl; Chapter 5, Hashes

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