The synopsis for Unicode::Collate does a reasonable job of setting the stage, but there is a nice discussion in chapter 6 of Programming Perl (the camel book), 4th edition as well. You might also look at the Unicode Technical Standard #10: Unicode Collation Algorithm.
Here's a brief example of doing comparisons at a lower (more relaxed) level using Unicode::Collate.
use warnings FATAL => 'utf8';
binmode STDOUT, ':encoding(UTF-8)';
my( $x, $y, $z ) = qw( α ά ὰ );
my $c = Unicode::Collate->new;
print "\nStrict collation rules: Level 4 (default)\n";
print "\t cmp('α','ά'): ", $c->cmp( $x, $y ), "\n";
print "\t cmp('ά','ὰ'): ", $c->cmp( $y, $z ), "\n";
print "\t cmp('α','ὰ'): ", $c->cmp( $x, $z ), "\n";
my $rc = Unicode::Collate->new( level => 1 );
print "\nRelaxed collation rules: Level 1\n";
print "\t cmp('α','ά'): ", $rc->cmp( $x, $y ), "\n";
print "\t cmp('ά','ὰ'): ", $rc->cmp( $y, $z ), "\n";
print "\t cmp('α','ὰ'): ", $rc->cmp( $x, $z ), "\n\n";
And the output...
Strict collation rules: Level 4 (default)
Relaxed collation rules: Level 1
And if the reason for doing comparisons is to handle sorting, Unicode::Collate does that too (you don't need to explicitly use Perl's core sort).
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