#!/usr/bin/perl 

use warnings;
use strict;

use Data::Dumper;

my @original_array = qw( THIS This That That ThAT ThAt ThAt THIS These
+ Those );
my %results;

map { $results{uc($_)}->{$_} = undef } @original_array;

print "Original\n", Dumper(@original_array), "\n";
print "Result\n", Dumper( %results ), "\n";

__END__
Original
$VAR1 = 'THIS';
$VAR2 = 'This';
$VAR3 = 'That';
$VAR4 = 'That';
$VAR5 = 'ThAT';
$VAR6 = 'ThAt';
$VAR7 = 'ThAt';
$VAR8 = 'THIS';
$VAR9 = 'These';
$VAR10 = 'Those';

Result
$VAR1 = 'THAT';
$VAR2 = {
          'ThAT' => undef,
          'ThAt' => undef,
          'That' => undef
        };
$VAR3 = 'THIS';
$VAR4 = {
          'THIS' => undef,
          'This' => undef
        };
$VAR5 = 'THOSE';
$VAR6 = {
          'Those' => undef
        };
$VAR7 = 'THESE';
$VAR8 = {
          'These' => undef
        };
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But then you'd lose the original case information.

No, it's still in the array. uc does not modify its argument, it returns a modified copy.

---

Caution: Contents may have been coded under pressure.

It leaves me wondering if there is any reason to use a hash to store a big list of words over an array and is it possible or sensible to turn %uniq into @uniq.

The hash is just a trick to enforce uniqueness, since, by definition, hashkeys are unique (any attempt to "duplicate" a hashkey at most changes the value that the key is associated with, but no duplicate is created).

If you want the array you can do

my @uniq = keys %{ +{ map +( uc() => undef ), @ar } };
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the lowliest monk