1. Pick a suitable default and use it if the URL doesn't contain a scheme.
2. Allow URI->canonical to lowercase it.

#!/bin/env perl
use strict;
use warnings;

use URI;

for my $search ('http://www.foo.com', 'https://www.foo.com', 'www.foo.
+com', 'WWW.FOO.COM', 'ftp://www.foo.com') {
  my $url = $search; # we can't modify $search directly 
  $url = 'http://' . $url unless $url =~ m!^\w+://!; # If there isn't 
+a schema, add http://
  my $uri = URI->new($url)->canonical->as_string;
  print "$search => $uri\n";
}
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