I'd do this by creating a hash of references to the various subroutines like this:

sub do_x {
  print "processing x\n";
}
sub do_y {
  print "processing y\n";
}

my %subs = ( x => \&do_x, y => \&do_y );
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Then when you know what type you're going to be processing, you can do something like this:

$subs{$type}->();
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"The first rule of Perl club is you don't talk about Perl club."