if      ($var eq undef) {
  ...
} elsif ($var eq '')    {
  ...
} elsif ($var eq 'foo') {
  ...
};
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As noted several times, 'eq' isn't "equals" it is "string equals" (and '==' is "number equals"). If you want to compare to 'undef', then you want 'given' (or 'when' or '~~', Perl6isms that'll appear in Perl5 soon enough -- I'd say more but searching for "given" is pretty useless, since I see patches to add them already being applied).