I don't think it makes semantic sense for exists to be applied to functions.

Nonetheless there are semantics for it.

sub E; # exists, but not defined
sub D { 1 }; # exists _and_ defined
# sub N does _not_ exist

$\="\n";

print exists(&N) ? "N exists" : "N doesn't exist";
print exists(&E) ? "E exists" : "E doesn't exist";
print exists(&D) ? "D exists" : "D doesn't exist";

print defined(&N) ? "N is defined" : "N is not defined";
print defined(&E) ? "E is defined" : "E is not defined";
print defined(&D) ? "D is defined" : "D is not defined";
__END__
N doesn't exist
E exists
D exists
N is not defined
E is not defined
D is defined
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