Is there a relationship between visitor pattern and DeMorgan's Law?
The best way to explain it is
$$\mathsf{Bool} \to C \cong C \times C,$$
which is a special case of
$$(A + B) \to C \cong (A \to C) \times (B \to C).$$
Read the above as follows: as sum is equivalent to a pair of visitors.
(By the way, this is not the de Morgan law. It does not have a name, as far as I know. It's a general consequence of the definition of the concepts involved.)