if we want to squint and talk about sets and functions from sets to other sets...

  function voidy() : void {
    return;
  }
  
  echo json_encode(voidy()); // -> "null"

so i'd say that for most purposes

  void ≡ {null}

a singleton set, more or less[1], sometimes called a "unit type". that's because a void function does return something, it's just entirely uninteresting :) that's different from an "empty" type

  impossible ≡ {} // or ∅

with no values. there are no values of type `impossible`, so `foo() : impossible` can never return anything at all, like this:

  function foo() : impossible {
    while(1){}
  }

see mypy's `NoReturn`, Rust's `!`, Haskell's `Void`. it's used for giving a type to functions like `exit()`

[1] kind of, because it won't let you `return null` explicitly.