Thus, we do not need to look through two different namespaces.
The only difference w.r.t. the core namespace semantics is that
a program symbol (pvsymbol, psymbol, plsymbol, or xsymbol) may
be introduced in the scope of an lsymbol of the same name and
overshadow it in program expressions, though not in specifications.
For example, the following declarations allow to use (!) both in
programs and specifications:

    type ref 'a = {| mutable contents : 'a |}
    function (!) (x: ref 'a) : 'a = x.contents
    let (!) (r: ref 'a) = {} r.contents { result = !r }

Notice, however, that itsymbols cannot overshadow pure tsymbols.

It is difficult to count all the used symbols in programs.
On the other hand, the pure API already cares about the missing
symbols in verification conditions. So we relieve the program API
of this duty, and trust typechecking (and any other API user) to
not forget to add all the necessary dependencies to a module.

The worst possible outcome, it seems, is that one can extract
an ill-formed OCaml code if the WhyML module is done via the API,
and VCs were not generated.

pow2, div and mod missing