I would want a spec of the basics of the language. Not a collection of vague statements and some examples.
> The tutorial goes into more depth [2].
A tutorial goes into more depth than the main documentation? Really?
If you read the tutorial, you see that the compiler is far from being able what a modern compiler for Lisp, SML, OCAML or Haskell does. The Wolfram compiler is mostly there to speed up some simple numeric processing. As you can see the parameters need to be numbers or 'logical variables'.
> compilation can speed up execution by a factor as large as 20.
Which is completely vague...
> For more complicated functions, such as BesselK or Eigenvalues, most of the computation time is spent executing internal Wolfram Language algorithms, on which compilation has no effect.
That more or less shows how primitive the compiler is.
> Compile can handle approximate real numbers that have machine precision, but it cannot handle arbitrary‐precision numbers
...
> An important feature of Compile is that it can handle not only mathematical expressions, but also various simple Wolfram Language programs.
Wow.
> Thus, for example, Compile can handle conditionals and control flow structures.
Really.