A PHP without external state is as powerful as a pure Lambda calculus. That's a fact.
PHP has features to talk to the external worls, save state, and whatnot, because it's designed to be (mostly) useful. A pure lambda calculus has not, because it's designed to prove computability theorems and related stuff.
From a mathematical PoV, that's rather superficial. You can write a Web server in COBOL or Intercal or even Brainfuck if you add the required features somehow, and you can write a Prolog theorem prover in them too.
Doesn't mean that doing any of this makes any practical sense whatsoever.