  Addressing machines have been introduced as a formalism to construct models
of the pure, untyped lambda-calculus. We extend the syntax of their programs by
adding instructions for executing arithmetic operations on natural numbers, and
introduce a reflection principle allowing certain machines to access their own
address and perform recursive calls. We prove that the resulting extended
addressing machines naturally model a weak call-by-name PCF with explicit
substitutions. Finally, we show that they are also well-suited for representing
regular PCF programs (closed terms) computing natural numbers.
