From page 2: "The presented theoretical model enables analytic investigations of differentiable programs through algebraic tools [...]; i.e. the presented operators can take the same role as higher order functions in functional programming."

So maybe we should think more in terms of lambda calculus and pure functional programming? There, you don't really write Y to memory location X.

In section 5.5 they describe how they "generalize the notion of an iteration from the integers, n ∈ N, to the reals, x ∈ R, and consider fractional iterations."