A basic question about recursive computation
In pure untyped lambda calculus functions are anonymous. Generally, when you want to define a function recursively, you can simply have it &quot;call&quot; itself, for example:

if $n=0$ then $f(n) = 1$
if $n&gt;0$ then $f(n) = nf(n-1)$.

In lambda calculus we don't have the same luxury, functions don't even have &quot;names&quot; in the first place, they are defined in terms of variable binding and variable substitution.
Still, there is a way to implement recursion, discovered by Haskell Curry, by using a particular lambda-term, called fixed-point combinator (if you are interested in details, any reasonable source on lambda calculus covers this aspect).
With the new notation, the authors are effectively introducing a mechanism to give names to functions, removing the problem entirely.