User:12AbBa/"Normal" OCFs vs a different version of R function

In this article, we will be rigorously defining OCFs, and comparing them to R Function. The real thing is too cumbersome for me to understand, so I rewrite the expressions in arrows. It turns out that Extended Up-Arrow Notation is curiously similar to R function, so I can do that.

Part I: Basic & Nested (Brace) notation
In this part we have no OCFs. All notations are evaluated starting from the right.

Basic Notation
Base Case: \(a\uparrow b=a^b\)

Recursive case: \(a\uparrow_nb=a\uparrow_{n-1}a\uparrow_n(b-1)\)