Question

In Lambda calculus, Y -combinator returns itself like this Y a = a Y a, specifially here. Suppose some trivial function such as y(x)=2*x+1 (suppose Church numbers for the sake of simplicity) and I want to do it Y y to which I want some sort of break-out -function. I want to do something like this

1. calculate y(1) —>3
2. calculate y(3) —>7
3. calculate y(7) …
4. …
5. terminate on the n-th case

How can I do this in R using the functional way of thinking? Is there something built-in?

Answer 1

I don’t really understand the notation of the lambda calculus, so can’t know for sure what the Y-combinator is, but I wonder if the R function Recall() (help page here) wouldn’t help you build what you’re after. Here is an example of its use to calculate a factorial:

# Calculate 4!
(function(n) {if (n<=1) 1 else n*Recall(n-1)})(4)

And here it is applied to the example you described:

(function(x, n) {if (n<=1) x else Recall(2*x+1, n-1)})(x=1, n=1)
# [1] 1
(function(x, n) {if (n<=1) x else Recall(2*x+1, n-1)})(x=1, n=2)
# [1] 3
(function(x, n) {if (n<=1) x else Recall(2*x+1, n-1)})(x=1, n=3)
# [1] 7