I found the article the "Y of R" in the latest R news to be very
interesting. It is certainly challenging me to learn more about how R works
"under the hood" as the author states. What is less clear to me is whether
this approach is primarily for teaching purposes or has a real world
application. What is meant by "fragility of reliance on the function
name defined as a global variable" as a downside to the classical recursive
formulation of function "s"? How can that impact the average R programmer?

Beyond that, empiricist that I am, I decided to put the examples to the
test. My source code and output is below, but the bottom line consists of 2
observations:

   - The Y function approach using csum is consistently slower on my machine
   that the s function approach
   - The Y function using csum gives recursive error with high input values
   just like the s function does
   - The Y function in fact reaches the limit of recursion BEFORE the s
   function does

Given that it is slower, is more cumbersome to write, and has a lower
nesting limit than the classical approach, I wonder about its utility for
the average programmer (or somewhat below average programmer like me).

Okay, here's my code, output, and sessionInfo()

s <- function(n) {
  if (n == 1) return(1)
  return(s(n-1)+n)
}


Y <- function(f) {
  g <- function(h) function(x) f(h(h))(x)
  g(g)
}

csum <- function(f) function(n) {
  if (n < 2) return(1);
  return(n+f(n-1))
}

recurs.time <- matrix(0, ncol = 3, nrow = 100)
Y.time <- matrix(0, ncol = 3, nrow = 100)

for (i in 1:100) recurs.time[i,] <- unclass(system.time(a <- s(996)))[1:3]
ave.recurs.time <- colSums(recurs.time)
ave.recurs.time

for (i in 1:100) Y.time[i,] <- unclass(system.time(b <- Y (csum)(996)))[1:3]
ave.Y.time <- colSums(Y.time)
ave.Y.time

u <- s(1000)
u

v <- Y (csum)(1000)
v

sessionInfo()

> s <- function(n) {
+   if (n == 1) return(1)
+   return(s(n-1)+n)
+ }
>
>
> Y <- function(f) {
+   g <- function(h) function(x) f(h(h))(x)
+   g(g)
+ }
>
> csum <- function(f) function(n) {
+   if (n < 2) return(1);
+   return(n+f(n-1))
+ }
>
> recurs.time <- matrix(0, ncol = 3, nrow = 100)
> Y.time <- matrix(0, ncol = 3, nrow = 100)
>
> for (i in 1:100) recurs.time[i,] <- unclass(system.time(a <- s(996)))[1:3]
> ave.recurs.time <- colSums(recurs.time)
> ave.recurs.time
[1] 0.356 0.004 0.355
>
> for (i in 1:100) Y.time[i,] <- unclass(system.time(b <- Y
(csum)(996)))[1:3]
> ave.Y.time <- colSums(Y.time)
> ave.Y.time
[1] 0.652 0.000 0.640
>
> u <- s(1000)
> u
[1] 500500
> v <- Y (csum)(1000)
Error: evaluation nested too deeply: infinite recursion /
options(expressions=)?
Error during wrapup: evaluation nested too deeply: infinite recursion /
options(expressions=)?
> v
Error: object "v" not found
No suitable frames for recover()
------------------------------------------------------------
Mark W. Kimpel MD  ** Neuroinformatics ** Dept. of Psychiatry
Indiana University School of Medicine

15032 Hunter Court, Westfield, IN  46074

(317) 490-5129 Work, & Mobile & VoiceMail
(317) 399-1219  Home
Skype:  mkimpel

"The real problem is not whether machines think but whether men do." -- B.
F. Skinner
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