R function that uses its output as its own input repeatedly

Question

Given R function auto (below), I was wondering if it might be possible that from the second run of the for loop output of ps be used a

Answer 1

I thought to use a different way. Although, I have not completed it but still thought to share with others for improvement ideas. I'm looking at very basic and crude way to solve it.

auto <- function(n, dat){
  pr = function(x) dbeta(x, 1, 1)
  lk = function(x) dbinom(dat[1], n[1], x)
  ps = function(x) pr(x)*lk(x) 
  #keep the funtion till now in psold 
  psold = ps
  #loop through 2nd to 2nd last element
  for(i in 2:length(n)-1){
    lk = function(x) dbinom(dat[i], n[i], x)
    #Use psold to evaluate new function ps
    ps = function(x) psold(x)*lk(x)
    psold = ps
  }
  lk = function(x) dbinom(dat[length(n)], n[length(n)], x)
  #Finaly function to be returned.
  ps = function(x) psold(x)*lk(x)  
}
# Example of use:
auto(n = c(100, 50), dat = c(55, 60) )