Consider the example that we come across during the lecture:

make.power <- function(n) {
  pow <- function(x)
  {
    x^n  
  } 
  pow 
}

cube <- make.power(3)
square <- make.power(2)

Question: How does the function compute the values of cube and square?

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Let’s try if breaking down these codes helps. Pay attention to the outer part first:

make.power <- function(n) {
  pow <- function(x)
#   {
#     x^n  
#   } 
  pow 
}

So basically make.power is a function, which takes n as the input argument, creates another function called pow, and finally prints out pow. Note that n is still unused so far.

It seems like that pow is what matters. Let’s take a look at pow.

# make.power <- function(n) {
  pow <- function(x)
  {
    x^n  
  } 
#   pow 
# }

Now we know that pow is a function, which takes x as the input argument, and calculates x^n. Note that the n is used here.

Let’s take cube for clarification:

cube <- make.power(3)
# What really heppens is like:
pow <- function(x) {
  x^3
}
cube <- pow

Thus, cube is pow now, and cube is a function as well.

cube(3)
# What really heppens is like:
# pow(3)
3^3

The answer is 27.