Question

mystery_method <- function(x) { function(z) Reduce(function(y, w) w(y), x, z) }

fn <- mystery_method(c(function(x) x + 1, function(x) x * x))

fn(3)

What is the value of fn(3)? Can you explain what is happening at each step?

Answer 1

Best seen in steps.

fn(3) requires mystery_method to be evaluated first.

mystery_method(c(function(x) x + 1, function(x) x * x)) evaluates to...

function(z) Reduce(function(y, w) w(y), c(function(x) x + 1, function(x) x * x), z)

Now, we can see the 3 in fn(3) is supposed to be z, giving us...

Reduce(function(y, w) w(y), c(function(x) x + 1, function(x) x * x), 3)

This Reduce call is wonky, taking three arguments. A three argument Reduce call will initialize at the third argument, which is 3.

The inner function, function(y, w) w(y) is meant to take an argument and a function and apply that function to the argument. Luckily for us, we have some functions to apply.

That means we intialize at 3 and apply the first function, function(x) x + 1. 3 + 1 = 4.