As I wrote before, I’m going to be working through some problems that caught my interest in Hadley Wickham’s second edition of Advanced R. I’m starting off with the functional programming chapter, where an exercise that literally made me go “wow” was a major source of inspiration for me to start this blog – I’m talking about Exercise 2 in Section 9.5.1.

The problem itself revolves around the mathematical idea of fixed points of functions, i.e. points \(x\) such that \(f(x) = x\) for a given function \(f\). This bit of code pops up in one possible implementation of a computational method to find such points:^{1}

```
try <- function(guess) {
if (good_enough(guess))
return(guess)
else
try(new(guess))
}
```

Isn’t that just great? Using functional programming coupled with meaningful names, we can essentially write out the idea of iteration in a block of fully functioning code that reads almost like prose.

Now, to be clear, the snippet above is clearly not the complete picture, nor the solution for the problem – but it’s the part that really made me stop and think, or “pause and ponder”^{2}, if you will.

My intention was to go through the fixed point algorithm problem more thoroughly already in this post, but on second thought, I think I’ll leave it for later. The beautiful function presented here deserves the highlight of a post of it’s own, don’t you think?

The implementation was presented as a Lisp function in Harold Abelson’s Structure and Interpretation of Computer Programs (1996). Here, I’ve just adapted it to the equivalent R code.↩

A phrase often used on Grant Sanderson’s 3Blue1Brown YouTube channel, where he publishes fantastic videos visualizing abstract mathematical concepts – highly recommended!↩