## 10.1 Introduction

A function factory is a function that makes functions. Here’s a very simple example: we use a function factory (power1()) to make two child functions (square() and cube()):

power1 <- function(exp) {
function(x) {
x ^ exp
}
}

square <- power1(2)
cube <- power1(3)

Don’t worry if this doesn’t make sense yet, it should by the end of the chapter!

I’ll call square() and cube() manufactured functions, but this is just a term to ease communication with other humans: from R’s perspective they are no different to functions created any other way.

square(3)
#> [1] 9
cube(3)
#> [1] 27

You have already learned about the individual components that make function factories possible:

• In Section 6.2.3, you learned about R’s first-class functions. In R, you bind a function to a name in the same way as you bind any object to a name: with <-.

• In Section 7.4.2, you learned that a function captures (encloses) the environment in which it is created.

• In Section 7.4.4, you learned that a function creates a new execution environment every time it is run. This environment is usually ephemeral, but here it becomes the enclosing environment of the manufactured function.

In this chapter, you’ll learn how the non-obvious combination of these three features leads to the function factory. You’ll also see examples of their usage in visualisation and statistics.

Of the three main functional programming tools (functionals, function factories, and function operators), function factories are the least used. Generally, they don’t tend to reduce overall code complexity but instead partition complexity into more easily digested chunks. Function factories are also an important building block for the very useful function operators, which you’ll learn about in Chapter 11.

### Outline

• Section 10.2 begins the chapter with an explanation of how function factories work, pulling together ideas from scoping and environments. You’ll also see how function factories can be used to implement a memory for functions, allowing data to persist across calls.

• Section 10.3 illustrates the use of function factories with examples from ggplot2. You’ll see two examples of how ggplot2 works with user supplied function factories, and one example of where ggplot2 uses a function factory internally.

• Section 10.4 uses function factories to tackle three challenges from statistics: understanding the Box-Cox transform, solving maximum likelihood problems, and drawing bootstrap resamples.

• Section 10.5 shows how you can combine function factories and functionals to rapidly generate a family of functions from data.

### Prerequisites

Make sure you’re familiar with the contents of Sections 6.2.3 (first-class functions), 7.4.2 (the function environment), and 7.4.4 (execution environments) mentioned above.

Function factories only need base R. We’ll use a little rlang to peek inside of them more easily, and we’ll use ggplot2 and scales to explore the use of function factories in visualisation.

library(rlang)
library(ggplot2)
library(scales)