# 5 Functions

## 5.1 Introduction

If you’re reading this book, you’ve probably already created many R functions and know how to use them to reduce duplication in your code. In this chapter, you’ll learn how to turn that informal, working knowledge into more rigorous, theoretical understanding. And while you’ll see some interesting tricks and techniques along the way, keep in mind that what you’ll learn here will be important for understanding the more advanced topics discussed later in the book.

### Quiz

Answer the following questions to see if you can safely skip this chapter. You can find the answers in Section 5.9.

1. What are the three components of a function?

2. What does the following code return?

x <- 10
f1 <- function(x) {
function() {
x + 10
}
}
f1(1)()
3. How would you usually write this code?

+(1, *(2, 3))
4. How could you make this call easier to read?

mean(, TRUE, x = c(1:10, NA))
5. Does the following code throw an error when executed? Why/why not?

f2 <- function(a, b) {
a * 10
}
f2(10, stop("This is an error!"))
6. What is an infix function? How do you write it? What’s a replacement function? How do you write it?

7. How do you ensure that cleanup action occurs regardless of how a function exits?

### Outline

• Section 5.2 describes the basics of creating a function, the three main components of a function, and the exception to many function rules: primitive functions (which are implemented in C, not R).

• Section 5.3 discusses the strengths and weaknesses of the three forms of function composition commonly used in R code.

• Section 5.4 shows you how R finds the value associated with a given name, i.e. the rules of lexical scoping.

• Section 5.5 is devoted to an important property of function arguments: they are only evaluated when used for the first time.

• Section 5.6 discusses the special ... argument, which allows you to pass on extra arguments to another function.

• Section 5.7 discusses the two primary ways that a function can exit, and how to define an exit handler, code that is run on exit, regardless of what triggers it.

• Section 5.8 shows you the various ways in which R disguises ordinary function calls, and how you can use the standard prefix form to better understand what’s going on.

## 5.2 Function fundamentals

To understand functions in R you need to internalise two important ideas:

• Functions can be broken down into three components: arguments, body, and environment.

There are exceptions to every rule, and in this case, there is a small selection of “primitive” base functions that are implemented purely in C.

• Functions are objects, just as vectors are objects.

### 5.2.1 Function components

A function has three parts:

• The formals(), the list of arguments that control how you call the function.

• The body(), the code inside the function.

• The environment(), the data structure that determines how the function finds the values associated with the names.

While the formals and body are specified explicitly when you create a function, the environment is specified implicitly, based on where you defined the function. The function environment always exists, but it is only printed when the function isn’t defined in the global environment.

f02 <- function(x, y) {
# A comment
x + y
}

formals(f02)
#> $x #> #> #>$y

body(f02)
#> {
#>     x + y
#> }

environment(f02)
#> <environment: R_GlobalEnv>

I’ll draw functions as in the following diagram. The black dot on the left is the environment. The two blocks to the right are the function arguments. I won’t draw the body, because it’s usually large, and doesn’t help you understand the “shape” of the function.

Like all objects in R, functions can also possess any number of additional attributes(). One attribute used by base R is “srcref”, short for source reference. It points to the source code used to create the function. The srcref is used for printing because, unlike body(), it contains code comments and other formatting.

attr(f02, "srcref")
#> function(x, y) {
#>   # A comment
#>   x + y
#> }

### 5.2.2 Primitive functions

There is one exception to the rule that a function has three components. Primitive functions, like sum() and [, call C code directly.

sum
#> function (..., na.rm = FALSE)  .Primitive("sum")
[
#> .Primitive("[")

They have type “builtin” or “special”:

typeof(sum)
#> [1] "builtin"
typeof([)
#> [1] "special"

These functions exist primarily in C, not R, so their formals(), body(), and environment() are all NULL:

formals(sum)
#> NULL
body(sum)
#> NULL
environment(sum)
#> NULL

Primitive functions are only found in the base package. While they have certain performance advantages, this benefit comes at a price: they are harder to write. For this reason, R-core generally avoids creating them unless there is no other option.

### 5.2.3 First-class functions

It’s very important to understand that R functions are objects in their own right, a language property often called “first-class functions”. Unlike in many other languages, there is no special syntax for defining and naming a function: you simply create a function object (with function) and bind it to a name with <-:

f01 <- function(x) {
sin(1 / x ^ 2)
}

While you almost always create a function and then bind it to a name, the binding step is not compulsory. If you choose not to give a function a name, you get an anonymous function. This is useful when it’s not worth the effort to figure out a name:

lapply(mtcars, function(x) length(unique(x)))
Filter(function(x) !is.numeric(x), mtcars)
integrate(function(x) sin(x) ^ 2, 0, pi)

A final option is to put functions in a list:

funs <- list(
half = function(x) x / 2,
double = function(x) x * 2
)

funs$double(10) #> [1] 20 In R, you’ll often see functions called closures. This name reflects the fact that R functions capture, or enclose, their environments. typeof(f01) #> [1] "closure" ### 5.2.4 Invoking a function You normally call a function by placing with arguments wrapped in parentheses: mean(1:10, na.rm = TRUE). But what happens if you have the arguments already in a data structure? args <- list(1:10, na.rm = TRUE) You can instead use do.call(): it has two arguments. The function to call, and a list containing the function arguments: do.call(mean, args) #> [1] 5.5 We’ll come back to this idea in Section 17.6. ### 5.2.5 Exercises 1. Given a function, like "mean", match.fun() lets you find a function. Given a function, can you find its name? Why doesn’t that make sense in R? 1. It’s possible (although typically not useful) to call an anonymous function. Which of the two approaches below is correct? Why? function(x) 3() #> function(x) 3() (function(x) 3)() #> [1] 3 2. A good rule of thumb is that an anonymous function should fit on one line and shouldn’t need to use {}. Review your code. Where could you have used an anonymous function instead of a named function? Where should you have used a named function instead of an anonymous function? 3. What function allows you to tell if an object is a function? What function allows you to tell if a function is a primitive function? 4. This code makes a list of all functions in the base package. objs <- mget(ls("package:base"), inherits = TRUE) funs <- Filter(is.function, objs) Use it to answer the following questions: 1. Which base function has the most arguments? 2. How many base functions have no arguments? What’s special about those functions? 3. How could you adapt the code to find all primitive functions? 5. What are the three important components of a function? 6. When does printing a function not show the environment it was created in? ## 5.3 Function composition Base R provides two ways to compose multiple function calls. For example, imagine you want to compute the population standard deviation using sqrt() and mean() as building blocks: square <- function(x) x^2 deviation <- function(x) x - mean(x) You either nest the function calls: x <- runif(100) sqrt(mean(square(deviation(x)))) #> [1] 0.274 Or you save the intermediate results as variables: out <- deviation(x) out <- square(out) out <- mean(out) out <- sqrt(out) out #> [1] 0.274 The magrittr package (Bache and Wickham 2014) provides a third option: the binary operator %>%, which is called the pipe and is pronounced as “and then”. library(magrittr) x %>% deviation() %>% square() %>% mean() %>% sqrt() #> [1] 0.274 x %>% f() is equivalent to f(x); x %>% f(y) is equivalent to f(x, y). The pipe is related to tacit or point-free programming21. In this style of programming, you don’t explicitly refer to variables. Instead, you focus on the high-level composition of functions rather than the low-level flow of data; the focus is on what’s being done (the verbs), rather than on what’s being modified (the nouns). This style is common in Haskell and F#, the main inspiration for magrittr, and is the default style in stack based programming languages like Forth and Factor. Each of the three options has its own strengths and weaknesses: • Nesting, f(g(x)), is concise, and well suited for short sequences. But longer sequences are hard to read because they are read inside out and right to left. As a result, arguments can get spread out over long distances creating the “Dagwood sandwich” problem. • Intermediate objects, y <- f(x); g(y), requires you to name intermediate objects. This is a strength when objects are important, but a weakness when values are truly intermediate. • Piping, x %>% f() %>% g(), allows you to read code in straightforward left-to-right fashion and doesn’t require you to name intermediate objects. But you can only use it with linear sequences of transformations of a single object. It also requires an additional third party package and assumes that the reader understands piping. Most code will use a combination of all three styles. Piping is more common in data analysis code, as much of an analysis consists of a sequence of transformations of an object (like a data frame or plot). I tend to use piping infrequently in packages; not because it is a bad idea, but because it’s often a less natural fit. ## 5.4 Lexical scoping In Chapter 2, we discussed assignment, the act of binding a name to a value. Here we’ll discuss scoping, the act of finding the value associated with a name. The basic rules of scoping are quite intuitive, and you’ve probably already internalised them, even if you never explicitly studied them. For example, what will the following code return, 10 or 20?22 x <- 10 g01 <- function() { x <- 20 x } g01() In this section, you’ll learn the formal rules of scoping as well as some of its more subtle details. A deeper understanding of scoping will help you to use more advanced functional programming tools, and eventually, even to write tools that translate R code into other languages. R uses lexical scoping23: it looks up the values of names based on how a function is defined, not how it is called. “Lexical” here is not the English adjective “relating to words or a vocabulary”. It’s a technical CS term that tells us that the scoping rules use a parse-time, rather than a run-time structure. R’s lexical scoping follows four primary rules: • Name masking • Functions vs. variables • A fresh start • Dynamic lookup ### 5.4.1 Name masking The basic principle of lexical scoping is that names defined inside a function mask names defined outside a function. This is illustrated in the following example. x <- 10 y <- 20 g02 <- function() { x <- 1 y <- 2 c(x, y) } g02() #> [1] 1 2 If a name isn’t defined inside a function, R looks one level up. x <- 2 g03 <- function() { y <- 1 c(x, y) } g03() #> [1] 2 1 The same rules apply if a function is defined inside another function. First, R looks inside the current function. Then, it looks where that function was defined (and so on, all the way up to the global environment). Finally, it looks in other loaded packages. Run the following code in your head, then confirm the result by running the code.24 x <- 1 g04 <- function() { y <- 2 i <- function() { z <- 3 c(x, y, z) } i() } g04() The same rules also apply to functions created by other functions, which I call manufactured functions, and are the topic of Chapter 9. Here I’ll focus on how they interact with scoping. The following function, g05(), returns a function. What do you think this function will return when it’s called?25 x <- 10 y <- 20 g05 <- function() { y <- 2 function() { c(x, y) } } g06 <- g05() g06() This seems a little magical: how does R know what the value of y is after g05() is returned? R knows because g06() preserves the environment where it was defined and that environment includes the value of y. You’ll learn more about how environments work in Chapter 6. ### 5.4.2 Functions vs. variables In R, functions are ordinary objects. This means the scoping rules described above also apply to functions: g07 <- function(x) x + 1 g08 <- function() { g07 <- function(x) x + 100 g07(10) } g08() #> [1] 110 However, when a function and a non-function share the same name (they must, of course, reside in different environments), applying these rules gets a little more complicated. When you use a name in a function call, R ignores non-function objects when looking for that value. For example, in the code below, g09 takes on two different values: g09 <- function(x) x + 100 g10 <- function() { g09 <- 10 g09(g09) } g10() #> [1] 110 Note that for the record, using the same name for two different things makes for confusing code, and is something best avoided! ### 5.4.3 A fresh start What happens to values between invocations of a function? Consider the example below. What will happen the first time you run this function? What will happen the second time?26 (If you haven’t seen exists() before, it returns TRUE if there’s a variable with that name and returns FALSE if not.) g11 <- function() { if (!exists("a")) { a <- 1 } else { a <- a + 1 } a } g11() g11() You might be surprised that g11() always returns the same value. This happens because every time a function is called a new environment is created to host its execution. This means that a function has no way to tell what happened the last time it was run; each invocation is completely independent. (We’ll see some ways to get around this in Section 9.2.3) ### 5.4.4 Dynamic lookup Lexical scoping determines where, but not when to look for values. R looks for values when the function is run, not when the function is created. Together, these two properties tell us that the output of a function can differ depending on the objects outside the function’s environment: g12 <- function() x + 1 x <- 15 g12() #> [1] 16 x <- 20 g12() #> [1] 21 This behaviour can be quite annoying. If you make a spelling mistake in your code, you won’t get an error message when you create the function. And depending on the variables defined in the global environment, you might not even get an error message when you run the function. To detect this problem, use codetools::findGlobals(). This function lists all the external dependencies (unbound symbols) within a function: codetools::findGlobals(g12) #> [1] "+" "x" To solve this problem, you can manually change the function’s environment to the emptyenv(), an environment which contains nothing: environment(g12) <- emptyenv() g12() #> Error in x + 1: #> could not find function "+" The problem and its solution reveal why this seemingly undesirable behaviour exists: R relies on lexical scoping to find everything, from the obvious, like mean(), to the less obvious, like + or even {. This gives R’s scoping rules a rather beautiful simplicity. ### 5.4.5 Exercises 1. What does the following code return? Why? Describe how each of the three c’s is interpreted. c <- 10 c(c = c) 2. What are the four principles that govern how R looks for values? 3. What does the following function return? Make a prediction before running the code yourself. f <- function(x) { f <- function(x) { f <- function() { x ^ 2 } f() + 1 } f(x) * 2 } f(10) ## 5.5 Lazy evaluation In R, function arguments are lazily evaluated: they’re only evaluated if accessed. For example, this code doesn’t generate an error because x is never used: h01 <- function(x) { 10 } h01(stop("This is an error!")) #> [1] 10 This is an important feature because it allows you to do things like include potentially expensive computations in function arguments that will only be evaluated if needed. ### 5.5.1 Forcing evaluation To compel the evaluation of an argument, use force(): h02 <- function(x) { force(x) 10 } h02(stop("This is an error!")) #> Error in force(x): #> This is an error! It’s usually not necessary to force evaluation. However, it is important for certain functional programming techniques, like the one we’ll cover in detail in Chapter 10. Here, I’m just going to show you what the basic issue is. Consider this small but surprisingly tricky function. It takes a single argument x, and returns a function that returns x when called. capture1 <- function(x) { function() { x } } The subtlety here is that the value of x will be captured not when you call capture1(), but when you call the function that capture1() returns: x <- 10 h03 <- capture1(x) h04 <- capture1(x) h03() #> [1] 10 x <- 20 h04() #> [1] 20 Even more confusingly this only happens once: the value is locked in after you have called h03()/h04() for the first time. x <- 30 h03() #> [1] 10 h04() #> [1] 20 This behaviour is a consequence of lazy evaluation. The x argument is evaluated once h03()/h04() is called, and then its value is cached. We can avoid the confusion by forcing x: capture2 <- function(x) { force(x) function() { x } } x <- 10 h05 <- capture2(x) x <- 20 h05() #> [1] 10 ### 5.5.2 Promises Lazy evaluation is powered by a data structure called a promise, or (less commonly) a thunk. It’s one of the features that makes R such an interesting programming language (we’ll return to promises again in Section 18.3). A promise has three components: • The expression, like x + y which gives rise to the delayed computation. • The environment where the expression should be evaluated. • The value, which is computed and cached the first time a promise is accessed when the expression is evaluated in the specified environment. The value cache ensures that the promise always returns the same value, even when it’s accessed multiple times. For example, you can see in the following code that runif(1) is only evaluated once: h06 <- function(x) { c(x, x, x) } h06(runif(1)) #> [1] 0.806 0.806 0.806 You can also create promises “by hand” using delayedAssign(): delayedAssign("x", {print("Executing code"); runif(1)}) x #> [1] "Executing code" #> [1] 0.814 x #> [1] 0.814 You’ll see this idea again in Section 6.2.6. You cannot manipulate promises with R code. Promises are like a quantum state: any attempt to inspect them with R code will force an immediate evaluation, making the promise disappear. Later, in Section 18.3, you’ll learn about quosures, which reify promises into an R object where you can easily inspect the expression and the environment. ### 5.5.3 Default arguments Thanks to lazy evaluation, default values can be defined in terms of other arguments, or even in terms of variables defined later in the function: h07 <- function(x = 1, y = x * 2, z = a + b) { a <- 10 b <- 100 c(x, y, z) } h07() #> [1] 1 2 110 Many base R functions use this technique, but I don’t recommend it. It makes the code harder to understand: to predict what will be returned, you need to know the exact order in which default arguments are evaluated. The evaluation environment is slightly different for default and user supplied arguments, as default arguments are evaluated inside the function. This means that seemingly identical calls can yield different results. It’s easiest to see this with an extreme example: h08 <- function(x = ls()) { a <- 1 x } # ls() evaluated inside h08: h08() #> [1] "a" "x" # ls() evaluated in global environment: h08(ls()) #> [1] "h08" ### 5.5.4 Missing arguments To determine if an argument’s value comes from the user or from a default, you can use missing(): h09 <- function(x = 10) { list(missing(x), x) } str(h09()) #> List of 2 #>$ : logi TRUE
#>  $: num 10 str(h09(10)) #> List of 2 #>$ : logi FALSE
#>  $: num 10 missing() is best used sparingly, however. Take sample(), for example. How many arguments are required? args(sample) #> function (x, size, replace = FALSE, prob = NULL) #> NULL It looks like both x and size are required, but in fact if it’s not supplied, sample() uses missing() to provide a default for size. If I were to rewrite sample, I’d use an explicit NULL to indicate that size is not required but can be supplied: sample <- function(x, size = NULL, replace = FALSE, prob = NULL) { if (is.null(size)) { size <- length(x) } x[sample.int(length(x), size, replace = replace, prob = prob)] } With the binary pattern created by the %||% infix function, which uses the LHS if it’s not NULL and the RHS otherwise, we can further simplify sample(): %||% <- function(lhs, rhs) { if (!is.null(lhs)) { lhs } else { rhs } } sample <- function(x, size = NULL, replace = FALSE, prob = NULL) { size <- size %||% length(x) x[sample.int(length(x), size, replace = replace, prob = prob)] } Because of lazy evaluation, you don’t need to worry about unnecessary computation: the RHS of %||% will only be evaluated if the LHS is NULL. ### 5.5.5 Exercises 1. What important property of && makes x_ok() work? x_ok <- function(x) { !is.null(x) && length(x) == 1 && x > 0 } x_ok(NULL) #> [1] FALSE x_ok(1) #> [1] TRUE x_ok(1:3) #> [1] FALSE What is different with this code? Why is this behaviour undesirable here? x_ok <- function(x) { !is.null(x) & length(x) == 1 & x > 0 } x_ok(NULL) #> logical(0) x_ok(1) #> [1] TRUE x_ok(1:3) #> [1] FALSE FALSE FALSE 2. The definition of force() is simple: force #> function (x) #> x #> <bytecode: 0x997cf8> #> <environment: namespace:base> Why is it better to force(x) instead of just x? 3. What does this function return? Why? Which principle does it illustrate? f2 <- function(x = z) { z <- 100 x } f2() 4. What does this function return? Why? Which principle does it illustrate? y <- 10 f1 <- function(x = {y <- 1; 2}, y = 0) { c(x, y) } f1() y 5. In hist(), the default value of xlim is range(breaks), the default value for breaks is "Sturges", and range("Sturges") #> [1] "Sturges" "Sturges" Explain how hist() works to get a correct xlim value. 6. Explain why this function works. Why is it confusing? show_time <- function(x = stop("Error!")) { stop <- function(...) Sys.time() print(x) } show_time() #> [1] "2018-12-14 14:17:57 UTC" 7. How many arguments are required when calling library()? ## 5.6... (dot-dot-dot) Functions can have a special argument ... (pronounced dot-dot-dot). With it, a function can take any number of additional arguments. In other programming languages, this type of argument is often called a varargs, and a function that uses it is said to be variadic. You can also use ... to pass those additional arguments on to another function. i01 <- function(y, z) { list(y = y, z = z) } i02 <- function(x, ...) { i01(...) } str(i02(x = 1, y = 2, z = 3)) #> List of 2 #>$ y: num 2
#>  $z: num 3 Using a special syntax, it’s possible (but rarely useful) to refer to elements of ... by position: i03 <- function(...) { list(first = ..1, third = ..3) } str(i03(1, 2, 3)) #> List of 2 #>$ first: num 1
#>  $third: num 3 More useful is list(...), which evaluates the arguments and stores them in a list: i04 <- function(...) { list(...) } str(i04(a = 1, b = 2)) #> List of 2 #>$ a: num 1
#>  $b: num 2 (See also rlang::list2() to support splicing and to silently ignore trailing commas, and rlang::enquos() to capture unevaluated arguments, the topic of quasiquotation.) There are two primary uses of ..., both of which we’ll come back to later in the book: • If your function takes a function as an argument, you want some way to pass additional arguments to that function. In this example, lapply() uses ... to pass na.rm on to mean(): x <- list(c(1, 3, NA), c(4, NA, 6)) str(lapply(x, mean, na.rm = TRUE)) #> List of 2 #>$ : num 2
#>  $visible: logi FALSE The most common function that returns invisibly is <-: a <- 2 (a <- 2) #> [1] 2 This is what makes it possible to chain assignments: a <- b <- c <- d <- 2 In general, any function called primarily for a side effect (like <-, print(), or plot()) should return an invisible value (typically the value of the first argument). ### 5.7.3 Errors If a function cannot complete its assigned task, it should throw an error with stop(), which immediately terminates the execution of the function. j05 <- function() { stop("I'm an error") return(10) } j05() #> Error in j05(): #> I'm an error An error indicates that something has gone wrong, and forces the user to deal with the problem. Some languages (like C, Go, and Rust) rely on special return values to indicate problems, but in R you should always throw an error. You’ll learn more about errors, and how to handle them, in Conditions. ### 5.7.4 Exit handlers Sometimes a function needs to make temporary changes to the global state. But having to cleanup those changes can be painful (what happens if there’s an error?). To ensure that your changes are undone and that the global state is restored when the function completes, set up an exit handler . You do so by calling on.exit() with the code to be run. When the function exits, this code executes regardless of whether the function returns a value or throws an error. To setup an exit handler: j06 <- function(x) { cat("Hello\n") on.exit(cat("Goodbye!\n"), add = TRUE) if (x) { return(10) } else { stop("Error") } } j06(TRUE) #> Hello #> Goodbye! #> [1] 10 j06(FALSE) #> Hello #> Error in j06(FALSE): #> Error #> Goodbye! on.exit() is important because it allows you to place clean-up actions next to other actions. cleanup <- function(dir, code) { old_dir <- setwd(dir) on.exit(setwd(old_dir), add = TRUE) old_opt <- options(stringsAsFactors = FALSE) on.exit(options(old_opt), add = TRUE) } Coupled with lazy evaluation, this creates a very useful pattern for running a block of code in an altered environment: with_dir <- function(dir, code) { old <- setwd(dir) on.exit(setwd(old), add = TRUE) force(code) } getwd() #> [1] "/home/travis/build/hadley/adv-r" with_dir("~", getwd()) #> [1] "/home/travis" See the withr package (Hester et al. 2018) for a collection of functions of this nature. In R 3.4 and earlier, on.exit() expressions are always run in order of creation: f <- function() { on.exit(message("a"), add = TRUE) on.exit(message("b"), add = TRUE) } f() #> a #> b This can make cleanup a little tricky if some actions need to happen in a specific order; typically you want the most recent added expression to be run first. In R 3.5 and later, you can control this by setting after = FALSE: f <- function() { on.exit(message("a"), add = TRUE, after = FALSE) on.exit(message("b"), add = TRUE, after = FALSE) } f() #> b #> a ### 5.7.5 Exercises 1. What does load() return? Why don’t you normally see these values? 2. What does write.table() return? What would be more useful? 3. How does the chdir parameter of source() compare to in_dir()? Why might you prefer one to the other? 4. Write a function that opens a graphics device, runs the supplied code, and closes the graphics device (always, regardless of whether or not the plotting code works). 5. We can use on.exit() to implement a simple version of capture.output(). capture.output2 <- function(code) { temp <- tempfile() on.exit(file.remove(temp), add = TRUE, after = TRUE) sink(temp) on.exit(sink(), add = TRUE, after = TRUE) force(code) readLines(temp) } capture.output2(cat("a", "b", "c", sep = "\n")) #> [1] "a" "b" "c" Compare capture.output() to capture.output2(). How do the functions differ? What features have I removed to make the key ideas easier to see? How have I rewritten the key ideas so they’re easier to understand? ## 5.8 Function forms “To understand computations in R, two slogans are helpful: • Everything that exists is an object. • Everything that happens is a function call." — John Chambers While everything that happens in R is a result of a function call, not all calls look the same. Function calls come in four varieties: • prefix: the function name comes before its arguments, like foofy(a, b, c). These constitute of the majority of function calls in R. • infix: the function name comes in between its arguments, like x + y. Infix forms are used for many mathematical operators, and for user-defined functions that begin and end with %. • replacement: functions that replace values by assignment, like names(df) <- c("a", "b", "c"). They actually look like prefix functions. • special: functions like [[, if, and for. While they don’t have a consistent structure, they play important roles in R’s syntax. While there are four forms, you actually only need one because any call can be written in prefix form. I’ll demonstrate this property, and then you’ll learn about each of the forms in turn. ### 5.8.1 Rewriting to prefix form An interesting property of R is that every infix, replacement, or special form can be rewritten in prefix form. Doing so is useful because it helps you better understand the structure of the language, it gives you the real name of every function, and it allows you to modify those functions for fun and profit. The following example shows three pairs of equivalent calls, rewriting an infix form, replacement form, and a special form into prefix form. x + y +(x, y) names(df) <- c("x", "y", "z") names<-(df, c("x", "y", "z")) for(i in 1:10) print(i) for(i, 1:10, print(i)) Knowing the function name of a non-prefix function allows you to override its behaviour. For example, if you’re ever feeling particularly evil, run the following code while a friend is away from their computer. It will introduce a fun bug: 10% of the time, it will add 1 to any numeric calculation inside the parentheses. ( <- function(e1) { if (is.numeric(e1) && runif(1) < 0.1) { e1 + 1 } else { e1 } } replicate(50, (1 + 2)) #> [1] 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 #> [36] 3 4 3 4 3 3 3 3 4 3 3 3 3 3 3 rm("(") Of course, overriding built-in functions like this is a bad idea, but, as you’ll learn in Section 19.2.5, it’s possible to apply it only to selected code blocks. This provides a clean and elegant approach to writing domain specific languages and translators to other languages. A more useful application comes up when using functional programming tools. For example, you could use sapply() to add 3 to every element of a list by first defining a function add(): add <- function(x, y) x + y sapply(1:10, add, 3) #> [1] 4 5 6 7 8 9 10 11 12 13 But we can also get the same result simply by relying on the existing + function: sapply(1:5, +, 3) #> [1] 4 5 6 7 8 We’ll explore this idea in detail in functionals. ### 5.8.2 Prefix form The prefix form is the most common form in R code, and indeed in the majority of programming languages. Prefix calls in R are a little special because you can specify arguments in three ways: • By position, like help(mean). • Using partial matching, like help(to = mean). • By name, like help(topic = mean). As illustrated by the following chunk, arguments are matched by exact name, then with unique prefixes, and finally by position. k01 <- function(abcdef, bcde1, bcde2) { list(a = abcdef, b1 = bcde1, b2 = bcde2) } str(k01(1, 2, 3)) #> List of 3 #>$ a : num 1
#>  $b1: num 2 #>$ b2: num 3
str(k01(2, 3, abcdef = 1))
#> List of 3
#>  $a : num 1 #>$ b1: num 2
#>  $b2: num 3 # Can abbreviate long argument names: str(k01(2, 3, a = 1)) #> List of 3 #>$ a : num 1
#>  $b1: num 2 #>$ b2: num 3

# But this doesn't work because abbreviation is ambiguous
str(k01(1, 3, b = 1))
#> Error in k01(1, 3, b = 1):
#>   argument 3 matches multiple formal arguments

In general, use positional matching only for the first one or two arguments; they will be the most commonly used, and most readers will know what they are. Avoid using positional matching for less commonly used arguments, and never use partial matching. See the tidyverse style guide, http://style.tidyverse.org/syntax.html#argument-names, for more advice.

### 5.8.3 Infix functions

Infix functions get their name from the fact the function name comes inbetween its arguments, and hence have two arguments. R comes with a number of built-in infix operators: :, ::, :::, \$, @, ^, *, /, +, -, >, >=, <, <=, ==, !=, !, &, &&, |, ||, ~, <-, and <<-. You can also create your own infix functions that start and end with %. Base R uses this pattern to define %%, %*%, %/%, %in%, %o%, and %x%.

Defining your own infix function is simple. You create a two argument function and bind it to a name that starts and ends with %:

%+% <- function(a, b) paste0(a, b)
"new " %+% "string"
#> [1] "new string"

The names of infix functions are more flexible than regular R functions: they can contain any sequence of characters except “%”. You will need to escape any special characters in the string used to define the function, but not when you call it:

% % <- function(a, b) paste(a, b)
%/\\% <- function(a, b) paste(a, b)

"a" % % "b"
#> [1] "a b"
"a" %/\% "b"
#> [1] "a b"

R’s default precedence rules mean that infix operators are composed left to right:

%-% <- function(a, b) paste0("(", a, " %-% ", b, ")")
"a" %-% "b" %-% "c"
#> [1] "((a %-% b) %-% c)"

There are two special infix functions that can be called with a single argument: + and -.

-1
#> [1] -1
+10
#> [1] 10

### 5.8.4 Replacement functions

Replacement functions act like they modify their arguments in place, and have the special name xxx<-. They must have arguments named x and value, and must return the modified object. For example, the following function modifies the second element of a vector:

second<- <- function(x, value) {
x[2] <- value
x
}

Replacement functions are used by placing the function call on the LHS of <-:

x <- 1:10
second(x) <- 5L
x
#>  [1]  1  5  3  4  5  6  7  8  9 10

I say they “act” like they modify their arguments in place, because, as discussed in Modify-in-place, they actually create a modified copy. We can see that by using tracemem():

x <- 1:10
tracemem(x)
#> <0x7ffae71bd880>

second(x) <- 6L
#> tracemem[0x7ffae71bd880 -> 0x7ffae61b5480]:
#> tracemem[0x7ffae61b5480 -> 0x7ffae73f0408]: second<- 

If you want to supply additional arguments, place them between x and value:

modify<- <- function(x, position, value) {
x[position] <- value
x
}
modify(x, 1) <- 10
x
#>  [1] 10  5  3  4  5  6  7  8  9 10

When you write modify(x, 1) <- 10, behind the scenes R turns it into:

x <- modify<-(x, 1, 10)

Combining replacement with other functions requires more complex translation. For example:

x <- c(a = 1, b = 2, c = 3)
names(x)
#> [1] "a" "b" "c"

names(x)[2] <- "two"
names(x)
#> [1] "a"   "two" "c"

Is translated into:

*tmp* <- x
x <- names<-(*tmp*, [<-(names(*tmp*), 2, "two"))
rm(*tmp*)

(Yes, it really does create a local variable named tmp, which is removed afterwards.)

### 5.8.5 Special forms

Finally, there are a bunch of language features that are usually written in special ways, but also have prefix forms. These include parentheses:

• (x) (((x))
• {x} ({(x)).

The subsetting operators:

• x[i] ([(x, i))
• x[[i]] ([[(x, i))

And the tools of control flow:

• if (cond) true (if(cond, true))
• if (cond) true else false (if(cond, true, false))
• for(var in seq) action (for(var, seq, action))
• while(cond) action (while(cond, action))
• repeat expr (repeat(expr))
• next (next())
• break (break())

Finally, the most complex is the “function” function:

• function(arg1, arg2) {body} (function(alist(arg1, arg2), body, env))

Knowing the name of the function that underlies a special form is useful for getting documentation: ?( is a syntax error; ?( will give you the documentation for parentheses.

Note that all special forms are implemented as primitive functions (i.e. in C); this means printing these functions is not informative:

for
#> .Primitive("for")

### 5.8.6 Exercises

1. Rewrite the following code snippets into prefix form:

1 + 2 + 3

1 + (2 + 3)

if (length(x) <= 5) x[[5]] else x[[n]]
2. Clarify the following list of odd function calls:

x <- sample(replace = TRUE, 20, x = c(1:10, NA))
y <- runif(min = 0, max = 1, 20)
cor(m = "k", y = y, u = "p", x = x)
3. Explain why the following code fails:

modify(get("x"), 1) <- 10
#> Error: target of assignment expands to non-language object
4. Create a replacement function that modifies a random location in a vector.

5. Write your own version of + that pastes its inputs together if they are character vectors but behaves as usual otherwise. In other words, make this code work:

1 + 2
#> [1] 3

"a" + "b"
#> [1] "ab"
6. Create a list of all the replacement functions found in the base package. Which ones are primitive functions? (Hint: use apropros())

7. What are valid names for user-created infix functions?

8. Create an infix xor() operator.

9. Create infix versions of the set functions intersect(), union(), and setdiff(). You might call them %n%, %u%, and %/% to match conventions from mathematics.

1. The three components of a function are its body, arguments, and environment.

2. f1(1)() returns 11.

3. You’d normally write it in infix style: 1 + (2 * 3).

4. Rewriting the call to mean(c(1:10, NA), na.rm = TRUE) is easier to understand.

5. No, it does not throw an error because the second argument is never used so it’s never evaluated.

6. See Sections 5.8.3 and 5.8.4.

7. You use on.exit(); see Section 5.7.4 for details.

### References

Bache, Stefan Milton, and Hadley Wickham. 2014. Magrittr: A Forward-Pipe Operator for R. http://magrittr.tidyverse.org/.

Hester, Jim, Kirill Müller, Kevin Ushey, Hadley Wickham, and Winston Chang. 2018. Withr: Run Code with Temporarily Modified Global State. http://withr.r-lib.org.

1. Point-free programming is related to point-free topology. It’s just a coincidence that many forms of point-free programming use . extensively. Point-free programming is sometimes humorously called pointless programming.

2. I’ll “hide” the answers to these challenges in the footnotes. Try solving them before looking at the answer; this will help you to better remember the correct answer. In this case, g01() will return 20.

3. Functions that automatically quote one or more arguments (sometimes called NSE functions) can override the default scoping rules to implement other varieties of scoping. You’ll learn more about that in Chapter 18.

4. g04() returns c(1, 2, 3).

5. g06() returns c(10, 2).

6. g11() returns 1 every time it’s called.

7. Functions can exit in other more esoteric ways like signalling a condition that is caught by an exit handler, invoking a restart, or pressing “Q” in an interactive browser.