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Functions

Functions are a fundamental building block of R: to master many of the more advanced techniques in this book, you need a solid foundation in how functions work. You've probably already created many R functions, and you're familiar with the basics of how they work. The focus of this chapter is to turn your existing, informal, knowledge of functions into a rigorous understanding of what functions are and how they work. You'll see some interesting tricks and techniques in this chapter, but most of what you'll learn will be more important as the building blocks for more advanced techniques.

The most important thing to understand about R is that functions are objects in their own right. You can work with them exactly the same way you work with any other type of object.

In this chapter you will learn:

  • The three main components of a function.

  • How scoping works, the process that looks up values from names.

  • How everything that happens in R is a result of a function call, even if it doesn't look like it

  • The three ways of supplying arguments to a function, how call a function given a list of arguments, and the impact of lazy evaluation.

  • About two types of special functions: infix and replacement functions.

  • What a function can return, and how invisible return values work

Components of a function

There are three properties that all R functions possess:

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

  • the formals(), the "formal" argument list, which controls how you can call the function.

  • the environment() which determines how variables referred to inside the function are found.

When you print a function in R, it shows you these three important components. If the environment isn't displayed, it means that the function was created in the global environment.

f <- function(x) x
f

formals(f)
body(f)
environment(f)

The assignment forms of body(), formals(), and environment() can also be used to modify functions. This is a useful technique which we'll explore in more detail in computing on the language.

Like all other objects in R, functions can also possess any number of additional attributes(). One attribute used by base R is "srcref", short for source reference, which points to the source code used to create the funtion. Unlike the body(), this contains codes comments and other formatting. You can also add your attributes to a function, for example, you can can set the class() and add a custom print() method.

Primitive functions

There is one exception to the rule that functions have three components. Primitive functions, like sum, call C code directly with .Primitive() and contain no R code. Therefore their formals(), body() and environment() are all NULL:

sum
formals(sum)
body(sum)
environment(sum)

Primitive functions are only found in the base package, and since they operate at a low level, they can be more efficient (primitive replacement functions don't have to make copies), and can have different rules for argument matching (e.g. switch and call). This, however, comes at a cost of behaving differently to all other function in R, and so R core generally avoids creating them unless there is no other option.

Exercises

  • 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 or not?

  • Create a list of all primitive functions in R. (Hint: use ls("package:base, all = TRUE) to get a list of all objects in the base package, get() to retrieve an object given its name, and the answer to the question above.)

  • What are the three important components of a function?

  • When does printing a function not show what environment it was created in?

Lexical scoping

Scoping is the set of rules that govern how R looks up the value of a symbol. In other words, scoping is the set of rules that R applies to go from the symbol x, to its value 10 in this example:

x <- 10
x
# [1] 10

Understanding scoping allows you to:

R has two types of scoping: lexical scoping, implemented automatically at the language level, and dynamic scoping, used in select functions to save typing during interactive analysis. We describe lexical scoping here because it is intimately tied to function creation. Dynamic scoping is described in the context of computing on the language.

Lexical scoping looks up symbol values based on functions were nested when they were created, not how they are nested when they are called. With lexical scoping, you can figure out where the value of each variable will be looked up only by looking at the definition of the function, you don't need to know anything about how the function is called.

The "lexical" in lexical scoping doesn't correspond to the usual English definition ("of or relating to words or the vocabulary of a language as distinguished from its grammar and construction") but comes from the computer science term "lexing", which is part of the process that converts code represented as text to meaningful pieces that the programming language understands. It's lexical scoping is lexical in this sense because you only need the definition of the functions, not how they are called.

There are four basic principles behind R's implementation of lexical scoping:

  • name masking
  • functions vs. variables
  • a fresh start
  • dynamic lookup

You probably know many of these principles already, although you might not have thought about them explicitly. Test your knowledge by mentally running the code in each block before looking at the answers.

Name masking

The following example illustrates the simplest principle, and you should have no problem predicting the output.

f <- function() { 
  x <- 1
  y <- 2
  c(x, y)
}
f()
rm(f)

If a name isn't defined inside a function, R will look one level up.

x <- 2
g <- function() { 
  y <- 1
  c(x, y)
}
g()
rm(x, g)

The same rules apply if a function is defined inside another function. First it looks inside the current function, then where that function was defined, and so on, all the way up to the global environment, and then on to other loaded packages. Run the following code in your head, then confirm the output by running the R code.

x <- 1
h <- function() { 
  y <- 2
  i <- function() {
    z <- 3
    c(x, y, z)
  }
  i()
}
h()
rm(x, h)

The same rules apply to closures, functions created by other functions. Closures will be described in more detail in functional programming; here we'll just look at how they interact with scoping. The following function, j(), returns a function. What do you think this function will return when we call it?

j <- function(x) {
  y <- 2
  function() {
    c(x, y)
  }
}
k <- j(1)
k()
rm(j, k)

This seems a little magical (how does R know what the value of y is after the function has been called), but it works because k keeps around the environment in which it was defined, which includes the value of y. Environments gives some pointers on how you can dive in and figure out what values are stored in the environment associated with each function.

Functions vs. variables

The same principles apply regardless of type of the associated value - finding functions works exactly the same way as finding variables:

l <- function(x) x + 1
m <- function() {
  l <- function(x) x * 2
  l(10)
}
m()
rm(l, m)

There is one small tweak to the rule for functions. If you are using a name in a context where it's obvious that you want a function (e.g. f(3)), R will ignore objects that are not functions while it is searching. In the following example n takes on a different value depending on whether R is looking for a function or a variable.

n <- function(x) x / 2
o <- function() {
  n <- 10
  n(n)
}
o()
rm(n, o)

However, using the same name for functions and other objects will make for confusing code, and is generally best avoided.

A fresh start

What happens to the values in between invocations of a function? What will happen the first time you run this function? What will happen the second time? (If you haven't seen exists before: it returns TRUE if there's a variable of that name, otherwise it returns FALSE)

j <- function() {
  if (!exists("a")) {  
    a <- 1
  } else {
    a <- a + 1
  }
  print(a)
}

You might be surprised that it returns the same value, 1, every time. This is because every time a function is called, a new environment is created to host execution. 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 functional programming)

Dynamic lookup

Lexical scoping determines where to look for values, not when to look for them. R looks for values when the function is run, not when it's created. This means that the output of a function can be different depending on objects outside its environment:

f <- function() x
x <- 15
f()

x <- 20
f()

You generally want to avoid this behavour because it means the function is no longer self-contained. This is a common error - if you make a spelling mistake in your code, you won't get an error when you create the function, and you might not even get one when you run the function, depending on what variables are defined in the global environment.

One way to detect this problem is the findGlobals() function from codetools. This function list all the external dependencies of a function:

f <- function() x + 1
codetools::findGlobals(f)

Another way to try and solve the problem would be to manually change the environment of the function to the emptyenv(), an environment which contains absolutely nothing:

environment(f) <- emptyenv()
f()

This doesn't work because R relies on lexical scoping to find everything, even the + operator. It's never possible to make a function completely self-contained because you must always rely on functions defined in base R or other packages.

You can use this same idea to do other things that are extremely ill-advised. For example, since all of the standard operators in R are functions, you can override them with your own alternatives. If you ever are feeling particularly evil, run the following code while your friend is away from their computer:

"(" <- function(e1) {
  if (is.numeric(e1) && runif(1) < 0.1) {
    e1 + 1
  } else {
    e1
  }
}
replicate(100, (1 + 2))
rm("(")

This will introduce a particularly pernicious bug: 10% of the time, 1 will be added to any numeric calculation inside parentheses. This is another good reason to regularly restart with a clean R session!

Exercises

  • What does the following code return? Why? What does each of the three c's mean?

    c <- 10
c(c = c)

  • What are the four principles that govern how R looks for values?

  • What does the following function return? Make a prediction before running the code yourself.

    f <- function(x) {
  f <- function(x) {
    f <- function(x) {
      x ^ 2
    }
    f(x) + 1
  }
  f(x) * 2
}
f(10)

Every operation is a function call

To understand computations in R, two slogans are helpful:

  • Everything that exists is an object.
  • Everything that happens is a function call.

--- John Chambers

The previous example of redefining ( works because every operation in R is a function call, whether or not it looks like it. This includes infix operators like +, control flow operators like for, if, and while, subsetting operators like [] and $ and even the curly braces {. This means that each of pairs of statements in the following example are exactly equivalent. Note that `, the backtick, lets you refer to functions or variables that have otherwise reserved or illegal names:

x + y
`+`(x, y)

for (i in 1:3) print(i)
`for`(i, 1:3, print(i))

if (i == 1) print("yes!") else print("no.")
`if`(i == 1, print("yes"), print("no."))

x[3]
`[`(x, 3)

{ print(1); print(2); print(3) }
`{`(print(1), print(2), print(3))

It is possible to override the definitions of these special functions, but this is almost certainly a bad idea. However, it can occasionally allow you to do something that would have otherwise been impossible. For example, this feature makes it possible for the dplyr package to translate R expressions into SQL expressions. The dsl chapter discusses using this idea to create domain specific languages that allow you to concisely express new concepts using existing R constructs.

It's more often useful to treat special functions as ordinary functions. For example, we could use lapply to add 3 to every element of a list by first defining a function add, like this:

add <- function(x, y) x + y
lapply(1:10, add, 3)

But we can get the same effect using the built-in + function.

lapply(1:10, `+`, 3)
lapply(1:10, "+", 3)

Note the difference between `+` and "+". The first one is the value of the object called +, and the second is a string containing the character +. The second version works because lapply can be given the name of a function instead of the function itself - if you read the source of lapply(), you'll see the first line uses match.fun() to find functions given their names.

A more useful application is combining lapply() with subsetting:

x <- list(1:3, 4:9, 10:12)
lapply(x, "[", 2)
# equivalent to
lapply(x, function(x) x[2])

That everything in R is represented as a function call is important to know for computing on the language.

Function arguments

It's useful to distinguish between the formal arguments and the actual arguments to a function. The formal arguments are a property of the function, whereas the actual or calling arguments vary each time you call the function. This section discusses how calling arguments are mapped to formal arguments, how you can call a function given a list of argunments, how default arguments work and the impact of lazy evaluation.

Calling functions

When calling a function you can specify arguments by position, by complete name, or by partial name. Arguments are matched first by exact name (perfect matching), then by prefix matching and finally by position.

f <- function(abcdef, bcde1, bcde2) {
  list(a = abcdef, b1 = bcde1, b2 = bcde2)
}
f(1, 2, 3)
f(2, 3, abcdef = 1)
# Can abbreviate long argument names:
f(2, 3, a = 1)
# Doesn't work because abbreviation is ambiguous
f(1, 3, b = 1)

Generally, you only want to use positional matching for the first one or two arguments: they will be the mostly commonly used, and most readers will know what they are. Avoid using positional matching for less commonly used arguments, and only use readable abbreviations with partial matching. (If you are writing code for a package that you want to publish on CRAN you can not use partial matching, and must use complete names.) Named arguments should always come after unnamed arguments. If an function uses ... (discussed in more detail below), you can only specify arguments listed after ... with their full name.

These are good calls:

mean(1:10)
mean(1:10, trim = 0.05)

This is probably overkill:

mean(x = 1:10)

And these are just confusing:

mean(1:10, n = T)
mean(1:10, , FALSE)
mean(1:10, 0.05)
mean(, TRUE, x = c(1:10, NA))

Calling a function given a list of arguments

Suppose you had a list of function arguments:

args <- list(1:10, na.rm = TRUE)

How could you then send that list to mean()? You need do.call():

do.call(mean, list(1:10, na.rm = TRUE))
# Equivalent to 
mean(1:10, na.rm = TRUE)

Default and missing arguments

Function arguments in R can have default values.

f <- function(a = 1, b = 2) {
  c(a, b)
}
f()

Since arguments in R are evaluated lazily (more on that below), the default value can be defined in terms of other arguments:

g <- function(a = 1, b = a * 2) {
  c(a, b)
}
g()
g(10)

Default arguments can even be defined in terms of variables created within the function. This is used frequently in base R functions, but I think it is bad practice, because you can't understand what the default values will be without reading the complete source code.

h <- function(a = 1, b = d) {
  d <- (a + 1) ^ 2
  c(a, b)
}
h()
h(10)

You can detect if an argument was supplied or not with the missing() function.

i <- function(a, b) {
  c(missing(a), missing(b))
}
i()
i(a = 1)
i(b = 2)
i(1, 2)

However, I generally recommend against using missing because it makes it difficult to call programmatically from other functions. Generally, it's better to set a default value of NULL and then check with is.null().

j <- function(a = NULL, b = NULL) {
  c(is.null(a), is.null(b))
}
j()
j(a = 1)
j(b = 2)
j(1, 2)

Lazy evaluation

By default, R function arguments are lazy - they're only evaluated if they're actually used:

f <- function(x) {
  10
}
system.time(f(Sys.sleep(10)))

If you want to ensure that an argument is evaluated you can use force:

f <- function(x) {
  force(x)
  10
}
system.time(f(Sys.sleep(10)))

This is important when creating closures with lapply or a loop:

add <- function(x) {
  function(y) x + y
}
adders <- lapply(1:10, add)
adders[[1]](10)
adders[[10]](10)

x is lazily evaluated the first time that you call one of the adder functions. At this point, the loop is complete and the final value of x is 10. Therefore all of the adder functions will add 10 on to their input, probably not what you wanted! Manually forcing evaluation fixes the problem:

add <- function(x) {
  force(x)
  function(y) x + y
}
adders2 <- lapply(1:10, add)
adders2[[1]](10)
adders2[[10]](10)

This code is exactly equivalent to

add <- function(x) {
  x
  function(y) x + y
}

because the force function is just defined as force <- function(x) x. However, using this function indicates clearly that you're forcing evaluation, not that you've accidentally typed x.

Default arguments are evaluated inside the function. This means that if the expression depends on the current environment the results will be different depending on whether you use the default value or explicitly provide it.

f <- function(x = ls()) {
  a <- 1
  x
}
# ls() evaluated inside f:
f()
# ls() evaluated in global environment:
f(ls())

More technically, an unevaluated argument is called a promise, or (less commonly) a thunk. A promise is made up of two parts:

  • an expression giving the delayed computation, which can be accessed with substitute (see [[controlling evaluation|evaluation] for more details)

  • the environment where the expression was created and where it should be evaluated

The first time a promise is accessed the expression is evaluated in the environment where it was created. This value is cached, so that subsequently access to the evaluted promise does not recompute the value (but the original expression is still associated with the value, so that substitute can continue to access it). You can find more information about a promise using pryr::promise_info. This uses some C++ code to extract information about the promise without evaluating it, which is impossible to do in pure R code.

Laziness is useful in if statements - the second statement below will be evaluated only if the first is true. If it wasn't, the statement would return an error because NULL > 0 is a logical vector of length 0 and not a valid input to if.

x <- NULL
if (!is.null(x) && x > 0) {

}

We could implement "&&" ourselves:

"&&" <- function(x, y) {
  if (!x) return(FALSE)
  if (!y) return(FALSE)

  TRUE
}
y <- NULL
!is.null(y) && y > 0

This function would not work without lazy evaluation because both x and y would always be evaluated, testing if y > 0 even if y was NULL.

Sometimes you can also use laziness to elimate an if statement altogether. For example, instead of:

if (is.null(y)) stop("Y is null")

You could write:

!is.null(y) || stop("Y is null")

...

There is a special argument called .... This argument will match any arguments not otherwise matched, and can be easily passed on to other functions. This is useful if you want to collect arguments to call another function, but you don't want to prespecify their possible names. ... is often used in conjunction with S3 generic functions to allow individual methods to be more flexible.

One relatively sophisticated user of ... is the base plot() function. plot() is a generic method with arguments x, y and ..... To understand what ... does for a given function we need to read the help: "Arguments to be passed to methods, such as graphical parameters". Most simple invocation of plot() ends up calling plot.default() which has many more arguments, but also has .... Again, reading the documentation reveals that ... accepts "other graphical parameters", which are listed the help for par(). This allows us to write code like:

plot(1:5, col = "red")
plot(1:5, cex = 5, pch = 20)

This illustrates both the advantages and disadvantages of ...: it makes plot() very flexible, but to understand how to use it, we have to carefully read the documentation. Additionally, if we read the source code for plot.default, we can discover undocumented features. It's possible to pass along other arguments to Axis() and box():

plot(1:5, bty = "u")
plot(1:5, labels = FALSE)

To capture ... in a form that is easier to work with, you can use list(...). (See Computing on the language for other ways to capture ... without evaluating the arguments).

f <- function(...) {
  names(list(...))
}
f(a = 1, b = 2)

Using ... comes with a cost - any misspelled arguments will not raise an error, and any arguments after ... must be fully named. This makes it easy for typos to go unnoticed:

sum(1, 2, na.mr = TRUE)

It's often better to be explicit rather than implicit, so you might instead ask users to supply a list of additional arguments. That's certainly easier if you're trying to use ... with multiple additional functions.

Exercises

Special calls

R supports two additional syntaxes for calling special types of functions: infix and replacement functions.

Infix functions

Most functions in R are "prefix" operators: the name of the function comes before the arguments. You can also create infix functions where the function name comes in between its arguments, like + or -. All user created infix functions names must start and end with % and R comes with the following infix functions predefined: %%, %*%, %/%, %in%, %o%, %x%. (The complete list of built-in infix operators that don't need % is: ::, $, @, ^, *, /, +, -, >, >=, <, <=, ==, !=, !, &, &&, |, ||, ~, <-, <<-)

For example, we could create a new operator that pastes together strings:

"%+%" <- function(a, b) paste(a, b, sep = "")
"new" %+% " string"

Note that when creating the function, you have to put the name in quotes because it's a special name. This is just a syntactic sugar for an ordinary function call; as far as R is concerned there is no difference between these two expressions:

"new" %+% " string"
`%+%`("new", " string")

Or indeed between

1 + 5
`+`(1, 5)

The names of infix functions are more flexible than regular R functions: they can contain any sequence of characters (except "%", of course). 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)
"%/\\%" <- function(a, b) paste(a, b)

"a" % % "b"
"a" %'% "b"
"a" %/\% "b"

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

"%-%" <- function(a, b) paste0("(", a, " %-% ", b, ")")
"a" %-% "b" %-% "c"

There's one infix function that I use very often. It's inspired by Ruby's || logical or operator, although it works a little differently in R because ruby has a more flexible definition of what evaluates to TRUE in an if statement. It's useful as a way of providing a default value in case the output of another function is NULL:

"%||%" <- function(a, b) if (!is.null(a)) a else b
function_that_might_return_null() %||% default value

Replacement functions

Replacement functions act like they modify their arguments in place, and have the special name xxx<-. They typically have two arguments (x and value), although they can have more, and they must return the modified object. For example, the following function allows you to modify the second element of a vector:

"second<-" <- function(x, value) {
  x[2] <- value
  x
}
x <- 1:10
second(x) <- 5L
x

When R evaluates the assignment second(x) <- 5, it notices that the left hand side of the <- is not a simple name, so it looks for a function named second<- to do the replacement.

I say they "act" like they modifying their arguments in place, because they actually create a modified copy. We can see that by using pryr::address() to find the memory address of the underlying object.

library(pryr)
address(x)
second(x) <- 6L
address(x)

Built in functions that are implemented using .Primitive will modify in place

address(x)
x[2] <- 7L
address(x)

It's important to be aware of this behaviour since it has important performance implications.

If you want to supply additional arguments, they go in between x and value:

"modify<-" <- function(x, position, value) {
  x[position] <- value
  x
}
modify(x, 1) <- 10
x

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

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

This means you can't do things like:

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

because that gets turned into the invalid code:

get("x") <- `modify<-`(get("x"), 1, 10)

It's often useful to combine replacement and subsetting, and this works out of the box:

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

This works because the expression names(x)[2] <- "two" is evaluated as if you had written:

`*tmp*` <- names(x)
`*tmp*`[2] <- "two"
names(x) <- `*tmp*`

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

Exercises

  • Create a list of all the replacement functions found in the base package. Which ones are primitive functions?

  • What are valid names for user created infix functions?

  • Create an infix xor() operator.

  • Create infix versions of set functions: intersect(), union(), setdiff()

  • Create an replacement function that modifies a random location in vector.

Return values

The last expression evaluated in a function becomes the return value, the result of invoking the function.

f <- function(x) {
  if (x < 10) {
    0
  } else {
    10
  }
}
f(5)
f(15)

Generally, I think it's good style to reserve the use of an explicit return() for when you are returning early, such as for an error, or a simple case of the function. This style of programming can also reduce the level of indentation, and generally make functions easier to understand because you can reason about them locally.

f <- function(x, y) {
  if (!x) return(y)

  # complicated processing here
}

Functions can return only a single value, but this is not a limitation in practice because you can always return a list containing any number of objects.

The functions that are the most easy to understand and reason about are pure functions, functions that always map the same input to the same output and have no other impact on the workspace. In other words, pure functions have no side-effects: they don't affect the state of the world in any way apart from the value they return.

R protects you from one type of side-effect: most R objects have copy-on-modify semantics, so modifying a function argument does not change the original value:

f <- function(x) {
  x$a <- 2
  x
}
x <- list(a = 1)
f(x)
x$a

(There are two important exceptions to the copy-on-modify rule: environments and reference classes. These can be modified in place, so extra care is needed when working with them.)

This is notably different to languages like Java where you can modify the inputs to a function. This copy-on-modify behaviour has important performance consequences which are discussed in depth in profiling. (Note that the performance consequences are a result of R's implementation of copy-on-modify semantics, they are not true in general. Clojure is a new language that makes extensive use of copy-on-modify semantics with limited performance consequences.)

Most base R functions are pure, with a few notable exceptions:

  • library which loads a package, and hence modifies the search path

  • setwd, Sys.setenv, Sys.setlocale which change the working directory, environment variables and the locale respectively

  • plot and friends which produce graphical output

  • write, write.csv, saveRDS etc which save output to disk

  • options and par which modify global settings

  • S4 related functions which modify global tables of classes and methods.

  • random number generators which produce different numbers each time you run them

It's generally a good idea to minimise the use of side effects, and where possible separate functions into pure and impure, isolating side effects to the smallest possible location. Pure functions are easier to test (because all you need to worry about are the input values and the output), and are less likely to work differently on different versions of R or on different platforms. For example, this is one of the motivating principles of ggplot2: most operations work on an object that represents a plot, and only the final print or plot call has the side effect of actually drawing the plot.

Functions can return invisible values, which are not printed out by default when you call the function.

f1 <- function() 1
f2 <- function() invisible(1)

f1()
f2()
f1() == 1
f2() == 1

You can always force an invisible value to be displayed by wrapping it in parentheses:

(f2())

The most common function that returns invisibly is <-:

a <- 2
(a <- 2)

And this is what makes it possible to assign one value to multiple variables:

a <- b <- c <- d <- 2

because that is parsed as:

(a <- (b <- (c <- (d <- 2))))

Exercises

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