Expressions

Expressions

In computing on the language, you learned the basics of accessing the expressions underlying computation in R, and evaluating them in new ways. In this chapter, you'll learn more about the underlying structure of expressions, and how you can compute on them directly.

• Calls in more detail

• Implement a function by calling another function (bad idea): write.csv(), xtabs()

• Parsing and evaluating text: source

• Walk the code tree: pryr:call_tree(), codetools::findGlobals, find assignments, find calls

  • List all assignments in a function
  • Replace T with TRUE and F with FALSE

  The codetools package, included in the base distribution, provides some other built-in tools based for automated code inspection:

  • findGlobals: locates all global variables used by a function. This can be useful if you want to check that your functions don't inadvertently rely on variables defined in their parent environment.

  • checkUsage: checks for a range of common problems including unused local variables, unused parameters and use of partial argument matching.

  • showTree: works in a similar way to the drawTree used above, but presents the parse tree in a more compact format based on Lisp's S-expressions

• Modifying calls: partial_eval

• Create functions by hand as an alternative to closures: pryr::make_function, pryr::unenclose, pryr::partial, memoise

It's generally a bad idea to create code by operating on its string representation: there is no guarantee that you'll create valid code. Don't get me wrong: pasting strings together will often allow you to solve your problem in the least amount of time, but it may create subtle bugs that will take your users hours to track down. Learning more about the structure of the R language and the tools that allow you to modify it is an investment that will pay off by allowing you to make more robust code.

Thoroughout this chapter we're going to use tools from the pryr package to help see what's going on. If you don't already have it, install it by running devtools::install_github("pryr")

Because code is a tree, we're going to need recursive functions to work with it. You now have basic understanding of how code in R is put together internally, and so we can now start to write some useful functions. In this section we'll write functions to:

Structure of expressions

To compute on the language, we first need to be understand the structure of the language. That's going to require some new vocabulary, some new tools and some new ways of thinking about R code. The first thing you need to understand is the distinction between an operation and its result:

x <- 4
y <- x * 10

We want to distinguish between the action of multiplying x by 10 and assigning the results to y versus the actual result (40). In R, we can capture the action with quote():

z <- quote(y <- x * 10)
z

quote() gives us back an expression, an object that represents an action that can be performed by R. (Confusingly the expression() function produces expression lists, but since you'll never need to use that function we can safely ignore it).

An expression is also called an abstract syntax tree (AST) because it represents the abstruct structure of the code in a tree form. We can use pryr::call_tree() to see the hierarchy more clearly:

library(pryr)
call_tree(z)

There are three basic things you'll commonly see in a call tree: constants, names and calls.

• constants are atomic vectors, like "a" or 10. These appear as is.

  call_tree(quote("a"))
  call_tree(quote(1))
  call_tree(quote(1L))
  call_tree(quote(TRUE))

• names which represent the name of a variable, not its value. (Names are also sometimes called symbols). These are prefixed with '

  call_tree(quote(x))
  call_tree(quote(mean))
  call_tree(quote(`an unusual name`))

• calls represent the action of calling a function, not its result. These are suffixed with (). The arguments to the function are listed below it, and can be constants, names or other calls.

  call_tree(quote(f()))
  call_tree(quote(f(1, 2)))
  call_tree(quote(f(a, b)))
  call_tree(quote(f(g(), h(1, a))))

  As mentioned in Functions, even things that don't look like function calls still follow this same hierarchical structre:

  call_tree(quote(a + b))
  call_tree(quote(if (x > 1) x else 1/x))
  call_tree(quote(function(x, y) {x * y}))

(In general, it's possible for any type of R object to live in a call tree, but these are the only three types you'll get from parsing R code. It's possible to put anything else inside an expression using the tools described below, but while technically correct, support is often patchy.)

Together, names and calls are sometimes called language objects, and can be tested for with is.language(). Note that str() is somewhat inconsistent with respect to this naming convention, describing names as symbols, and calls as a language objects:

str(quote(a))
str(quote(a + b))

Together, constants, names and calls define the structure of all R code. The following section provides more detail about each in turn.

Constants

Quoting a single atomic vector gives it back to you:

is.atomic(quote(1))
identical(1, quote(1))
is.atomic(quote("test"))
identical("test", quote("test"))

But quoting a vector of values gives you something different because you always use a function to create a vector:

identical(1:3, quote(1:3))
identical(c(FALSE, TRUE), quote(c(FALSE, TRUE)))

It's possible to use substitute() to directly insert a vector into a call tree, but use this with caution as you are creating a call that is not be generated during the normal operation of R.

y <- substitute(f(x), list(x = 1:3))
is.atomic(y)

Names

As well as capturing names with quote(), it's also possible to convert strings to names. This is mostly useful your function recieves strings as input, as it's more typing than using quote():

as.name("name")
identical(quote(name), as.name("name"))

as.name("a b")

Note that the second example produces the name a + b : the backticks are the standard way of escape non-standard names in R. (And are explained more in Functions)

There's one special name that needs a little extra discussion: the name that represents missing values. You can get this from the formals of a function, or with alist():

formals(plot)$x
alist(x =)[[1]]

It is basically a special name, that you can create by using quote() in a slightly unusual way:

quote(expr =)

Note that this object is behaves strangely, and is rarely useful, except when (as we'll see later) you want to try a function with arguments that don't have defaults.

x <- quote(expr =)
x

Calls

As well as capturing complete calls using quote(), modifing existing calls using substitute() you can also create calls from their constituent pieces using using as.call() or call().

The first argument to call() is a string giving a function name, and the other arguments should be expressions that are used as the arguments to the call.

call(":", 1, 10)
call("mean", 1:10, na.rm = TRUE)

as.call() is a minor variation takes a list where the first argument is the name of a function (not a string), and the subsequent values are the arguments.

mean_call <- as.call(list(quote(mean), x_call))
identical(mean_call, quote(mean(1:10)))

Note that the following two calls look the same, but are actually different:

(a <- call("mean", 1:10))
(b <- call("mean", quote(1:10)))
identical(a, b)
call_tree(a)
call_tree(b)

In a, the first argument to mean is a integer vector containing the numbers 1 to 10, and in b the first argument is a call to :. You can put any R object into a expression, but the printing of expression objects will not always show the difference.

The key difference is where/when evaluation occurs:

a <- call("print", Sys.time())
b <- call("print", quote(Sys.time()))
eval(a); Sys.sleep(1); eval(a)
eval(b); Sys.sleep(1); eval(b)

The first element of a call doesn't have to be the name of a function, and instead can be a call that generates a function:

(function(x) x + 1)(10))
add <- function(y) function(x) x + y
add(1)(10)

# Note that you can't create this sort of call with call
call("add(1)", 10)
# But you can with as.call
as.call(list(quote(add(1)), 10))

An interesting use of call()

One interesting use of call lies inside the mode<- function which is an alternative way to change the mode of a vector. The important part of the function is extracted in to the mode2<- function below.

`mode2<-` <- function (x, value) {
  mde <- paste0("as.", value)
  eval(call(mde, x), parent.frame())
}
x <- 1:10
mode2(x) <- "character"
x

Another way to achieve the same goal would be find the function and then call it:

`mode3<-` <- function(x, value) {
  mde <- match.fun(paste0("as.", value))
  mde(x)
}
x <- 1:10
mode3(x) <- "character"
x

Generally, I'd prefer mode3<- over mode2<- because it uses concepts familiar to more R programmers, and generally it's a good idea to use the simplest and most commonly understand techniques that solve a given problem.

Extracting elements of a call

When it comes to extracting pieces from calls or for putting new pieces in, they behave almost the same way as a list: a call has length, '[[ and [ methods. The length of a call minus 1 gives the number of arguments:

x <- quote(read.csv("important.csv", row.names = FALSE))
length(x) - 1

The first element of the call is the name of the function:

x[[1]]
# read.csv

The remaining elements are the arguments to the function, which can be extracted by name or by position.

x$row.names
x[[3]]

names(x)

Standardising function calls

Generally, extracting arguments by position is dangerous, because R's function calling semantics are so flexible. It's better to match by name, but all arguments might not be named. The solution to this problem is to use match.call(), which takes a function and a call as arguments:

y <- match.call(read.csv, x)
names(y)
# Or if you don't know in advance what the function is
match.call(eval(x[[1]]), x)
# read.csv(file = x, header = "important.csv", row.names = FALSE)

As we mentionIf you provide call and definition arguments to match.call() you can use it as a general tool for standardising function calls:

call <- quote(mean(n = 5, x = 1:10))
match.call(call = call, def = mean)
match.call(call = call, def = mean.default)

This will be an important tool when we start manipulating existing function calls. If we don't use match.call we'll need a lot of extra code to deal with all the possible ways to call a function.

We can wrap this up into a function. To figure out the definition of the associated function we evaluate the first component of the call, the name of the function. We need to specify an environment here, because the function might be different in different places. Whenever we provide an environment parameter, parent.frame() is usually a good default. Note the check for primitive functions: they don't have formals() and handle argument matching specially, so there's nothing we can do.

standardise_call <- function(call, env = parent.frame()) {
  stopifnot(is.call(call))
  f <- eval(call[[1]], env)
  if (is.primitive(f)) return(call)

  match.call(f, call)
}
standardise_call(call)

standardise_call(quote(f(d = 2, 2)))

Modifying a call

You can add, modify and delete elements of the call with the standard replacement operators, $<- and [[<-:

y$row.names <- TRUE
y$col.names <- FALSE
y

y[[2]] <- "less-important.csv"
y[[4]] <- NULL
y

y$file <- quote(paste0(filename, ".csv"))
y

Calls also support the [ method, but use it with care: it produces a call object, and it's easy to produce invalid calls since the first element of a call is the function to be called. Be careful not to remove the first element: you're unlikely to get a call that will evaluate without error.

x[-3] # remove the second argument
x[-1] # remove the function name - but it's still a call!
x

If you want to get a list of the unevaluated arguments, explicitly convert it to a list:

# A list of the unevaluated arguments
as.list(x[-1])

A cautionary tale: write.csv

write.csv() is a base R function where call manipulation is used in a suboptimal manner. It captures the call to write.csv() and mangles it to instead call write.table():

write.csv <- function (...) {
  Call <- match.call(expand.dots = TRUE)
  for (argname in c("append", "col.names", "sep", "dec", "qmethod")) {
    if (!is.null(Call[[argname]])) {
      warning(gettextf("attempt to set '%s' ignored", argname), domain = NA)
    }
  }
  rn <- eval.parent(Call$row.names)
  Call$append <- NULL
  Call$col.names <- if (is.logical(rn) && !rn) TRUE else NA
  Call$sep <- ","
  Call$dec <- "."
  Call$qmethod <- "double"
  Call[[1L]] <- as.name("write.table")
  eval.parent(Call)
}

We could write a function that behaves identically using regular function call semantics:

write.csv <- function(x, file = "", sep = ",", qmethod = "double", ...) {
  write.table(x = x, file = file, sep = sep, qmethod = qmethod, ...)
}

This makes the function much easier to understand: it's just calling write.table with different defaults. This also fixes a subtle bug in the original write.csv: write.csv(mtcars, row = FALSE) raises an error, but write.csv(mtcars, row.names = FALSE) does not. There's also no reason that write.csv shouldn't accept the append argument. Generally, you always want to use the simplest tool that will solve a problem - that makes it more likely that others will understand your code. Again, there's no point in using non-standard evaluation unless there's a big win: non-standard evaluation will make your function behave much less predictably.

Parsing and deparsing

You can convert quoted calls back and forth between text with parse() and deparse(). You've seen deparse() already it: takes an epxression and returns a character vector. parse() does the opposite: it takes a character vector and returns a list of expressions, also known as an expression object or expression list.

Note that because the primary use of parse() is parsing files of code on disk, the first argument is a file path, and if you have the code in a character vector, you need to use the text argument.

z <- quote(y <- x * 10)
deparse(z)

parse(text = deparse(z))

deparse() returns a character vector with an entry for each line, and by default it will try to make lines that are around 60 characters long. If you want a single string be sure to paste() it back together, and read the other options in the documentation.

parse() can't return just a single expression, because there might be many top-level calls in an file. So instead it returns expression objects, or expression lists. You should never need to create expression objects yourself, and all you need to know about them is that they're a list of calls:

exp <- parse(text = c("x <- 4\ny <- x * 10"))
length(exp)
exp[[1]]
is.call(exp[[1]])
call_tree(exp)

It's not possible for parse() and deparse() be completely symmetric. See the help for deparse() for more details.

Sourcing files from disk

With parse() and eval() you can write your own simple version of source(). We read in the file on disk, parse() it and then eval() each component in the specified environment. This version defaults to a new environment, so it doesn't affect existing objects. source() invisibly returns the result of the last expression in the file, so simple_source() does the same.

simple_source <- function(file, envir = new.env()) {
  stopifnot(file.exists(file))
  stopifnot(is.environment(envir))

  lines <- readLines(file, warn = FALSE)
  exprs <- parse(text = lines, n = -1)

  n <- length(exprs)
  if (n == 0L) return(invisible())

  for (i in seq_len(n - 1)) {
    eval(exprs[i], envir)
  }
  invisible(eval(exprs[n], envir))
}

The real source() is considerably more complicated because it preserves the underlying source course, can echo input and output, and has many additional settings to control behaviour.

Capturing the current call

You may want to capture the expression that caused the current function to be run. There are two ways to do this:

• sys.call() captures exactly what the user typed

• match.call() uses R's regular argument matching rules and converts everything to full name matching. This is usually easier to work with because you know that the call will always have the same structure.

The following example illustrates the difference:

f <- function(abc = 1, def = 2, ghi = 3, ...) {
  list(sys = sys.call(), match = match.call())
}
f(d = 2, 2)

Getting the name of an argument

fname <- function(call) {
  f <- eval(call, parent.frame())
  if (is.character(f)) {
    fname <- f
    f <- match.fun(f)
  } else if (is.function(f)) {
    fname <- if (is.name(call)) as.character(call) else "<anonymous>"
  }
  list(f, fname)
}
f <- function(f) {
  fname(substitute(f))
}
f("mean")
f(mean)
f(function(x) mean(x))

Creating a function

str(quote(function(x, y = 1) x + y)[[2]])

Building up a function by hand is also useful when you can't use a closure because you don't know in advance what the arguments will be. We'll use pryr::make_function to build up a function from its components pieces: an argument list, a quoted body (the code to run) and the environment in which it is defined (which defaults to the current environment):

add <- make_function(alist(a = 1, b = 2), quote(a + b))

Note that to use this function we need to use the special alist function to create an argument list.

add2 <- make_function(alist(a = 1, b = a), quote(a + b))
add(1)
add(1, 2)

add3 <- make_function(alist(a = , b = ), quote(a + b))

We could use make_function to create an unenclose function that takes a closure and modifies it so when you look at the source you can see what's going on:

unenclose <- function(f) {
  stopifnot(is.function(f))
  env <- environment(f)

  make_function(formals(f), substitute2(body(f), env), parent.env(env))
}

f <- function(x) {
  function(y) { 
    x + y
  }
}
f(1)
unenclose(f(1))

(Note we need to use substitute2 here, because substitute uses non-standard evaluation).

(Exercise: modify this function so it only substitutes in atomic vectors, not more complicated objects.)

Look at the source code for partial.

Find assignment

The key to any function that works with the parse tree right is getting the recursion right, which means making sure that you know what the base case is (the leaves of the tree) and figuring out how to combine the results from the recursive case.

The nodes of the tree can be any recursive data structure that can appear in a quoted object: pairlists, calls, and expressions. The leaves can be 0-argument calls (e.g. f()), atomic vectors, names or NULL. The easiest way to tell the difference is the is.recursive function.

In this section, we will write a function that figures out all variables that are created by assignment in an expression. We'll start simply, and make the function progressively more rigorous. One reason to start with this function is because the recursion is a little bit simpler - we never need to go all the way down to the leaves because we are looking for assignment, a call to <-.

This means that our base case is simple: if we're at a leaf, we've gone too far and can immediately return. We have two other cases: we have hit a call, in which case we should check if it's <-, otherwise it's some other recursive structure and we should call the function recursively on each element. Note the use of identical to compare the call to the name of the assignment function, and recall that the second element of a call object is the first argument, which for <- is the left hand side: the object being assigned to.

is_call_to <- function(x, name) {
  is.call(x) && identical(x[[1]], as.name(name))
}

find_assign <- function(obj) {
  # Base case
  if (!is.recursive(obj)) return(character())

  if (is_call_to(obj, "<-")) {
    obj[[2]]
  } else {
    lapply(obj, find_assign)
  }
}
find_assign(quote(a <- 1))
find_assign(quote({
  a <- 1
  b <- 2
}))

This function seems to work for these simple cases, but it's a bit verbose. Instead of returning a list, let's keep it simple and stick with a character vector. We'll also test it with two slightly more complicated examples:

find_assign <- function(obj) {
  # Base case
  if (!is.recursive(obj)) return(character())

  if (is_call_to(obj, "<-")) {
    as.character(obj[[2]])
  } else {
    unlist(lapply(obj, find_assign))
  }
}
find_assign(quote({
  a <- 1
  b <- 2
  a <- 3
}))
# [1] "a" "b" "a"
find_assign(quote({
  system.time(x <- print(y <- 5))
}))
# [1] "x"

This is better, but we have two problems: repeated names, and we miss assignments inside function calls. The fix for the first problem is easy: we need to wrap unique around the recursive case to remove duplicate assignments. The second problem is a bit more subtle: it's possible to do assignment within the arguments to a call, but we're failing to recurse down in to this case.

find_assign <- function(obj) {
  # Base case
  if (!is.recursive(obj)) return(character())

  if (is_call_to(obj, "<-")) {
    call <- as.character(obj[[2]])
    c(call, unlist(lapply(obj[[3]], find_assign)))
  } else {
    unique(unlist(lapply(obj, find_assign)))
  }
}
find_assign(quote({
  a <- 1
  b <- 2
  a <- 3
}))
# [1] "a" "b"
find_assign(quote({
  system.time(x <- print(y <- 5))
}))
# [1] "x" "y"

There's one more case we need to test:

find_assign(quote({
  ls <- list()
  ls$a <- 5
  names(ls) <- "b"
}))
# [1] "ls"        "ls$a"      "names(ls)"
draw_tree(quote({
  ls <- list()
  ls$a <- 5
  names(ls) <- "b"
}))
# \- {()
#    \- <-()
#       \- ls
#       \- list()
#    \- <-()
#       \- $()
#          \- ls
#          \- a
#       \- 5
#    \- <-()
#       \- names()
#          \- ls
#       \- "b"

This behaviour might be ok, but we probably just want assignment into whole objects, not assignment that modifies some property of the object. Drawing the tree for that quoted object helps us see what condition we should test for - we want the object on the left hand side of assignment to be a name. This gives the final version of the find_assign function.

find_assign <- function(obj) {
  # Base case
  if (!is.recursive(obj)) return(character())

  if (is_call_to(obj, "<-")) {
    call <- if (is.name(obj[[2]])) as.character(obj[[2]])
    c(call, unlist(lapply(obj[[3]], find_assign)))
  } else {
    unique(unlist(lapply(obj, find_assign)))
  }
}
find_assign(quote({
  ls <- list()
  ls$a <- 5
  names(ls) <- "b"
}))
[1] "ls"

Making this function work absolutely correct requires quite a lot more work, because we need to figure out all the other ways that assignment might happen: with =, assign, or delayedAssign.

Modifying the call tree

Differences with macros: occurs at runtime, not compile time (which doesn't have any meaning in R). Returns results, not expression. More like fexprs. a fexpr is like a function where the arguments aren't evaluated by default; or a macro where the result is a value, not code.

A more useful function might solve a common problem encountered when running R CMD check: you've used T and F instead of TRUE and FALSE. Again, we'll pursue the same strategy of starting simple and then gradually building up our function to deal with more cases.

First we'll start just by locating logical abbreviations. A logical abbreviation is the name T or F. We need to recursively breakup any recursive objects, anything else is not a short cut.

find_logical_abbr <- function(obj) {
  if (!is.recursive(obj)) {
    identical(obj, as.name("T")) || identical(obj, as.name("F"))
  } else {
    any(vapply(obj, find_logical_abbr, logical(1)))
  }
}


f <- function(x = T) 1
g <- function(x = 1) 2
h <- function(x = 3) T

find_logical_abbr(body(f))
find_logical_abbr(formals(f))
find_logical_abbr(body(g))
find_logical_abbr(formals(g))
find_logical_abbr(body(h))
find_logical_abbr(formals(h))

To replace T with TRUE and F with FALSE, we need to make our recursive function return either the original object or the modified object, making sure to put calls back together appropriately. The main difference here is that we need to be much more careful with recursive objects, because each type needs to be treated differently:

• pairlists, which are used for function formals, can be processed as lists, but need to be turned back into pairlists with as.pairlist

• expressions, again can be processed like lists, but need to be turned back into expressions objects with as.expression. You won't find these inside a quoted object, but this might be the quoted object that you're passing in.

• calls require the most special treatment: don't process first element (that's the name of the function), and turn back into a call with as.call

We'll wrap this behaviour up into a function

capply <- function(X, FUN, ...) {
  if (is.call(X)) {
    args <- lapply(X[-1], FUN, ...)
    as.call(c(list(X[[1]]), args))
  } else {
    out <- lapply(X, FUN, ...)

    if (is.function(X)) {
      out <- as.function(out, environment(X))
    } else {
      mode(out) <- mode(X)
    }
    out
  }
}
capply(expression(1, 2, 3), identity)
capply(quote(f(1, 2, 3)), identity)
capply(formals(data.frame), identity)
capply(quote(function(x) x + 1), identity)

This leads to:

fix_logical_abbr <- function(obj) {
  # Base case
  if (!is.recursive(obj)) {
    if (identical(obj, as.name("T"))) return(TRUE)
    if (identical(obj, as.name("F"))) return(FALSE)
    return(obj)
  }

  capply(obj, fix_logical_abbr)
}

However, this function is still not that useful because it loses all non-code structure:

g <- parse(text = "f <- function(x = T) {
  # This is a comment
  if (x)                  return(4)
  if (emergency_status()) return(T)
}")
f <- function(x = T) {
  # This is a comment
  if (x)                  return(4)
  if (emergency_status()) return(T)
}
fix_logical_abbr(g)
fix_logical_abbr(f)

It is possible to work around this problem using srcrefs and getParseData, but neither solution naturally fits this hierarchical framework. You effectively end up having to recreate huge chunks of R's internal code in order to handle the majority of R code. So the above approach can be useful in simple cases (particularly when you don't care what the output code looks like), but it's very hard to automatically transform R code, and is hence beyond the scope of this book.

Flexible quoting and unquoting

bquote() is a slightly more general form of quote: it allows you to optionally quote and unquote some parts of an expression (it's similar to the backtick operator in lisp). Everything is quoted, unless it's encapsulated in .() in which case it's evaluated and the result is inserted.

a <- 1
b <- 3
bquote(a + b)
bquote(a + .(b))
bquote(.(a) + .(b))
bquote(.(a + b))

This provides a fairly easy way to control what gets evaluated when you call bquote(), and what gets evaluated when the expression is evaluated.

How does bquote() work?

bquote2 <- function (expr, where = parent.frame()) {
    unquote <- function(e) {
      if (is.pairlist(e)) {
        cat("pl")
        as.pairlist(lapply(e, unquote))
      } else if (length(e) <= 1L) {
        e
      } else if (e[[1L]] == as.name(".")) {
        eval(e[[2L]], where)
      } else {
        as.call(lapply(e, unquote))
      } 
    }
    
    unquote(substitute(expr))
}

Formulas

There is one other approach we could use: a formula. ~ works much like quote, but it also captures the environment in which it is created. We need to extract the second component of the formula because the first component is ~.

subset <- function(x, f) {
  r <- eval(f[[2]], x, environment(f))
  x[r, ]
}
subset(mtcars, ~ cyl == x)

Exercises

• Read the source code for pryr::partial and refer to XXX for uses. How does it work?