In programming languages, we find logical operators for and and or. In fact, Python uses the actual words and and or for these operators.

# Python via the reticulate package
x = True
y = False
x and y
#> False
x or y
#> True

In Javascript, we see && for and and || for or instead.

// Javascript via `engine = "node"` in knitr
let x = true;
let y = false;
console.log(x && y);
console.log(x || y);
// false
// true

In R, we have two versions of logical and (& and &&) and logical or (| and ||). What’s going on?

Documentation in help("Logic", package = "base") provides the following:

& and && indicate logical AND and | and || indicate logical OR. The shorter form performs elementwise comparisons in much the same way as arithmetic operators. The longer form evaluates left to right examining only the first element of each vector. Evaluation proceeds only until the result is determined. The longer form is appropriate for programming control-flow and typically preferred in if clauses.

Let’s unpack this paragraph

The shorter operators are vectorized

The crucial difference is that the shorter versions (&, |) are vectorized. Given two vectors, they will apply logical and/or on pairs of elements from each vector. In the example below, ttff[1] is and-ed with tftf[1], ttff[2] is and-ed with tftf[2], and so on. This vectorization is a pretty important feature, for example, when we are comparing columns in a dataframe in order to filter rows.

# Returns something of length four
ttff <- c(TRUE,  TRUE, FALSE, FALSE)
tftf <- c(TRUE, FALSE,  TRUE, FALSE)
ttff & tftf
#> [1]  TRUE FALSE FALSE FALSE
ttff | tftf
#> [1]  TRUE  TRUE  TRUE FALSE

In contrast, && and || only work on scalars (length-one values). They return just one element. In this example, they look at ttff[1] and tftf[1].

# Returns something of length one
ttff && tftf
#> [1] TRUE
ttff || tftf
#> [1] TRUE

To help remember the distinction, think of the longer versions (&&, ||) as stricter forms of the logical operators. They don’t just care about truthiness or falsiness, but they also care about length. The extra and/or characters are there because the operators are extra, if you will.

Okay, that was the point of this post: to describe the difference between the short and long operators and introduce the intuition that the longer forms are stricter. The rest of this post will dig into some other oddities and notes about and and or.

Short circuit evaluation

You may have noticed a strange or unclear detail in the documentation.

The longer form evaluates left to right examining only the first element of each vector. Evaluation proceeds only until the result is determined.

This part is describing the semantics of short-circuit evaluation. Here are two facts about and and or:

• x and y is false when either x or y is false. Therefore, if x is false, we don’t need to look at y at all.
• x or y is true when either x or y is true. Therefore, if x is true, we don’t need to look at y at all.

R will not evaluate the second operand for && and || if it can learn the answer from the first operand. Thus, short-circuit evaluation will ignore the stop() calls in the examples below.

FALSE && stop("this is an error")
#> [1] FALSE
TRUE || stop("this is an error")
#> [1] TRUE

# Short-circuiting doesn't apply. Need the second operand.
TRUE && stop("this is an error")
#> Error in eval(expr, envir, enclos): this is an error
FALSE || stop("this is an error")
#> Error in eval(expr, envir, enclos): this is an error

The NULL-or-default pattern

Logically, the short-circuit evaluation for || is equivalent to a particular kind of if statement:

if_x_then_x_else_y <- function(x, y) {
  if (x) x else y 
}
if_x_then_x_else_y(TRUE, FALSE)
#> [1] TRUE
# short-circuited
if_x_then_x_else_y(TRUE, stop("this is an error"))
#> [1] TRUE

In languages that treat undefined values as falsy and defined values as truthy, this if (x) x else y behavior is sometimes used as an idiom to set a default, backup value for a variable. In the Javascript code below, the undefined variable name is treated as falsy, the string "I don't know your name" is treated as truthy, so the or returns the second string. In other words, “the first truthy value is returned”.

let name;
let fallback = name || "I don't know your name!";
console.log(name);
console.log(fallback);
// undefined
// I don't know your name!

(This pattern, incidentally, appears to have earned its own operator in Javascript with the “nullish coalescing operator” ??.)

Why do I mention this programming idiom from Javascript? Because setting a default for missing values is pretty useful, and this syntax is pretty nice. The tidyverse provides a nullish coalescing operator, inspired by Ruby’s || operator.

library(purrr)
1 %||% 2
#> [1] 1
NULL %||% 2
#> [1] 2
# Not exactly or-like. It just cares about NULL-ness.
FALSE %||% 2
#> [1] FALSE

# See the source code
`%||%`
#> function (x, y) 
#> {
#>     if (is_null(x)) 
#>         y
#>     else x
#> }
#> <bytecode: 0x000000001f08c228>
#> <environment: namespace:rlang>

if() statements want the stricter operators

Recall the following from the documentation:

The longer form is appropriate for programming control-flow and typically preferred in if clauses.

if() statements are not vectorized. (See ifelse() instead.) if() statements complain when they see a vector:

if (ttff | tftf) {
  "We are going to get a warning."  
}
#> Warning in if (ttff | tftf) {: the condition has length > 1 and only the first
#> element will be used
#> [1] "We are going to get a warning."

The idea behind the documentation is that because & and | return vectors and because if() only likes scalars, we should not use the shorter forms in if() statements. They provide the wrong output for if(). But that does not mean the following code with the stricter or operator is correct.

if (ttff || tftf) {
  "No warning but this code is not right."  
}
#> [1] "No warning but this code is not right."

Although the code here does not raise any warnings, it reduces all of the information in ttff and tftf into just ttff[1] and tftf[1]. Those values likely will not be appropriate for the programming task at hand, so we should provide the scalars ourselves.

all() and any() can apply and and or down a vector

Because I am talking about and and or and about creating logical scalars, I want to advertise two particular functions that can reduce a logical vector into a scalar. all() is TRUE when all of the elements are TRUE. For a vector, it would be like replacing the commas in c(TRUE, TRUE, FALSE) with &s. any() provides the analogous down-vector behavior for |. any() is TRUE when any of the elements in the vector are TRUE (and not NA—more on that later).

all(c(TRUE, TRUE, TRUE))
#> [1] TRUE
c(TRUE & TRUE & TRUE)
#> [1] TRUE

all(c(TRUE, FALSE, TRUE))
#> [1] FALSE
c(TRUE & FALSE & TRUE)
#> [1] FALSE

c(TRUE | FALSE | TRUE)
#> [1] TRUE

# The input can be scalars or vectors
all(TRUE, TRUE, TRUE, c(TRUE, FALSE))
#> [1] FALSE
any(FALSE, FALSE, FALSE, c(FALSE, TRUE))
#> [1] TRUE

# These appear not to short circuit
any(TRUE, stop("this is an error"))
#> Error in eval(expr, envir, enclos): this is an error
all(FALSE, stop("this is an error"))
#> Error in eval(expr, envir, enclos): this is an error

We can make the strict operators even stricter

Recall the following unsettling example where just ttff[1] and tftf[1] are considered in the if() statement.

if (ttff || tftf) {
  "No warning but this code is not right."  
}
#> [1] "No warning but this code is not right."

It would be nice to rule out this behavior outright and make this behavior illegal. In fact, we can make our code stricter by setting the system environment variable _R_CHECK_LENGTH_1_LOGIC2_. Once set, using the strict forms on inputs longer than 1 will throw an error.

Sys.setenv("_R_CHECK_LENGTH_1_LOGIC2_" = "TRUE")
ttff && tftf
#> Error in ttff && tftf: 'length(x) = 4 > 1' in coercion to 'logical(1)'
ttff || tftf
#> Error in ttff || tftf: 'length(x) = 4 > 1' in coercion to 'logical(1)'

# Default behavior
Sys.unsetenv("_R_CHECK_LENGTH_1_LOGIC2_")
ttff && tftf
#> [1] TRUE
ttff || tftf
#> [1] TRUE

A related environment variable is _R_CHECK_LENGTH_1_CONDITION_ that turn vectors inside of if() into errors instead of warnings.

Sys.setenv("_R_CHECK_LENGTH_1_CONDITION_" = "TRUE")
if (ttff | tftf) { 
  "This code will not even be seen."
}
#> Error in if (ttff | tftf) {: the condition has length > 1

# Default behavior
Sys.unsetenv("_R_CHECK_LENGTH_1_CONDITION_")
if (ttff | tftf) { 
  "We are going to get a warning."
}
#> Warning in if (ttff | tftf) {: the condition has length > 1 and only the first
#> element will be used
#> [1] "We are going to get a warning."

To make project code more robust, one might consider setting these inside of a .Renviron file or using them with dotenv. (But if I remember correctly, these checks apply to package code so you get errors for legal-but-dodgy R code in other people’s packages.)

NAs infect other values

All of the above examples conveniently avoided NAs. These are missing values that infect other logical values, turning them into NAs. For this section, I want to briefly highlight some behaviors of NAs and some functions that can help us work around them.

For and, an NA with any non-FALSE value is NA. For or, an NA with any non-TRUE value is NA. That’s a funny sentence, but it reflects the case where we can infer the answer without seeing the NA value. TRUE | NA (and NA | TRUE) returns TRUE because it would return TRUE if the NA was actually a TRUE or FALSE. The same holds for FALSE & NA (and NA & FALSE) returning FALSE. If we un-missing-ed the NA into TRUE or FALSE, the statement would still be FALSE.

tfnn <- c(TRUE, FALSE, NA, NA)
nntf <- c(NA, NA, TRUE, FALSE)
tfnn & nntf
#> [1]    NA FALSE    NA FALSE
tfnn | nntf
#> [1] TRUE   NA TRUE   NA

# Infecting in all() and any()
TRUE && NA
#> [1] NA
FALSE || NA
#> [1] NA
all(TRUE, TRUE, NA)
#> [1] NA
any(FALSE, FALSE, NA)
#> [1] NA

# These return FALSE and TRUE because they would return TRUE and FALSE
# regardless of whether the NA was a TRUE or a FALSE.
FALSE && NA
#> [1] FALSE
TRUE || NA
#> [1] TRUE
all(NA, FALSE, FALSE)
#> [1] FALSE
any(TRUE, FALSE, NA)
#> [1] TRUE

This uhh complicates things, so how do I check if what I have is TRUE or FALSE? isTRUE() and isFALSE() provide direct tests of whether the input is the scalar TRUE or the scalar FALSE.

c(isTRUE(TRUE), isTRUE(FALSE), isTRUE(NA))
#> [1]  TRUE FALSE FALSE
c(isFALSE(TRUE), isFALSE(FALSE), isFALSE(NA))
#> [1] FALSE  TRUE FALSE

The documentation notes that

if(isTRUE(cond)) may be preferable to if(cond) because of NAs

so isTRUE() is something we run into packaged code.

isTRUE() and isFALSE() are not vectorized, but we can check elements in a vector are TRUE and only TRUE in a few different ways.

# Make a new function
Vectorize(FUN = isTRUE)(tfnn)
#> [1]  TRUE FALSE FALSE FALSE

# Apply the function on a vector
vapply(X = tfnn, FUN = isTRUE, FUN.VALUE = logical(1))
#> [1]  TRUE FALSE FALSE FALSE

# Use table-lookup or set operations
tfnn %in% TRUE
#> [1]  TRUE FALSE FALSE FALSE
is.element(el = tfnn, set = TRUE)
#> [1]  TRUE FALSE FALSE FALSE

I think that’s just about every useful thing I want to say about and and or in R. But just remember, && and || are longer operators because they are stricter.

Last knitted on 2021-07-01. Source code on GitHub.¹

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