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<title>Operator Overloading in R: Define Custom +, -, ==, [ & print Methods</title>
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<h1>Operator Overloading in R: Define Custom +, -, ==, [ & print Methods</h1>
<p class="lead">R lets you define what <code>+</code>, <code>-</code>, <code>==</code>, <code>[</code>, and other operators do for your custom classes. This is called <strong>operator overloading</strong>. Both S3 and S4 support it, and it's how base R makes <code>+</code> work differently for numbers, dates, and strings.</p>
<p>When you type <code>Sys.Date() + 1</code>, R doesn't use the same <code>+</code> as <code>2 + 3</code>. It dispatches to a method specialized for Date objects. You can define the same behavior for your own classes.</p>
<h2>S3 Operator Overloading Basics</h2>
<p>In S3, operators are generic functions. Define a method named <code>operator.ClassName</code> to overload it.</p>
<div class="webr-container">
<div class="webr-code-block">
<div class="webr-editor" data-language="r"># A simple 2D point class
Point <- function(x, y) {
structure(list(x = x, y = y), class = "Point")
}
print.Point <- function(p, ...) {
cat("(", p$x, ",", p$y, ")\n")
}
# Overload + for Point
`+.Point` <- function(e1, e2) {
if (inherits(e2, "Point")) {
Point(e1$x + e2$x, e1$y + e2$y)
} else if (is.numeric(e2)) {
Point(e1$x + e2, e1$y + e2)
} else {
stop("Cannot add Point and ", class(e2))
}
}
# Overload - for Point
`-.Point` <- function(e1, e2) {
if (missing(e2)) {
Point(-e1$x, -e1$y) # Unary minus
} else if (inherits(e2, "Point")) {
Point(e1$x - e2$x, e1$y - e2$y)
} else {
stop("Cannot subtract")
}
}
# Overload == for Point
`==.Point` <- function(e1, e2) {
e1$x == e2$x && e1$y == e2$y
}
a <- Point(3, 4)
b <- Point(1, 2)
print(a)
print(a + b) # Point + Point
print(a + 10) # Point + scalar
print(a - b) # Point - Point
print(-a) # Unary minus
cat("a == b:", a == b, "\n")
cat("a == a:", a == Point(3, 4), "\n")</div>
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<h2>The Ops Group Generic</h2>
<p>Instead of defining <code>+.MyClass</code>, <code>-.MyClass</code>, <code>*.MyClass</code> separately, you can define <code>Ops.MyClass</code> to handle all arithmetic and comparison operators at once.</p>
<div class="webr-container">
<div class="webr-code-block">
<div class="webr-editor" data-language="r"># A Money class using the Ops group generic
Money <- function(amount, currency = "USD") {
structure(list(amount = amount, currency = currency), class = "Money")
}
print.Money <- function(x, ...) {
cat(x$currency, formatC(x$amount, format = "f", digits = 2), "\n")
}
Ops.Money <- function(e1, e2) {
# .Generic holds the operator being used
op <- .Generic
# Extract amounts
a1 <- if (inherits(e1, "Money")) e1$amount else e1
a2 <- if (inherits(e2, "Money")) e2$amount else e2
# Get currency (from whichever is Money)
curr <- if (inherits(e1, "Money")) e1$currency else e2$currency
# Check currency match for two Money objects
if (inherits(e1, "Money") && inherits(e2, "Money")) {
if (e1$currency != e2$currency) stop("Currency mismatch")
}
# Compute result
result <- switch(op,
"+" = a1 + a2,
"-" = a1 - a2,
"*" = a1 * a2,
"/" = a1 / a2,
"==" = a1 == a2,
"!=" = a1 != a2,
"<" = a1 < a2,
"<=" = a1 <= a2,
">" = a1 > a2,
">=" = a1 >= a2,
stop("Operator ", op, " not supported for Money")
)
# Comparisons return logical; arithmetic returns Money
if (op %in% c("==", "!=", "<", "<=", ">", ">=")) {
return(result)
}
Money(result, curr)
}
price <- Money(29.99)
tax <- Money(2.40)
print(price + tax)
print(price * 3)
cat("price > tax:", price > tax, "\n")
cat("price == price:", price == Money(29.99), "\n")</div>
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<h2>Overloading [ and [[</h2>
<p>The subset operators <code>[</code> and <code>[[</code> are internal generics. You can define methods for them.</p>
<div class="webr-container">
<div class="webr-code-block">
<div class="webr-editor" data-language="r"># A named collection class
Collection <- function(...) {
items <- list(...)
structure(items, class = "Collection")
}
print.Collection <- function(x, ...) {
cat("Collection with", length(x), "items:\n")
for (i in seq_along(x)) {
name <- names(x)[i]
if (is.null(name) || name == "") name <- paste0("[", i, "]")
cat(" ", name, ":", x[[i]], "\n")
}
}
# Override [ to return a Collection (not a plain list)
`[.Collection` <- function(x, i) {
result <- unclass(x)[i]
structure(result, class = "Collection")
}
# Override [[ for single element access
`[[.Collection` <- function(x, i) {
unclass(x)[[i]]
}
# Override length
length.Collection <- function(x) {
length(unclass(x))
}
coll <- Collection(a = 10, b = 20, c = 30, d = 40)
print(coll)
cat("\nSubset [2:3]:\n")
print(coll[2:3])
cat("\nElement [[1]]:", coll[[1]], "\n")</div>
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<h2>Overloading print, summary, and format</h2>
<p>These are the most commonly overloaded generics. Every class should have at least a <code>print</code> method.</p>
<div class="webr-container">
<div class="webr-code-block">
<div class="webr-editor" data-language="r"># A regression result class
RegResult <- function(formula, r_squared, coefficients) {
structure(
list(formula = formula, r_squared = r_squared, coefficients = coefficients),
class = "RegResult"
)
}
print.RegResult <- function(x, ...) {
cat("Linear Regression:", deparse(x$formula), "\n")
cat("R-squared:", round(x$r_squared, 4), "\n")
}
summary.RegResult <- function(object, ...) {
cat("=== Regression Summary ===\n")
cat("Formula:", deparse(object$formula), "\n")
cat("R-squared:", round(object$r_squared, 4), "\n")
cat("Coefficients:\n")
for (nm in names(object$coefficients)) {
cat(" ", nm, "=", round(object$coefficients[[nm]], 4), "\n")
}
}
format.RegResult <- function(x, ...) {
paste0("RegResult(R2=", round(x$r_squared, 3), ")")
}
# Use it
fit <- lm(mpg ~ wt + hp, data = mtcars)
result <- RegResult(
formula = mpg ~ wt + hp,
r_squared = summary(fit)$r.squared,
coefficients = as.list(coef(fit))
)
print(result)
cat("\n")
summary(result)
cat("\nFormatted:", format(result), "\n")</div>
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<h2>S4 Operator Overloading</h2>
<p>S4 uses <code>setMethod()</code> for operators. The approach is more formal but the result is the same.</p>
<div class="webr-container">
<div class="webr-code-block">
<div class="webr-editor" data-language="r">setClass("Fraction",
slots = list(num = "integer", den = "integer"),
validity = function(object) {
if (object@den == 0L) "denominator cannot be zero"
else TRUE
}
)
Fraction <- function(num, den) {
new("Fraction", num = as.integer(num), den = as.integer(den))
}
setMethod("show", "Fraction", function(object) {
cat(object@num, "/", object@den, "\n")
})
setMethod("+", signature("Fraction", "Fraction"), function(e1, e2) {
new_num <- e1@num * e2@den + e2@num * e1@den
new_den <- e1@den * e2@den
Fraction(new_num, new_den)
})
setMethod("*", signature("Fraction", "Fraction"), function(e1, e2) {
Fraction(e1@num * e2@num, e1@den * e2@den)
})
setMethod("==", signature("Fraction", "Fraction"), function(e1, e2) {
e1@num * e2@den == e2@num * e1@den
})
a <- Fraction(1, 3)
b <- Fraction(1, 6)
cat("a: "); show(a)
cat("b: "); show(b)
cat("a + b: "); show(a + b)
cat("a * b: "); show(a * b)
cat("a == a:", a == a, "\n")</div>
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<h2>Summary Table</h2>
<table class="table table-striped">
<thead>
<tr>
<th>Operator</th>
<th>S3 Method Name</th>
<th>S4 Signature</th>
<th>Group</th>
</tr>
</thead>
<tbody>
<tr>
<td><code>+</code>, <code>-</code>, <code>*</code>, <code>/</code></td>
<td><code>+.Class</code>, etc.</td>
<td><code>setMethod("+", ...)</code></td>
<td>Ops</td>
</tr>
<tr>
<td><code>==</code>, <code>!=</code>, <code><</code>, <code>></code></td>
<td><code>==.Class</code>, etc.</td>
<td><code>setMethod("==", ...)</code></td>
<td>Ops</td>
</tr>
<tr>
<td><code>[</code></td>
<td><code>[.Class</code></td>
<td><code>setMethod("[", ...)</code></td>
<td>N/A (internal)</td>
</tr>
<tr>
<td><code>[[</code></td>
<td><code>[[.Class</code></td>
<td><code>setMethod("[[", ...)</code></td>
<td>N/A (internal)</td>
</tr>
<tr>
<td><code>$</code></td>
<td><code>$.Class</code></td>
<td><code>setMethod("$", ...)</code></td>
<td>N/A (internal)</td>
</tr>
<tr>
<td><code>print</code></td>
<td><code>print.Class</code></td>
<td><code>setMethod("show", ...)</code></td>
<td>N/A</td>
</tr>
<tr>
<td><code>summary</code></td>
<td><code>summary.Class</code></td>
<td><code>setMethod("summary", ...)</code></td>
<td>N/A</td>
</tr>
<tr>
<td><code>format</code></td>
<td><code>format.Class</code></td>
<td><code>setMethod("format", ...)</code></td>
<td>N/A</td>
</tr>
<tr>
<td><code>abs</code>, <code>sqrt</code>, <code>log</code></td>
<td><code>Math.Class</code> (group)</td>
<td><code>setMethod("Math", ...)</code></td>
<td>Math</td>
</tr>
</tbody>
</table>
<h2>Practice Exercises</h2>
<p><strong>Exercise 1:</strong> Create a <code>Percentage</code> class where <code>Percentage(50) + Percentage(30)</code> returns <code>Percentage(80)</code>, <code>print</code> shows <code>"50%"</code>, and <code>as.numeric</code> returns <code>0.5</code>.</p>
<details><summary>Click to reveal solution</summary>
```r
<div class="webr-container">
<div class="webr-code-block">
<div class="webr-editor" data-language="r">Percentage <- function(x) {
structure(list(value = x), class = "Percentage")
}
print.Percentage <- function(x, ...) cat(x$value, "%\n")
as.numeric.Percentage <- function(x, ...) x$value / 100
`+.Percentage` <- function(e1, e2) {
v1 <- if (inherits(e1, "Percentage")) e1$value else e1
v2 <- if (inherits(e2, "Percentage")) e2$value else e2
Percentage(v1 + v2)
}
print(Percentage(50) + Percentage(30))
cat("As numeric:", as.numeric(Percentage(50)), "\n")</div>
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</details>
<p><strong>Exercise 2:</strong> Create a <code>Matrix2x2</code> class with overloaded <code>*</code> for matrix multiplication and <code>print</code> for formatted display.</p>
<details><summary>Click to reveal solution</summary>
```r
<div class="webr-container">
<div class="webr-code-block">
<div class="webr-editor" data-language="r">Matrix2x2 <- function(a, b, c, d) {
structure(list(data = matrix(c(a, c, b, d), 2, 2)), class = "Matrix2x2")
}
print.Matrix2x2 <- function(x, ...) {
cat("| ", x$data[1,1], x$data[1,2], "|\n")
cat("| ", x$data[2,1], x$data[2,2], "|\n")
}
`*.Matrix2x2` <- function(e1, e2) {
r <- e1$data %*% e2$data
Matrix2x2(r[1,1], r[1,2], r[2,1], r[2,2])
}
A <- Matrix2x2(1, 2, 3, 4)
B <- Matrix2x2(5, 6, 7, 8)
cat("A:\n"); print(A)
cat("B:\n"); print(B)
cat("A * B:\n"); print(A * B)</div>
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</details>
<h2>FAQ</h2>
<p><strong>Q: Which operators can I overload in R?</strong> Almost all of them: arithmetic (<code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>, <code>^</code>, <code>%%</code>, <code>%/%</code>), comparison (<code>==</code>, <code>!=</code>, <code><</code>, <code>></code>, <code><=</code>, <code>>=</code>), logical (<code>&</code>, <code>|</code>, <code>!</code>), subsetting (<code>[</code>, <code>[[</code>, <code>$</code>), and display (<code>print</code>, <code>format</code>, <code>summary</code>). You can also define custom infix operators like <code>%between%</code>.</p>
<p><strong>Q: What happens when the left operand is not my class (e.g., 5 + MyObj)?</strong> For S3, R checks the class of both operands. If neither has a method, it falls back to the default. In your Ops method, use <code>.Generic</code> and check which argument has your class.</p>
<p><strong>Q: Should I use Ops group generic or individual operator methods?</strong> Use the Ops group generic when the logic is similar for all operators (e.g., extract values, apply operator, wrap result). Use individual methods when different operators need very different logic.</p>
<h2>What's Next</h2>
<ul>
<li><a href="S3-Method-Dispatch-in-R.html">S3 Method Dispatch in R</a> -- Understand the dispatch mechanism behind operator methods</li>
<li><a href="S4-Methods-in-R.html">S4 Methods & Multiple Dispatch</a> -- Formal operator overloading with S4</li>
<li><a href="OOP-in-R.html">OOP in R Overview</a> -- Compare all four OOP systems</li>
</ul>
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