# Operators

version 2.5.2

This chapter covers the operators of the Groovy programming language.

## 1. Arithmetic operators

Groovy supports the usual familiar arithmetic operators you find in mathematics and in other programming languages like Java. All the Java arithmetic operators are supported. Let’s go through them in the following examples.

### 1.1. Normal arithmetic operators

The following binary arithmetic operators are available in Groovy:

Operator | Purpose | Remarks
--- | --- | ---
`+` | addition |
`-` | subtraction |
`*` | multiplication |
`/` | division | Use `intdiv()` for integer division, and see the section about integer division for more information on the return type of the division.
`%` | remainder |
`**` | power | See the section about the power operation for more information on the return type of the operation.

Here are a few examples of usage of those operators:

    assert  1  + 2 == 3
    assert  4  - 3 == 1
    assert  3  * 5 == 15
    assert  3  / 2 == 1.5
    assert 10  % 3 == 1
    assert  2 ** 3 == 8

### 1.2. Unary operators

The `+` and `-` operators are also available as unary operators:

    assert +3 == 3
    assert -4 == 0 - 4

    assert -(-1) == 1  (1)

1 | Note the usage of parentheses to surround an expression to apply the unary minus to that surrounded expression.

In terms of unary arithmetics operators, the `++` (increment) and `--` (decrement) operators are available, both in prefix and postfix notation:

    def a = 2
    def b = a++ * 3             (1)

    assert a == 3 && b == 6

    def c = 3
    def d = c-- * 2             (2)

    assert c == 2 && d == 6

    def e = 1
    def f = ++e + 3             (3)

    assert e == 2 && f == 5

    def g = 4
    def h = --g + 1             (4)

    assert g == 3 && h == 4

1 | The postfix increment will increment `a` after the expression has been evaluated and assigned into `b`
2 | The postfix decrement will decrement `c` after the expression has been evaluated and assigned into `d`
3 | The prefix increment will increment `e` before the expression is evaluated and assigned into `f`
4 | The prefix decrement will decrement `g` before the expression is evaluated and assigned into `h`

### 1.3. Assignment arithmetic operators

The binary arithmetic operators we have seen above are also available in an assignment form:

- `+=`

- `-=`

- `*=`

- `/=`

- `%=`

- `**=`

Let’s see them in action:

    def a = 4
    a += 3

    assert a == 7

    def b = 5
    b -= 3

    assert b == 2

    def c = 5
    c *= 3

    assert c == 15

    def d = 10
    d /= 2

    assert d == 5

    def e = 10
    e %= 3

    assert e == 1

    def f = 3
    f **= 2

    assert f == 9

## 2. Relational operators

Relational operators allow comparisons between objects, to know if two objects are the same or different, or if one is greater than, less than, or equal to the other.

The following operators are available:

Operator | Purpose
--- | ---
`==` | equal
`!=` | different
`<` | less than
`<=` | less than or equal
`>` | greater than
`>=` | greater than or equal

Here are some examples of simple number comparisons using these operators:

    assert 1 + 2 == 3
    assert 3 != 4

    assert -2 < 3
    assert 2 <= 2
    assert 3 <= 4

    assert 5 > 1
    assert 5 >= -2

## 3. Logical operators

Groovy offers three logical operators for boolean expressions:

- `&&`: logical "and"

- `||`: logical "or"

- `!`: logical "not"

Let’s illustrate them with the following examples:

    assert !false           (1)
    assert true && true     (2)
    assert true || false    (3)

1 | "not" false is true
2 | true "and" true is true
3 | true "or" false is true

### 3.1. Precedence

The logical "not" has a higher priority than the logical "and".

    assert (!false && false) == false   (1)

1 | Here, the assertion is true (as the expression in parentheses is false), because "not" has a higher precedence than "and", so it only applies to the first "false" term; otherwise, it would have applied to the result of the "and", turned it into true, and the assertion would have failed

The logical "and" has a higher priority than the logical "or".

    assert true || true && false        (1)

1 | Here, the assertion is true, because "and" has a higher precedence than "or", therefore the "or" is executed last and returns true, having one true argument; otherwise, the "and" would have executed last and returned false, having one false argument, and the assertion would have failed

### 3.2. Short-circuiting

The logical `||` operator supports short-circuiting: if the left operand is true, it knows that the result will be true in any case, so it won’t evaluate the right operand. The right operand will be evaluated only if the left operand is false.

Likewise for the logical `&&` operator: if the left operand is false, it knows that the result will be false in any case, so it won’t evaluate the right operand. The right operand will be evaluated only if the left operand is true.

    boolean checkIfCalled() {   (1)
        called = true
    }

    called = false
    true || checkIfCalled()
    assert !called              (2)

    called = false
    false || checkIfCalled()
    assert called               (3)

    called = false
    false && checkIfCalled()
    assert !called              (4)

    called = false
    true && checkIfCalled()
    assert called               (5)

1 | We create a function that sets the `called` flag to true whenever it’s called
2 | In the first case, after resetting the called flag, we confirm that if the left operand to `||` is true, the function is not called, as `||` short-circuits the evaluation of the right operand
3 | In the second case, the left operand is false and so the function is called, as indicated by the fact our flag is now true
4 | Likewise for `&&`, we confirm that the function is not called with a false left operand
5 | But the function is called with a true left operand

## 4. Bitwise operators

Groovy offers 4 bitwise operators:

- `&`: bitwise "and"

- `|`: bitwise "or"

- `^`: bitwise "xor" (exclusive "or")

- `~`: bitwise negation

Bitwise operators can be applied on a `byte` or an `int` and return an `int`:

    int a = 0b00101010
    assert a == 42
    int b = 0b00001000
    assert b == 8
    assert (a & a) == a                     (1)
    assert (a & b) == b                     (2)
    assert (a | a) == a                     (3)
    assert (a | b) == a                     (4)

    int mask = 0b11111111                   (5)
    assert ((a ^ a) & mask) == 0b00000000   (6)
    assert ((a ^ b) & mask) == 0b00100010   (7)
    assert ((~a) & mask)    == 0b11010101   (8)

1 | bitwise and
2 | bitwise and returns common bits
3 | bitwise or
4 | bitwise or returns all '1' bits
5 | setting a mask to check only the last 8 bits
6 | bitwise exclusive or on self returns 0
7 | bitwise exclusive or
8 | bitwise negation

It’s worth noting that the internal representation of primitive types follow the Java Language Specification. In particular, primitive types are signed, meaning that for a bitwise negation, it is always good to use a mask to retrieve only the necessary bits.

In Groovy, bitwise operators have the particularity of being overloadable, meaning that you can define the behavior of those operators for any kind of object.

## 5. Conditional operators

### 5.1. Not operator

The "not" operator is represented with an exclamation mark (`!`) and inverts the result of the underlying boolean expression. In particular, it is possible to combine the `not` operator with the Groovy truth:

    assert (!true)    == false                      (1)
    assert (!'foo')   == false                      (2)
    assert (!'')      == true                       (3)

1 | the negation of `true` is `false`
2 | 'foo' is a non empty string, evaluating to `true`, so negation returns `false`
3 | '' is an empty string, evaluating to `false`, so negation returns `true`

### 5.2. Ternary operator

The ternary operator is a shortcut expression that is equivalent to an if/else branch assigning some value to a variable.

Instead of:

    if (string!=null && string.length()>0) {
        result = 'Found'
    } else {
        result = 'Not found'
    }

You can write:

    result = (string!=null && string.length()>0) ? 'Found' : 'Not found'

The ternary operator is also compatible with the Groovy truth, so you can make it even simpler:

    result = string ? 'Found' : 'Not found'

### 5.3. Elvis operator

The "Elvis operator" is a shortening of the ternary operator. One instance of where this is handy is for returning a 'sensible default' value if an expression resolves to `false`-ish (as in Groovy truth). A simple example might look like this:

    displayName = user.name ? user.name : 'Anonymous'   (1)
    displayName = user.name ?: 'Anonymous'              (2)

1 | with the ternary operator, you have to repeat the value you want to assign
2 | with the Elvis operator, the value, which is tested, is used if it is not `false`-ish

Usage of the Elvis operator reduces the verbosity of your code and reduces the risks of errors in case of refactorings, by removing the need to duplicate the expression which is tested in both the condition and the positive return value.

## 6. Object operators

### 6.1. Safe navigation operator

The Safe Navigation operator is used to avoid a `NullPointerException`. Typically when you have a reference to an object you might need to verify that it is not `null` before accessing methods or properties of the object. To avoid this, the safe navigation operator will simply return `null` instead of throwing an exception, like so:

    def person = Person.find { it.id == 123 }    (1)
    def name = person?.name                      (2)
    assert name == null                          (3)

1 | `find` will return a `null` instance
2 | use of the null-safe operator prevents from a `NullPointerException`
3 | result is `null`

### 6.2. Direct field access operator

Normally in Groovy, when you write code like this:

    class User {
        public final String name                 (1)
        User(String name) { this.name = name}
        String getName() { "Name: $name" }       (2)
    }
    def user = new User('Bob')
    assert user.name == 'Name: Bob'              (3)

1 | public field `name`
2 | a getter for `name` that returns a custom string
3 | calls the getter

The `user.name` call triggers a call to the property of the same name, that is to say, here, to the getter for `name`. If you want to retrieve the field instead of calling the getter, you can use the direct field access operator:

    assert user.@name == 'Bob'                   (1)

1 | use of `.@` forces usage of the field instead of the getter

### 6.3. Method pointer operator

The method pointer operator (`.&`) call be used to store a reference to a method in a variable, in order to call it later:

    def str = 'example of method reference'            (1)
    def fun = str.&toUpperCase                         (2)
    def upper = fun()                                  (3)
    assert upper == str.toUpperCase()                  (4)

1 | the `str` variable contains a `String`
2 | we store a reference to the `toUpperCase` method on the `str` instance inside a variable named `fun`
3 | `fun` can be called like a regular method
4 | we can check that the result is the same as if we had called it directly on `str`

There are multiple advantages in using method pointers. First of all, the type of such a method pointer is a `groovy.lang.Closure`, so it can be used in any place a closure would be used. In particular, it is suitable to convert an existing method for the needs of the strategy pattern:

    def transform(List elements, Closure action) {                    (1)
        def result = []
        elements.each {
            result << action(it)
        }
        result
    }
    String describe(Person p) {                                       (2)
        "$p.name is $p.age"
    }
    def action = this.&describe                                       (3)
    def list = [
        new Person(name: 'Bob',   age: 42),
        new Person(name: 'Julia', age: 35)]                           (4)
    assert transform(list, action) == ['Bob is 42', 'Julia is 35']    (5)

1 | the `transform` method takes each element of the list and calls the `action` closure on them, returning a new list
2 | we define a function that takes a `Person` and returns a `String`
3 | we create a method pointer on that function
4 | we create the list of elements we want to collect the descriptors
5 | the method pointer can be used where a `Closure` was expected

Method pointers are bound by the receiver and a method name. Arguments are resolved at runtime, meaning that if you have multiple methods with the same name, the syntax is not different, only resolution of the appropriate method to be called will be done at runtime:

    def doSomething(String str) { str.toUpperCase() }    (1)
    def doSomething(Integer x) { 2*x }                   (2)
    def reference = this.&doSomething                    (3)
    assert reference('foo') == 'FOO'                     (4)
    assert reference(123)   == 246                       (5)

1 | define an overloaded `doSomething` method accepting a `String` as an argument
2 | define an overloaded `doSomething` method accepting an `Integer` as an argument
3 | create a single method pointer on `doSomething`, without specifying argument types
4 | using the method pointer with a `String` calls the `String` version of `doSomething`
5 | using the method pointer with an `Integer` calls the `Integer` version of `doSomething`

## 7. Regular expression operators

### 7.1. Pattern operator

The pattern operator (`~`) provides a simple way to create a `java.util.regex.Pattern` instance:

    def p = ~/foo/
    assert p instanceof Pattern

while in general, you find the pattern operator with an expression in a slashy-string, it can be used with any kind of `String` in Groovy:

    p = ~'foo'                                                        (1)
    p = ~"foo"                                                        (2)
    p = ~$/dollar/slashy $ string/$                                   (3)
    p = ~"${pattern}"                                                 (4)

1 | using single quote strings
2 | using double quotes strings
3 | the dollar-slashy string lets you use slashes and the dollar sign without having to escape them
4 | you can also use a GString!

### 7.2. Find operator

Alternatively to building a pattern, you can directly use the find operator `=~` to build a `java.util.regex.Matcher` instance:

    def text = "some text to match"
    def m = text =~ /match/                                           (1)
    assert m instanceof Matcher                                       (2)
    if (!m) {                                                         (3)
        throw new RuntimeException("Oops, text not found!")
    }

1 | `=~` creates a matcher against the `text` variable, using the pattern on the right hand side
2 | the return type of `=~` is a `Matcher`
3 | equivalent to calling `if (!m.find())`

Since a `Matcher` coerces to a `boolean` by calling its `find` method, the `=~` operator is consistent with the simple use of Perl’s `=~` operator, when it appears as a predicate (in `if`, `while`, etc.).

### 7.3. Match operator

The match operator (`==~`) is a slight variation of the find operator, that does not return a `Matcher` but a boolean and requires a strict match of the input string:

    m = text ==~ /match/                                              (1)
    assert m instanceof Boolean                                       (2)
    if (m) {                                                          (3)
        throw new RuntimeException("Should not reach that point!")
    }

1 | `==~` matches the subject with the regular expression, but match must be strict
2 | the return type of `==~` is therefore a `boolean`
3 | equivalent to calling `if (text ==~ /match/)`

## 8. Other operators

### 8.1. Spread operator

The Spread Operator (`*.`) is used to invoke an action on all items of an aggregate object. It is equivalent to calling the action on each item and collecting the result into a list:

    class Car {
        String make
        String model
    }
    def cars = [
           new Car(make: 'Peugeot', model: '508'),
           new Car(make: 'Renault', model: 'Clio')]       (1)
    def makes = cars*.make                                (2)
    assert makes == ['Peugeot', 'Renault']                (3)

1 | build a list of `Car` items. The list is an aggregate of objects.
2 | call the spread operator on the list, accessing the `make` property of each item
3 | returns a list of strings corresponding to the collection of `make` items

The spread operator is null-safe, meaning that if an element of the collection is null, it will return null instead of throwing a `NullPointerException`:

    cars = [
       new Car(make: 'Peugeot', model: '508'),
       null,                                              (1)
       new Car(make: 'Renault', model: 'Clio')]
    assert cars*.make == ['Peugeot', null, 'Renault']     (2)
    assert null*.make == null                             (3)

1 | build a list for which of of the elements is `null`
2 | using the spread operator will not throw a `NullPointerException`
3 | the receiver might also be null, in which case the return value is `null`

The spread operator can be used on any class which implements the `Iterable` interface:

    class Component {
        Long id
        String name
    }
    class CompositeObject implements Iterable<Component> {
        def components = [
            new Component(id: 1, name: 'Foo'),
            new Component(id: 2, name: 'Bar')]

        @Override
        Iterator<Component> iterator() {
            components.iterator()
        }
    }
    def composite = new CompositeObject()
    assert composite*.id == [1,2]
    assert composite*.name == ['Foo','Bar']

#### 8.1.1. Spreading method arguments

There may be situations when the arguments of a method call can be found in a list that you need to adapt to the method arguments. In such situations, you can use the spread operator to call the method. For example, imagine you have the following method signature:

    int function(int x, int y, int z) {
        x*y+z
    }

then if you have the following list:

    def args = [4,5,6]

you can call the method without having to define intermediate variables:

    assert function(*args) == 26

It is even possible to mix normal arguments with spread ones:

    args = [4]
    assert function(*args,5,6) == 26

#### 8.1.2. Spread list elements

When used inside a list literal, the spread operator acts as if the spread element contents were inlined into the list:

    def items = [4,5]                      (1)
    def list = [1,2,3,*items,6]            (2)
    assert list == [1,2,3,4,5,6]           (3)

1 | `items` is a list
2 | we want to insert the contents of the `items` list directly into `list` without having to call `addAll`
3 | the contents of `items` has been inlined into `list`

#### 8.1.3. Spread map elements

The spread map operator works in a similar manner as the spread list operator, but for maps. It allows you to inline the contents of a map into another map literal, like in the following example:

    def m1 = [c:3, d:4]                   (1)
    def map = [a:1, b:2, *:m1]            (2)
    assert map == [a:1, b:2, c:3, d:4]    (3)

1 | `m1` is the map that we want to inline
2 | we use the `*:m1` notation to spread the contents of `m1` into `map`
3 | `map` contains all the elements of `m1`

The position of the spread map operator is relevant, like illustrated in the following example:

    def m1 = [c:3, d:4]                   (1)
    def map = [a:1, b:2, *:m1, d: 8]      (2)
    assert map == [a:1, b:2, c:3, d:8]    (3)

1 | `m1` is the map that we want to inline
2 | we use the `*:m1` notation to spread the contents of `m1` into `map`, but redefine the key `d` after spreading
3 | `map` contains all the expected keys, but `d` was redefined

### 8.2. Range operator

Groovy supports the concept of ranges and provides a notation (`..`) to create ranges of objects:

    def range = 0..5                                    (1)
    assert (0..5).collect() == [0, 1, 2, 3, 4, 5]       (2)
    assert (0..<5).collect() == [0, 1, 2, 3, 4]         (3)
    assert (0..5) instanceof List                       (4)
    assert (0..5).size() == 6                           (5)

1 | a simple range of integers, stored into a local variable
2 | an `IntRange`, with inclusive bounds
3 | an `IntRange`, with exclusive upper bound
4 | a `groovy.lang.Range` implements the `List` interface
5 | meaning that you can call the `size` method on it

Ranges implementation is lightweight, meaning that only the lower and upper bounds are stored. You can create a range from any `Comparable` object that has `next()` and `previous()` methods to determine the next / previous item in the range. For example, you can create a range of characters this way:

    assert ('a'..'d').collect() == ['a','b','c','d']

### 8.3. Spaceship operator

The spaceship operator (`<=>`) delegates to the `compareTo` method:

    assert (1 <=> 1) == 0
    assert (1 <=> 2) == -1
    assert (2 <=> 1) == 1
    assert ('a' <=> 'z') == -1

### 8.4. Subscript operator

The subscript operator is a short hand notation for `getAt` or `putAt`, depending on whether you find it on the left hand side or the right hand side of an assignment:

    def list = [0,1,2,3,4]
    assert list[2] == 2                         (1)
    list[2] = 4                                 (2)
    assert list[0..2] == [0,1,4]                (3)
    list[0..2] = [6,6,6]                        (4)
    assert list == [6,6,6,3,4]                  (5)

1 | `[2]` can be used instead of `getAt(2)`
2 | if on left hand side of an assignment, will call `putAt`
3 | `getAt` also supports ranges
4 | so does `putAt`
5 | the list is mutated

The subscript operator, in combination with a custom implementation of `getAt`/`putAt` is a convenient way for destructuring objects:

    class User {
        Long id
        String name
        def getAt(int i) {                                             (1)
            switch (i) {
                case 0: return id
                case 1: return name
            }
            throw new IllegalArgumentException("No such element $i")
        }
        void putAt(int i, def value) {                                 (2)
            switch (i) {
                case 0: id = value; return
                case 1: name = value; return
            }
            throw new IllegalArgumentException("No such element $i")
        }
    }
    def user = new User(id: 1, name: 'Alex')                           (3)
    assert user[0] == 1                                                (4)
    assert user[1] == 'Alex'                                           (5)
    user[1] = 'Bob'                                                    (6)
    assert user.name == 'Bob'                                          (7)

1 | the `User` class defines a custom `getAt` implementation
2 | the `User` class defines a custom `putAt` implementation
3 | create a sample user
4 | using the subscript operator with index 0 allows retrieving the user id
5 | using the subscript operator with index 1 allows retrieving the user name
6 | we can use the subscript operator to write to a property thanks to the delegation to `putAt`
7 | and check that it’s really the property `name` which was changed

### 8.5. Membership operator

The membership operator (`in`) is equivalent to calling the `isCase` method. In the context of a `List`, it is equivalent to calling `contains`, like in the following example:

    def list = ['Grace','Rob','Emmy']
    assert ('Emmy' in list)                     (1)

1 | equivalent to calling `list.contains('Emmy')` or `list.isCase('Emmy')`

### 8.6. Identity operator

In Groovy, using `==` to test equality is different from using the same operator in Java. In Groovy, it is calling `equals`. If you want to compare reference equality, you should use `is` like in the following example:

    def list1 = ['Groovy 1.8','Groovy 2.0','Groovy 2.3']        (1)
    def list2 = ['Groovy 1.8','Groovy 2.0','Groovy 2.3']        (2)
    assert list1 == list2                                       (3)
    assert !list1.is(list2)                                     (4)

1 | Create a list of strings
2 | Create another list of strings containing the same elements
3 | using `==`, we test object equality
4 | but using `is`, we can check that references are distinct

### 8.7. Coercion operator

The coercion operator (`as`) is a variant of casting. Coercion converts object from one type to another without them being compatible for assignment. Let’s take an example:

    Integer x = 123
    String s = (String) x                                   (1)

1 | `Integer` is not assignable to a `String`, so it will produce a `ClassCastException` at runtime

This can be fixed by using coercion instead:

    Integer x = 123
    String s = x as String                                  (1)

1 | `Integer` is not assignable to a `String`, but use of `as` will coerce it to a `String`

When an object is coerced into another, unless the target type is the same as the source type, coercion will return a new object. The rules of coercion differ depending on the source and target types, and coercion may fail if no conversion rules are found. Custom conversion rules may be implemented thanks to the `asType` method:

    class Identifiable {
        String name
    }
    class User {
        Long id
        String name
        def asType(Class target) {                                              (1)
            if (target == Identifiable) {
                return new Identifiable(name: name)
            }
            throw new ClassCastException("User cannot be coerced into $target")
        }
    }
    def u = new User(name: 'Xavier')                                            (2)
    def p = u as Identifiable                                                   (3)
    assert p instanceof Identifiable                                            (4)
    assert !(p instanceof User)                                                 (5)

1 | the `User` class defines a custom conversion rule from `User` to `Identifiable`
2 | we create an instance of `User`
3 | we coerce the `User` instance into an `Identifiable`
4 | the target is an instance of `Identifiable`
5 | the target is not an instance of `User` anymore

### 8.8. Diamond operator

The diamond operator (`<>`) is a syntactic sugar only operator added to support compatibility with the operator of the same name in Java 7. It is used to indicate that generic types should be inferred from the declaration:

    List<String> strings = new LinkedList<>()

In dynamic Groovy, this is totally unused. In statically type checked Groovy, it is also optional since the Groovy type checker performs type inference whether this operator is present or not.

### 8.9. Call operator

The call operator `()` is used to call a method named `call` implicitly. For any object which defines a `call` method, you can omit the `.call` part and use the call operator instead:

    class MyCallable {
        int call(int x) {           (1)
            2*x
        }
    }

    def mc = new MyCallable()
    assert mc.call(2) == 4          (2)
    assert mc(2) == 4               (3)

1 | `MyCallable` defines a method named `call`. Note that it doesn’t need to implement `java.util.concurrent.Callable`
2 | we can call the method using the classic method call syntax
3 | or we can omit `.call` thanks to the call operator

## 9. Operator precedence

The table below lists all groovy operators in order of precedence.

Level | Operator(s) | Name(s)
--- | --- | ---
1 | `new` `()` | object creation, explicit parentheses
| `()` `{}` `[]` | method call, closure, literal list/map
| `.` `.&` `.@` | member access, method closure, field/attribute access
| `?.` `*` `*.` `*:` | safe dereferencing, spread, spread-dot, spread-map
| `~` `!` `(type)` | bitwise negate/pattern, not, typecast
| `[]` `++` `--` | list/map/array index, post inc/decrement
2 | `**` | power
3 | `++` `--` `+` `-` | pre inc/decrement, unary plus, unary minus
4 | `*` `/` `%` | multiply, div, remainder
5 | `+` `-` | addition, subtraction
6 | `<<` `>>` `>>>` `..` `..<` | left/right (unsigned) shift, inclusive/exclusive range
7 | `<` `<=` `>` `>=` `in` `instanceof` `as` | less/greater than/or equal, in, instanceof, type coercion
8 | `==` `!=` `<=>` | equals, not equals, compare to
| `=~` `==~` | regex find, regex match
9 | `&` | binary/bitwise and
10 | `^` | binary/bitwise xor
11 | `|` | binary/bitwise or
12 | `&&` | logical and
13 | `||` | logical or
14 | `? :` | ternary conditional
| `?:` | elvis operator
15 | `=` `**=` `*=` `/=` `%=` `+=` `-=` `<<=` `>>=` `>>>=` `&=` `^=` `|=` | various assignments

## 10. Operator overloading

Groovy allows you to overload the various operators so that they can be used with your own classes. Consider this simple class:

    class Bucket {
        int size

        Bucket(int size) { this.size = size }

        Bucket plus(Bucket other) {                     (1)
            return new Bucket(this.size + other.size)
        }
    }

1 | `Bucket` implements a special method called `plus()`

Just by implementing the `plus()` method, the `Bucket` class can now be used with the `+` operator like so:

    def b1 = new Bucket(4)
    def b2 = new Bucket(11)
    assert (b1 + b2).size == 15                         (1)

1 | The two `Bucket` objects can be added together with the `+` operator

All (non-comparator) Groovy operators have a corresponding method that you can implement in your own classes. The only requirements are that your method is public, has the correct name, and has the correct number of arguments. The argument types depend on what types you want to support on the right hand side of the operator. For example, you could support the statement

    assert (b1 + 11).size == 15

by implementing the `plus()` method with this signature:

    Bucket plus(int capacity) {
        return new Bucket(this.size + capacity)
    }

Here is a complete list of the operators and their corresponding methods:

Operator | Method | Operator | Method
--- | --- | --- | ---
`+` | a.plus(b) | `a[b]` | a.getAt(b)
`-` | a.minus(b) | `a[b] = c` | a.putAt(b, c)
`*` | a.multiply(b) | `a in b` | b.isCase(a)
`/` | a.div(b) | `<<` | a.leftShift(b)
`%` | a.mod(b) | `>>` | a.rightShift(b)
`**` | a.power(b) | `>>>` | a.rightShiftUnsigned(b)
`|` | a.or(b) | `++` | a.next()
`&` | a.and(b) | `--` | a.previous()
`^` | a.xor(b) | `+a` | a.positive()
`as` | a.asType(b) | `-a` | a.negative()
`a()` | a.call() | `~a` | a.bitwiseNegate()