# Operators

In Scala, operators are methods. Any method with a single parameter can be used as an infix operator. For example, + can be called with dot-notation:

10.+(1)


However, it’s easier to read as an infix operator:

10 + 1


## Defining and using operators

You can use any legal identifier as an operator. This includes a name like add or a symbol(s) like +.

case class Vec(x: Double, y: Double) {
def +(that: Vec) = Vec(this.x + that.x, this.y + that.y)
}

val vector1 = Vec(1.0, 1.0)
val vector2 = Vec(2.0, 2.0)

val vector3 = vector1 + vector2
vector3.x  // 3.0
vector3.y  // 3.0



The class Vec has a method + which we used to add vector1 and vector2. Using parentheses, you can build up complex expressions with readable syntax. Here is the definition of class MyBool which includes methods and and or:

case class MyBool(x: Boolean) {
def and(that: MyBool): MyBool = if (x) that else this
def or(that: MyBool): MyBool = if (x) this else that
def negate: MyBool = MyBool(!x)
}



It is now possible to use and and or as infix operators:

def not(x: MyBool) = x.negate
def xor(x: MyBool, y: MyBool) = (x or y) and not(x and y)



This helps to make the definition of xor more readable.

## Precedence

When an expression uses multiple operators, the operators are evaluated based on the priority of the first character:

(characters not shown below)
* / %
+ -
:
= !
< >
&
^
|
(all letters)



This applies to functions you define. For example, the following expression:

a + b ^? c ?^ d less a ==> b | c



Is equivalent to

((a + b) ^? (c ?^ d)) less ((a ==> b) | c)


?^ has the highest precedence because it starts with the character ?. + has the second highest precedence, followed by ==>, ^?, |, and less.

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