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# Operators reference
This document is a complete reference of operators in Elixir, how they are parsed, how they can be defined, and how they can be overridden.
## Operator precedence and associativity
The following is a list of all operators that Elixir is capable of parsing, ordered from higher to lower precedence, alongside their associativity:
Operator | Associativity
---------------------------------------------- | -------------
`@` | Unary
`.` | Left
`+` `-` `!` `^` `not` | Unary
`**` | Left
`*` `/` | Left
`+` `-` | Left
`++` `--` `+++` `---` `..` `<>` | Right
`in` `not in` | Left
`\|>` `<<<` `>>>` `<<~` `~>>` `<~` `~>` `<~>` | Left
`<` `>` `<=` `>=` | Left
`==` `!=` `=~` `===` `!==` | Left
`&&` `&&&` `and` | Left
`\|\|` `\|\|\|` `or` | Left
`=` | Right
`&`, `...` | Unary
`=>` (valid only inside `%{}`) | Right
`\|` | Right
`::` | Right
`when` | Right
`<-` `\\` | Left
## General operators
Elixir provides the following built-in operators:
* [`+`](`+/1`) and [`-`](`-/1`) - unary positive/negative
* [`+`](`+/2`), [`-`](`-/2`), [`*`](`*/2`), and [`/`](`//2`) - basic arithmetic operations
* [`++`](`++/2`) and [`--`](`--/2`) - list concatenation and subtraction
* [`and`](`and/2`) and [`&&`](`&&/2`) - strict and relaxed boolean "and"
* [`or`](`or/2`) and [`||`](`||/2`) - strict and relaxed boolean "or"
* [`not`](`not/1`) and [`!`](`!/1`) - strict and relaxed boolean "not"
* [`in`](`in/2`) and [`not in`](`in/2`) - membership
* [`@`](`@/1`) - module attribute
* [`..`](`../0`), [`..`](`../2`), and [`..//`](`..///3`) - range creation
* [`<>`](`<>/2`) - binary concatenation
* [`|>`](`|>/2`) - pipeline
* [`=~`](`=~/2`) - text-based match
Many of those can be used in guards; consult the [list of allowed guard functions and operators](patterns-and-guards.md#list-of-allowed-functions-and-operators).
Additionally, there are a few other operators that Elixir parses but doesn't actually use.
See [Custom and overridden operators](#custom-and-overridden-operators) below for a list and for guidelines about their use.
Some other operators are special forms and cannot be overridden:
* [`^`](`^/1`) - pin operator
* [`.`](`./2`) - dot operator
* [`=`](`=/2`) - match operator
* [`&`](`&/1`) - capture operator
* [`::`](`::/2`) - type operator
Finally, these operators appear in the precedence table above but are only meaningful within certain constructs:
* `=>` - see [`%{}`](`%{}/1`)
* `when` - see [Guards](patterns-and-guards.md#guards)
* `<-` - see [`for`](`for/1`) and [`with`](`with/1`)
* `\\` - see [Default arguments](`Kernel#def/2-default-arguments`)
## Comparison operators
Elixir provides the following built-in comparison operators (all of which can be used in guards):
* [`==`](`==/2`) - equal to
* [`===`](`===/2`) - strictly equal to
* [`!=`](`!=/2`) - not equal to
* [`!==`](`!==/2`) - strictly not equal to
* [`<`](`</2`) - less-than
* [`>`](`>/2`) - greater-than
* [`<=`](`<=/2`) - less-than or equal to
* [`>=`](`>=/2`) - greater-than or equal to
The only difference between [`==`](`==/2`) and [`===`](`===/2`) is that [`===`](`===/2`) is strict when it comes to comparing integers and floats:
```elixir
iex> 1 == 1.0
true
iex> 1 === 1.0
false
```
[`!=`](`!=/2`) and [`!==`](`!==/2`) act as the negation of [`==`](`==/2`) and [`===`](`===/2`), respectively.
## Custom and overridden operators
### Defining custom operators
Elixir is capable of parsing a predefined set of operators. It's not possible to define new operators (as supported by some languages). However, not all operators that Elixir can parse are *used* by Elixir: for example, `+` and `||` are used by Elixir for addition and boolean *or*, but `<~>` is not used (but valid).
To define an operator, you can use the usual `def*` constructs (`def`, `defp`, `defmacro`, and so on) but with a syntax similar to how the operator is used:
```elixir
defmodule MyOperators do
# We define ~> to return the maximum of the given two numbers,
# and <~ to return the minimum.
def a ~> b, do: max(a, b)
def a <~ b, do: min(a, b)
end
```
To use the newly defined operators, you **have to** import the module that defines them:
```elixir
iex> import MyOperators
iex> 1 ~> 2
2
iex> 1 <~ 2
1
```
The following is a table of all the operators that Elixir is capable of parsing, but that are not used by default:
* `|||`
* `&&&`
* `<<<`
* `>>>`
* `<<~`
* `~>>`
* `<~`
* `~>`
* `<~>`
* `+++`
* `---`
* `...`
The following operators are used by the `Bitwise` module when imported: [`&&&`](`Bitwise.&&&/2`), [`<<<`](`Bitwise.<<</2`), [`>>>`](`Bitwise.>>>/2`), and [`|||`](`Bitwise.|||/2`). See the `Bitwise` documentation for more information.
Note that the Elixir community generally discourages custom operators. They can be hard to read and even more to understand, as they don't have a descriptive name like functions do. That said, some specific cases or custom domain specific languages (DSLs) may justify these practices.
It is also possible to replace predefined operators, such as `+`, but doing so is extremely discouraged.
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