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((Short description|Encapsulation of an optional value in programming or type theory))
((for|families of option contracts in finance|Option style))
((multiple issues|section=|
((More citations needed|date=July 2019))
((Original research|date=July 2019))
))

In [[programming language]]s (especially [[functional programming]] languages) and [[type theory]], an '''option type''' or '''maybe type''' is a [[parametric polymorphism|polymorphic type]] that represents encapsulation of an optional value; e.g., it is used as the return type of functions which may or may not return a meaningful value when they are applied. It consists of a constructor which either is empty (often named <code>None</code> or <code>Nothing</code>), or which encapsulates the original data type <code>A</code> (often written <code>Just A</code> or <code>Some A</code>).

A distinct, but related concept outside of functional programming, which is popular in [[object-oriented programming]], is called [[nullable type]]s (often expressed as <code>A?</code>). The core difference between option types and nullable types is that option types support nesting (e.g. <code>Maybe (Maybe String)</code> ≠ <code>Maybe String</code>), while nullable types do not (e.g. <code>String??</code> = <code>String?</code>).

==Theoretical aspects==
((multiple issues|section=yes|((Importance section|section|date=July 2019))
((Original research|section|date=August 2019))))

In [[type theory]], it may be written as: <math>A^{?} = A + 1</math>. This expresses the fact that for a given set of values in <math>A</math>, an option type adds exactly one additional value (the empty value) to the set of valid values for <math>A</math>. This is reflected in programming by the fact that in languages having [[tagged union]]s, option types can be expressed as the tagged union of the encapsulated type plus a [[unit type]].<ref>((cite web|url=https://bartoszmilewski.com/2015/01/13/simple-algebraic-data-types/|title=Simple Algebraic Data Types|last=Milewski|first=Bartosz|date=2015-01-13|website=Bartosz Milewski's Programming Cafe|at=Sum types. "We could have encoded Maybe as: data Maybe a = Either () a"|language=en|archive-url=https://web.archive.org/web/20190818084741/https://bartoszmilewski.com/2015/01/13/simple-algebraic-data-types/|archive-date=2019-08-18|url-status=live|access-date=2019-08-18))</ref>

In the [[Curry–Howard correspondence]], option types are related to the [[absorption law|annihilation law]] for ∨: x∨1=1.((How|date=August 2019|title=It is unclear how this is the case, and there are no links to external references that explain this.))

An option type can also be seen as a [[collection (abstract data type)|collection]] containing either one or zero elements.((Original research inline|date=July 2019))

The option type is also a [[Maybe monad|monad]] where:<ref>((cite web|url=http://www.learnyouahaskell.com/a-fistful-of-monads|title=A Fistful of Monads - Learn You a Haskell for Great Good!|website=www.learnyouahaskell.com|access-date=2019-08-18))</ref>

<syntaxhighlight lang="haskell">
return = Just -- Wraps the value into a maybe

Nothing  >>= f = Nothing -- Fails if the previous monad fails
(Just x) >>= f = f x     -- Succeeds when both monads succeed
</syntaxhighlight>

The monadic nature of the option type is useful for efficiently tracking failure and errors.<ref>((cite web|url=https://www.youtube.com/watch?v=t1e8gqXLbsU |archive-url=https://ghostarchive.org/varchive/youtube/20211220/t1e8gqXLbsU |archive-date=2021-12-20 |url-status=live|title=What is a Monad?|last=Hutton|first=Graham|date=Nov 25, 2017|website=Computerphile Youtube|access-date=Aug 18, 2019))((cbignore))</ref>

== Examples ==
<!--
Gentle reminder to not add language examples that do not satisfy the laws.
If you do not know what this means, please refrain from adding examples.

List of things that are NOT option types and therefore do not need to be added:
- std::optional<T> in C++
- Nullable<T> (T?) in C#
- Null (T?) in Dart
- Optional<T> in Java
- Nullable{T} in Julia
- Nullable types (T?) in Kotlin
- typing.Optional[T] (T | None) in Python
- Definiteness (:D) in Raku
-->

=== Agda ===
((Expand section|with=example usage|date=July 2022))
((Further|Agda (programming language)))

In Agda, the option type is named ((code|2=agda|Maybe)) with variants ((code|2=agda|nothing)) and ((code|2=agda|just a)).

=== C++ ===
Since C++17, the option type is defined in the standard library as ((code|2=C++|1=template<typename T> std::optional<T> )).

=== Coq ===
((Expand section|with=example usage|date=July 2022))
((Further|Coq (software)))

In Coq, the option type is defined as ((code|2=coq|1=Inductive option (A:Type) : Type := ((!)) Some : A -> option A ((!)) None : option A. )).

=== Elm ===
((Expand section|with=example usage|date=July 2022))
((Further|Elm (programming language)))

In Elm, the option type is defined as ((code|2=elm|1=type Maybe a = Just a ((!)) Nothing)).<ref>((cite web |title=Maybe · An Introduction to Elm |url=https://guide.elm-lang.org/error_handling/maybe.html |website=guide.elm-lang.org))</ref>

=== F# ===
((Expand section|with=the definition|date=July 2022))
((Further|F Sharp (programming language)))

<syntaxhighlight lang="fsharp">
let showValue =
    Option.fold (fun _ x -> sprintf "The value is: %d" x) "No value"

let full = Some 42
let empty = None

showValue full |> printfn "showValue full -> %s"
showValue empty |> printfn "showValue empty -> %s"
</syntaxhighlight>

<syntaxhighlight lang="output">
showValue full -> The value is: 42
showValue empty -> No value
</syntaxhighlight>

=== Haskell ===
((Further|Haskell (programming language)))

In Haskell, the option type is defined as ((code|2=haskell|1=data Maybe a = Nothing ((!)) Just a)).<ref>((Cite web |title=6 Predefined Types and Classes |url=https://www.haskell.org/onlinereport/haskell2010/haskellch6.html#x13-1250006.1.8 |access-date=2022-06-15 |website=www.haskell.org))</ref>

<syntaxhighlight lang="haskell">
showValue :: Maybe Int -> String
showValue = foldl (\_ x -> "The value is: " ++ show x) "No value"

main :: IO ()
main = do
    let full = Just 42
    let empty = Nothing

    putStrLn $ "showValue full -> " ++ showValue full
    putStrLn $ "showValue empty -> " ++ showValue empty
</syntaxhighlight>

<syntaxhighlight lang="output">
showValue full -> The value is: 42
showValue empty -> No value
</syntaxhighlight>

=== Idris ===
((Further|Idris (programming language)))

In Idris, the option type is defined as ((code|2=idris|1=data Maybe a = Nothing ((!)) Just a)).

<syntaxhighlight lang="idris">
showValue : Maybe Int -> String
showValue = foldl (\_, x => "The value is " ++ show x) "No value"

main : IO ()
main = do
    let full = Just 42
    let empty = Nothing

    putStrLn $ "showValue full -> " ++ showValue full
    putStrLn $ "showValue empty -> " ++ showValue empty
</syntaxhighlight>

<syntaxhighlight lang="output">
showValue full -> The value is: 42
showValue empty -> No value
</syntaxhighlight>

=== Nim ===
((Expand section|with=the definition|date=July 2022))
((Further|Nim (programming language)))

<syntaxhighlight lang="nim">
import std/options

proc showValue(opt: Option[int]): string =
  opt.map(proc (x: int): string = "The value is: " & $x).get("No value")

let
  full = some(42)
  empty = none(int)

echo "showValue(full) -> ", showValue(full)
echo "showValue(empty) -> ", showValue(empty)
</syntaxhighlight>

<syntaxhighlight lang="output">
showValue(full) -> The Value is: 42
showValue(empty) -> No value
</syntaxhighlight>

=== OCaml ===
((Further|OCaml))

In OCaml, the option type is defined as ((code|2=ocaml|1=type 'a option = None ((!)) Some of 'a)).<ref>((Cite web |title=OCaml library : Option |url=https://v2.ocaml.org/releases/4.13/api/Option.html#TYPEt |access-date=2022-06-15 |website=v2.ocaml.org))</ref>

<syntaxhighlight lang="ocaml">
let show_value =
  Option.fold ~none:"No value" ~some:(fun x -> "The value is: " ^ string_of_int x)

let () =
  let full = Some 42 in
  let empty = None in

  print_endline ("show_value full -> " ^ show_value full);
  print_endline ("show_value empty -> " ^ show_value empty)
</syntaxhighlight>

<syntaxhighlight lang="output">
show_value full -> The value is: 42
show_value empty -> No value
</syntaxhighlight>

=== Rust ===
((Further|Rust (programming language)))

In Rust, the option type is defined as ((code|2=rust|enum Option<T> { None, Some(T) } )).<ref>((cite web |url=https://doc.rust-lang.org/core/option/enum.Option.html |title=Option in core::option - Rust |date=2022-05-18 |access-date=2022-06-15 |website=doc.rust-lang.org))</ref>

<syntaxhighlight lang="rust">
fn show_value(opt: Option<i32>) -> String {
    opt.map_or("No value".to_owned(), |x| format!("The value is: {}", x))
}

fn main() {
    let full = Some(42);
    let empty = None;

    println!("show_value(full) -> {}", show_value(full));
    println!("show_value(empty) -> {}", show_value(empty));
}
</syntaxhighlight>

<syntaxhighlight lang="output">
show_value(full) -> The value is: 42
show_value(empty) -> No value
</syntaxhighlight>

=== Scala ===
((Further|Scala (programming language)))

In Scala, the option type is defined as ((code|2=scala|1=sealed abstract class Option[+A])), a type extended by ((code|2=scala|1=final case class Some[+A](value: A))) and ((code|2=scala|1=case object None)).

<syntaxhighlight lang="scala">
object Main:
  def showValue(opt: Option[Int]): String =
    opt.fold("No value")(x => s"The value is: $x")

  def main(args: Array[String]): Unit =
    val full = Some(42)
    val empty = None

    println(s"showValue(full) -> ${showValue(full)}")
    println(s"showValue(empty) -> ${showValue(empty)}")


</syntaxhighlight>

<syntaxhighlight lang="output">
showValue(full) -> The value is: 42
showValue(empty) -> No value
</syntaxhighlight>

=== Standard ML ===
((Expand section|with=example usage|date=July 2022))
((Further|Standard ML))

In Standard ML, the option type is defined as ((code|2=sml|1=datatype 'a option = NONE ((!)) SOME of 'a)).

=== Swift ===
((Further|Swift (programming language)))

In Swift, the option type is defined as ((code|2=swift|enum Optional<T> { case none, some(T) } )) but is generally written as ((code|2=swift|T?)).<ref>((cite web|title=Apple Developer Documentation|url=https://developer.apple.com/documentation/swift/optional|access-date=2020-09-06|website=developer.apple.com))</ref>

<syntaxhighlight lang="swift">
func showValue(_ opt: Int?) -> String {
    return opt.map { "The value is: \($0)" } ?? "No value"
}

let full = 42
let empty: Int? = nil

print("showValue(full) -> \(showValue(full))")
print("showValue(empty) -> \(showValue(empty))")
</syntaxhighlight>

<syntaxhighlight lang="output">
showValue(full) -> The value is: 42
showValue(empty) -> No value
</syntaxhighlight>

=== Zig ===
((Further|Zig (programming language)))

In Zig, add ? before the type name like <code>?i32</code> to make it an optional type.

Payload <var>n</var> can be captured in an ''if'' or ''while'' statement, such as ((code|2=zig|if (opt) ((!))n((!)) { ... } else { ... } )), and an ''else'' clause is evaluated if it is <code>null</code>.

<syntaxhighlight lang="zig">
const std = @import("std");

fn showValue(allocator: std.mem.Allocator, opt: ?i32) ![]u8 {
    return if (opt) |n|
        std.fmt.allocPrint(allocator, "The value is: {}", .{n})
    else
        allocator.dupe(u8, "No value");
}

pub fn main() !void {
    // Set up an allocator, and warn if we forget to free any memory.
    var gpa = std.heap.GeneralPurposeAllocator(.{}){};
    defer std.debug.assert(gpa.deinit() == .ok);
    const allocator = gpa.allocator();

    // Prepare the standard output stream.
    const stdout = std.io.getStdOut().writer();

    // Perform our example.
    const full = 42;
    const empty = null;

    const full_msg = try showValue(allocator, full);
    defer allocator.free(full_msg);
    try stdout.print("showValue(allocator, full) -> {s}\n", .{full_msg});

    const empty_msg = try showValue(allocator, empty);
    defer allocator.free(empty_msg);
    try stdout.print("showValue(allocator, empty) -> {s}\n", .{empty_msg});
}
</syntaxhighlight>

<syntaxhighlight lang="output">
showValue(allocator, full) -> The value is: 42 
showValue(allocator, empty) -> No value
</syntaxhighlight>

== See also ==
* [[Result type]]
* [[Tagged union]]
* [[Nullable type]]
* [[Null object pattern]]
* [[Exception handling]]
* [[Pattern matching]]

== References ==
((Reflist))

((Data types))

[[Category:Functional programming]]
[[Category:Data types]]
[[Category:Type theory]]

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