Option type

For families of option contracts in finance, see Option style.

In programming languages (especially functional programming languages) and type theory, an option type or maybe type is a 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 None or Nothing), or which encapsulates the original data type A (often written Just A or Some A).

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

Theoretical aspects

In type theory, it may be written as: ${\displaystyle A^{?}=A+1}$. This expresses the fact that for a given set of values in ${\displaystyle A}$, an option type adds exactly one additional value (the empty value) to the set of valid values for ${\displaystyle A}$. This is reflected in programming by the fact that in languages having tagged unions, option types can be expressed as the tagged union of the encapsulated type plus a unit type.^[1]

In the Curry–Howard correspondence, option types are related to the annihilation law for ∨: x∨1=1.^[how?]

An option type can also be seen as a collection containing either one or zero elements.^{[original research?]}

The option type is also a monad where:^[2]

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

The monadic nature of the option type is useful for efficiently tracking failure and errors.^[3]

Examples

Agda

Further information: Agda (programming language)

In Agda, the option type is named Maybe with variants nothing and just a.

ATS

Further information: ATS (programming language)

In ATS, the option type is defined as

datatype option_t0ype_bool_type (a: t@ype+, bool) = 
	| Some(a, true) of a
 	| None(a, false)
stadef option = option_t0ype_bool_type
typedef Option(a: t@ype) = [b:bool] option(a, b)

#include "share/atspre_staload.hats"

fn show_value (opt: Option int): string =
	case+ opt of
	| None() => "No value"
	| Some(s) => tostring_int s

implement main0 (): void = let
	val full = Some 42
	and empty = None
in
	println!("show_value full → ", show_value full);
	println!("show_value empty → ", show_value empty);
end

show_value full → 42
show_value empty → No value

C++

Since C++17, the option type is defined in the standard library as template<typename T> std::optional<T>.

Coq

Further information: Coq (software)

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

Elm

Further information: Elm (programming language)

In Elm, the option type is defined as type Maybe a = Just a | Nothing.^[4]

F#

Further information: F Sharp (programming language)

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"

showValue full -> The value is: 42
showValue empty -> No value

Haskell

Further information: Haskell (programming language)

In Haskell, the option type is defined as data Maybe a = Nothing | Just a.^[5]

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

showValue full -> The value is: 42
showValue empty -> No value

Idris

Further information: Idris (programming language)

In Idris, the option type is defined as data Maybe a = Nothing | Just a.

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

showValue full -> The value is: 42
showValue empty -> No value

Nim

Further information: Nim (programming language)

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)

showValue(full) -> The Value is: 42
showValue(empty) -> No value

OCaml

Further information: OCaml

In OCaml, the option type is defined as type 'a option = None | Some of 'a.^[6]

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)

show_value full -> The value is: 42
show_value empty -> No value

Rust

Further information: Rust (programming language)

In Rust, the option type is defined as enum Option<T> { None, Some(T) }.^[7]

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));
}

show_value(full) -> The value is: 42
show_value(empty) -> No value

Scala

Further information: Scala (programming language)

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

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)}")

showValue(full) -> The value is: 42
showValue(empty) -> No value

Standard ML

Further information: Standard ML

In Standard ML, the option type is defined as datatype 'a option = NONE | SOME of 'a.

Swift

Further information: Swift (programming language)

In Swift, the option type is defined as enum Optional<T> { case none, some(T) } but is generally written as T?.^[8]

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))")

showValue(full) -> The value is: 42
showValue(empty) -> No value

Zig

Further information: Zig (programming language)

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

Payload n can be captured in an if or while statement, such as if (opt) |n| { ... } else { ... }, and an else clause is evaluated if it is null.

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});
}

showValue(allocator, full) -> The value is: 42 
showValue(allocator, empty) -> No value

See also

• Result type
• Tagged union
• Nullable type
• Null object pattern
• Exception handling
• Pattern matching

References

1. Milewski, Bartosz (2015-01-13). "Simple Algebraic Data Types". Bartosz Milewski's Programming Cafe. Sum types. "We could have encoded Maybe as: data Maybe a = Either () a". Archived from the original on 2019-08-18. Retrieved 2019-08-18.
2. "A Fistful of Monads - Learn You a Haskell for Great Good!". www.learnyouahaskell.com. Retrieved 2019-08-18.
3. Hutton, Graham (Nov 25, 2017). "What is a Monad?". Computerphile Youtube. Archived from the original on 2021-12-20. Retrieved Aug 18, 2019.
4. "Maybe · An Introduction to Elm". guide.elm-lang.org.
5. "6 Predefined Types and Classes". www.haskell.org. Retrieved 2022-06-15.
6. "OCaml library : Option". v2.ocaml.org. Retrieved 2022-06-15.
7. "Option in core::option - Rust". doc.rust-lang.org. 2022-05-18. Retrieved 2022-06-15.
8. "Apple Developer Documentation". developer.apple.com. Retrieved 2020-09-06.