Option type
Encapsulation of an optional value in programming or type theory
(Learn how and when to remove this message) 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
(Learn how and when to remove this message) In type theory, it may be written as:
. This expresses the fact that for a given set of values in
, an option type adds exactly one additional value (the empty value) to the set of valid values for
. 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
In Agda, the option type is named Maybe
with variants nothing
and just a
.
C++
Since C++17, the option type is defined in the standard library as template<typename T> std::optional<T>
.
Coq
In Coq, the option type is defined as Inductive option (A:Type) : Type := | Some : A -> option A | None : option A.
.
Elm
In Elm, the option type is defined as type Maybe a = Just a | Nothing
.[4]
F#
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
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
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
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
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
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
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
In Standard ML, the option type is defined as datatype 'a option = NONE | SOME of 'a
.
Swift
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
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
- ^ 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.
- ^ "A Fistful of Monads - Learn You a Haskell for Great Good!". www.learnyouahaskell.com. Retrieved 2019-08-18.
- ^ Hutton, Graham (Nov 25, 2017). "What is a Monad?". Computerphile Youtube. Archived from the original on 2021-12-20. Retrieved Aug 18, 2019.
- ^ "Maybe · An Introduction to Elm". guide.elm-lang.org.
- ^ "6 Predefined Types and Classes". www.haskell.org. Retrieved 2022-06-15.
- ^ "OCaml library : Option". v2.ocaml.org. Retrieved 2022-06-15.
- ^ "Option in core::option - Rust". doc.rust-lang.org. 2022-05-18. Retrieved 2022-06-15.
- ^ "Apple Developer Documentation". developer.apple.com. Retrieved 2020-09-06.
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