# Option type

In programming languages (more so 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 (Maybe (Maybe A)Maybe A), while nullable types do not (String?? = String?).

## Theoretical aspects

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In type theory, it may be written as: $A^{?} = A + 1$. This expresses the fact that for a given set of values in $A$, an option type adds exactly one additional value (the empty value) to the set of valid values for $A$. 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.

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

The option type is also a monad where:

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.

## Names and definitions

In different programming languages, the option type has various names and definitions.

• In Agda, it is named Maybe with variants nothing and just a.
• In Coq, it is defined as Inductive option (A:Type) : Type := | Some : A -> option A | None : option A..
• In Haskell, it is named Maybe, and defined as data Maybe a = Nothing | Just a.
• In Idris, it is defined as data Maybe a = Nothing | Just a.
• In OCaml, it is defined as type 'a option = None | Some of 'a.
• In Rust, it is defined as enum Option<T> { None, Some(T) }.
• In Scala, it is defined as sealed abstract class Option[+A], a type extended by final case class Some[+A](value: A) and case object None.
• In Standard ML, it is defined as datatype 'a option = NONE | SOME of 'a.
• In Swift, it is defined as enum Optional<T> { case none, some(T) } but is generally written as T?.

## Examples

Ada does not implement option-types directly, however it provides discriminated types which can be used to parameterize a record. To implement a Option type, a Boolean type is used as the discriminant; the following example provides a generic to create an option type from any non-limited constrained type:

Generic
-- Any constrained & non-limited type.
Type Element_Type is private;
Package Optional_Type is
-- When the discriminant, Has_Element, is true there is an element field,
-- when it is false, there are no fields (hence the null keyword).
Type Optional( Has_Element : Boolean ) is record
case Has_Element is
when False => Null;
when True  => Element : Element_Type;
end case;
end record;
end Optional_Type;

### Scala

Scala implements Option as a parameterized type, so a variable can be an Option, accessed as follows:

// Defining variables that are Options of type Int
val res1: Option[Int] = Some(42)
val res2: Option[Int] = None

// sample 1 :  This function uses pattern matching to deconstruct Options
def compute(opt: Option[Int]) = opt match {
case None => "No value"
case Some(x) => "The value is: " + x
}

// sample 2 :  This function uses built-in fold method
def compute(opt: Option[Int]) = opt.fold("No value")(v => "The value is: " + v )

println(compute(res1))  // The value is: 42
println(compute(res2))  // No value

Two main ways to use an Option value exist. The first, not the best, is the pattern matching, as in the first example. The second, the best practice is a monadic approach, as in the second example. In this way, a program is safe, as it can generate no exception or error (e.g., by trying to obtain the value of an Option variable that is equal to None). Thus, it essentially works as a type-safe alternative to the null value.

### OCaml

OCaml implements Option as a parameterized variant type. Options are constructed and deconstructed as follows:

(* Deconstructing options *)
let compute opt = match opt with
| None -> "No value"
| Some x -> "The value is: " ^ string_of_int x

print_endline (compute None) (* "No value" *)
print_endline (compute (Some 42)) (* "The value is: 42" *)

### F#

(* This function uses pattern matching to deconstruct Options *)
let compute = function
| None   -> "No value"
| Some x -> sprintf "The value is: %d" x

printfn "%s" (compute <| Some 42)(* The value is: 42 *)
printfn "%s" (compute None)      (* No value         *)

-- This function uses pattern matching to deconstruct Maybes
compute :: Maybe Int -> String
compute Nothing  = "No value"
compute (Just x) = "The value is: " ++ show x

main :: IO ()
main = do
print $compute (Just 42) -- The value is: 42 print$ compute Nothing -- No value

### Swift

func compute(_ x: Int?) -> String {
// This function uses optional binding to deconstruct optionals
if let y = x {
// y is now the non-optional Int content of x, if it has any
return "The value is: \(y)"
} else {
return "No value"
}
}

print(compute(42)) // The value is: 42
print(compute(nil)) // No value

### Rust

fn main() {
// This function uses pattern matching to deconstruct optionals
fn compute(x: Option<i32>) -> String {
match x {
Some(a) => format!("The value is: {}", a),
None => format!("No value"),
}
}

println!("{}", compute(Some(42))); // The value is: 42
println!("{}", compute(None)); // No value
}

### Nim

import options #Module must be imported

proc compute(a : Option[int])=
if(a.isSome): echo "The Value is: " & \$a.get
else: echo "The Value is None"

var
a : Option[int] = option(42)
b : Option[int]

compute(a) #The Value is: 42
compute(b) #The Value is None