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## Tutorial

### Motivation

Consider these functions which should return a value but which might not have a value to return:

- (A) `double sqrt(double n );`
- (B) `char get_async_input();`
- (C) `point polygon::get_any_point_effectively_inside();`

There are different approaches to the issue of not having a value to return.

A typical approach is to consider the existence of a valid return value as a postcondition, so that if the function cannot compute the value to return, it has either undefined behavior (and can use assert in a debug build) or uses a runtime check and throws an exception if the postcondition is violated. This is a reasonable choice for example, for function (A), because the lack of a proper return value is directly related to an invalid parameter (out of domain argument), so it is appropriate to require the callee to supply only parameters in a valid domain for execution to continue normally.

However, function (B), because of its asynchronous nature, does not fail just because it can't find a value to return; so it is incorrect to consider such a situation an error and assert or throw an exception. This function must return, and somehow, must tell the callee that it is not returning a meaningful value.

A similar situation occurs with function (C): it is conceptually an error to ask a null-area polygon to return a point inside itself, but in many applications, it is just impractical for performance reasons to treat this as an error (because detecting that the polygon has no area might be too expensive to be required to be tested previously), and either an arbitrary point (typically at infinity) is returned, or some efficient way to tell the callee that there is no such point is used.

There are various mechanisms to let functions communicate that the returned value is not valid. One such mechanism, which is quite common since it has zero or negligible overhead, is to use a special value which is reserved to communicate this. Classical examples of such special values are `EOF`, `string::npos`, points at infinity, etc...

When those values exist, i.e. the return type can hold all meaningful values plus the signal value, this mechanism is quite appropriate and well known. Unfortunately, there are cases when such values do not exist. In these cases, the usual alternative is either to use a wider type, such as `int` in place of `char`; or a compound type, such as `std::pair<point,bool>`.

Returning a `std::pair<T,bool>`, thus attaching a boolean flag to the result which indicates if the result is meaningful, has the advantage that can be turned into a consistent idiom since the first element of the pair can be whatever the function would conceptually return. For example, the last two functions could have the following interface:

    std::pair<char,bool> get_async_input();
    std::pair<point,bool> polygon::get_any_point_effectively_inside();

These functions use a consistent interface for dealing with possibly nonexistent results:

    std::pair<point,bool> p = poly.get_any_point_effectively_inside();
    if ( p.second )
        flood_fill(p.first);

However, not only is this quite a burden syntactically, it is also error prone since the user can easily use the function result (first element of the pair) without ever checking if it has a valid value.

Clearly, we need a better idiom.

### Design Overview

#### The models

In C++, we can declare an object (a variable) of type `T`, and we can give this variable an initial value (through an initializer. (cf. 8.5)). When a declaration includes a non-empty initializer (an initial value is given), it is said that the object has been initialized. If the declaration uses an empty initializer (no initial value is given), and neither default nor value initialization applies, it is said that the object is uninitialized. Its actual value exist but has an indeterminate initial value (cf. 8.5/11). `optional<T>` intends to formalize the notion of initialization (or lack of it) allowing a program to test whether an object has been initialized and stating that access to the value of an uninitialized object is undefined behavior. That is, when a variable is declared as `optional<T>` and no initial value is given, the variable is formally uninitialized. A formally uninitialized optional object has conceptually no value at all and this situation can be tested at runtime. It is formally undefined behavior to try to access the value of an uninitialized optional. An uninitialized optional can be assigned a value, in which case its initialization state changes to initialized. Furthermore, given the formal treatment of initialization states in optional objects, it is even possible to reset an optional to uninitialized.

In C++ there is no formal notion of uninitialized objects, which means that objects always have an initial value even if indeterminate. As discussed on the previous section, this has a drawback because you need additional information to tell if an object has been effectively initialized. One of the typical ways in which this has been historically dealt with is via a special value: `EOF`, `npos`, -1, etc... This is equivalent to adding the special value to the set of possible values of a given type. This super set of `T` plus some nil_t—where `nil_t` is some stateless POD—can be modeled in modern languages as a discriminated union of T and nil_t. Discriminated unions are often called variants. A variant has a current type, which in our case is either `T` or `nil_t`. Using the Boost.Variant library, this model can be implemented in terms of `boost::variant<T,nil_t>`. There is precedent for a discriminated union as a model for an optional value: the Haskell Maybe built-in type constructor. Thus, a discriminated union `T+nil_t` serves as a conceptual foundation.

A `variant<T,nil_t>` follows naturally from the traditional idiom of extending the range of possible values adding an additional sentinel value with the special meaning of Nothing. However, this additional Nothing value is largely irrelevant for our purpose since our goal is to formalize the notion of uninitialized objects and, while a special extended value can be used to convey that meaning, it is not strictly necessary in order to do so.

The observation made in the last paragraph about the irrelevant nature of the additional `nil_t` with respect to purpose of `optional<T>` suggests an alternative model: a container that either has a value of `T` or nothing.

As of this writing I don't know of any precedent for a variable-size fixed-capacity (of 1) stack-based container model for optional values, yet I believe this is the consequence of the lack of practical implementations of such a container rather than an inherent shortcoming of the container model.

In any event, both the discriminated-union or the single-element container models serve as a conceptual ground for a class representing optional—i.e. possibly uninitialized—objects. For instance, these models show the exact semantics required for a wrapper of optional values:

Discriminated-union:

- deep-copy semantics: copies of the variant implies copies of the value.
- deep-relational semantics: comparisons between variants matches both current types and values
- If the variant's current type is `T`, it is modeling an initialized optional.
- If the variant's current type is not `T`, it is modeling an uninitialized optional.
- Testing if the variant's current type is `T` models testing if the optional is initialized
- Trying to extract a `T` from a variant when its current type is not `T`, models the undefined behavior of trying to access the value of an uninitialized optional

Single-element container:

- deep-copy semantics: copies of the container implies copies of the value.
- deep-relational semantics: comparisons between containers compare container size and if match, contained value
- If the container is not empty (contains an object of type `T`), it is modeling an initialized optional.
- If the container is empty, it is modeling an uninitialized optional.
- Testing if the container is empty models testing if the optional is initialized
- Trying to extract a `T` from an empty container models the undefined behavior of trying to access the value of an uninitialized optional

#### The semantics

Objects of type `optional<T>` are intended to be used in places where objects of type `T` would but which might be uninitialized. Hence, `optional<T>`'s purpose is to formalize the additional possibly uninitialized state. From the perspective of this role, `optional<T>` can have the same operational semantics of `T` plus the additional semantics corresponding to this special state. As such, `optional<T>` could be thought of as a supertype of `T`. Of course, we can't do that in C++, so we need to compose the desired semantics using a different mechanism. Doing it the other way around, that is, making `optional<T>` a subtype of `T` is not only conceptually wrong but also impractical: it is not allowed to derive from a non-class type, such as a built-in type.

We can draw from the purpose of `optional<T>` the required basic semantics:

- Default Construction: To introduce a formally uninitialized wrapped object.
- Direct Value Construction via copy: To introduce a formally initialized wrapped object whose value is obtained as a copy of some object.
- Deep Copy Construction: To obtain a new yet equivalent wrapped object.
- Direct Value Assignment (upon initialized): To assign a value to the wrapped object.
- Direct Value Assignment (upon uninitialized): To initialize the wrapped object with a value obtained as a copy of some object.
- Assignment (upon initialized): To assign to the wrapped object the value of another wrapped object.
- Assignment (upon uninitialized): To initialize the wrapped object with value of another wrapped object.
- Deep Relational Operations (when supported by the type T): To compare wrapped object values taking into account the presence of uninitialized states.
- Value access: To unwrap the wrapped object.
- Initialization state query: To determine if the object is formally initialized or not.
- Swap: To exchange wrapped objects. (with whatever exception safety guarantees are provided by `T`'s swap).
- De-initialization: To release the wrapped object (if any) and leave the wrapper in the uninitialized state.

Additional operations are useful, such as converting constructors and converting assignments, in-place construction and assignment, and safe value access via a pointer to the wrapped object or null.

#### The Interface

Since the purpose of optional is to allow us to use objects with a formal uninitialized additional state, the interface could try to follow the interface of the underlying `T` type as much as possible. In order to choose the proper degree of adoption of the native `T` interface, the following must be noted: Even if all the operations supported by an instance of type `T` are defined for the entire range of values for such a type, an `optional<T>` extends such a set of values with a new value for which most (otherwise valid) operations are not defined in terms of `T`.

Furthermore, since `optional<T>` itself is merely a `T` wrapper (modeling a `T` supertype), any attempt to define such operations upon uninitialized optionals will be totally artificial w.r.t. `T`.

This library chooses an interface which follows from `T`'s interface only for those operations which are well defined (w.r.t the type `T`) even if any of the operands are uninitialized. These operations include: construction, copy-construction, assignment, swap and relational operations.

For the value access operations, which are undefined (w.r.t the type `T`) when the operand is uninitialized, a different interface is chosen (which will be explained next).

Also, the presence of the possibly uninitialized state requires additional operations not provided by `T` itself which are supported by a special interface.

###### Lexically-hinted Value Access in the presence of possibly uninitialized optional objects: The operators * and ->

A relevant feature of a pointer is that it can have a null pointer value. This is a special value which is used to indicate that the pointer is not referring to any object at all. In other words, null pointer values convey the notion of nonexistent objects.

This meaning of the null pointer value allowed pointers to became a de facto standard for handling optional objects because all you have to do to refer to a value which you don't really have is to use a null pointer value of the appropriate type. Pointers have been used for decades—from the days of C APIs to modern C++ libraries—to refer to optional (that is, possibly nonexistent) objects; particularly as optional arguments to a function, but also quite often as optional data members.

The possible presence of a null pointer value makes the operations that access the pointee's value possibly undefined, therefore, expressions which use dereference and access operators, such as: `( *p = 2 )` and `( p->foo() )`, implicitly convey the notion of optionality, and this information is tied to the syntax of the expressions. That is, the presence of operators `*` and `->` tell by themselves —without any additional context— that the expression will be undefined unless the implied pointee actually exist.

Such a de facto idiom for referring to optional objects can be formalized in the form of a concept: the OptionalPointee concept. This concept captures the syntactic usage of operators `*`, `->` and contextual conversion to `bool` to convey the notion of optionality.

However, pointers are good to refer to optional objects, but not particularly good to handle the optional objects in all other respects, such as initializing or moving/copying them. The problem resides in the shallow-copy of pointer semantics: if you need to effectively move or copy the object, pointers alone are not enough. The problem is that copies of pointers do not imply copies of pointees. For example, as was discussed in the motivation, pointers alone cannot be used to return optional objects from a function because the object must move outside from the function and into the caller's context.

A solution to the shallow-copy problem that is often used is to resort to dynamic allocation and use a smart pointer to automatically handle the details of this. For example, if a function is to optionally return an object `X`, it can use `shared_ptr<X>` as the return value. However, this requires dynamic allocation of `X`. If `X` is a built-in or small POD, this technique is very poor in terms of required resources. Optional objects are essentially values so it is very convenient to be able to use automatic storage and deep-copy semantics to manipulate optional values just as we do with ordinary values. Pointers do not have this semantics, so are inappropriate for the initialization and transport of optional values, yet are quite convenient for handling the access to the possible undefined value because of the idiomatic aid present in the OptionalPointee concept incarnated by pointers.

###### Optional<T> as a model of OptionalPointee

For value access operations `optional<>` uses operators `*` and `->` to lexically warn about the possibly uninitialized state appealing to the familiar pointer semantics w.r.t. to null pointers.

| Warning
However, it is particularly important to note that `optional<>` objects are not pointers. `optional<>` is not, and does not model, a pointer.

For instance, `optional<>` does not have shallow-copy so does not alias: two different optionals never refer to the same value unless `T` itself is a reference (but may have equivalent values). The difference between an `optional<T>` and a pointer must be kept in mind, particularly because the semantics of relational operators are different: since `optional<T>` is a value-wrapper, relational operators are deep: they compare optional values; but relational operators for pointers are shallow: they do not compare pointee values. As a result, you might be able to replace `optional<T>` by `T*` on some situations but not always. Specifically, on generic code written for both, you cannot use relational operators directly, and must use the template functions `equal_pointees()` and `less_pointees()` instead.