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### 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