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Consider these functions which should return a value but which might not have a value to return:
double sqrt(double n );
          char get_async_input();
          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.
          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:
T,
              it is modeling an initialized optional.
            T,
              it is modeling an uninitialized optional.
            T
              models testing if the optional is initialized
            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:
T), it is modeling an initialized
              optional.
            T
              from an empty container models the undefined behavior of trying to
              access the value of an uninitialized optional
            
          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:
        
T's swap).
            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.
          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.
        
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.
        
          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]](../../../../../doc/src/images/warning.png) | Warning | 
|---|---|
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            However, it is particularly important to note that  | 
          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.