What is singular and non-singular values in the context of STL iterators?

Question

The section §24.1/5 from the C++ Standard (2003) reads,

Just as a regular pointer to an array guarantees that there is a pointer value pointing pa

Answer 1

What is singular value and nonsingular value? How are they defined? And where?

Let us use the simplest incarnation of an Iterator: the pointer.

For a pointer:

• the singular value alluded to is the NULL value an uninitialized value.
• a non-singular value is an explicitly initialized value, it may not be dereferencable still (the past-the-end pointer shall not be dereferenced)

I would say that the NULL pointer is a singular value, though not the only one, since it represents the absence of value.

What is the equivalence for regular iterators ?

std::vector::iterator it;, the default constructor of most iterators (those linked to a container) create a singular value. Since it's not tied to a container, any form of navigation (increment, decrement, ...) is meaningless.

How and why dereferenceable values are always nonsingular ?

Singular values, by definition, represent the absence of a real value. They appear in many languages: Python's None, C#'s null, C's NULL, C++'s std::nullptr. The catch is that in C or C++, they may also be simple garbage... (whatever was there in memory before)

Is a default constructed iterator a singular value ?

Not necessarily, I guess. It is not required by the standard, and one could imagine the use of a sentinel object.