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new files for iterator concepts

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[SVN r22004]
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Jeremy Siek
2004-01-27 17:03:46 +00:00
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Interoperable Iterator Concept
..............................
A class or built-in type ``X`` that models Single Pass Iterator is
*interoperable with* a class or built-in type ``Y`` that also models
Single Pass Iterator if the following expressions are valid and
respect the stated semantics. In the tables below, ``x`` is an object
of type ``X``, ``y`` is an object of type ``Y``, ``Distance`` is
``iterator_traits<Y>::difference_type``, and ``n`` represents a
constant object of type ``Distance``.
+-----------+-----------------------+---------------------------------------------------+
|Expression |Return Type |Assertion/Precondition/Postcondition |
+===========+=======================+===================================================+
|``y = x`` |``Y`` |post: ``y == x`` |
+-----------+-----------------------+---------------------------------------------------+
|``Y(x)`` |``Y`` |post: ``Y(x) == x`` |
+-----------+-----------------------+---------------------------------------------------+
|``x == y`` |convertible to ``bool``|``==`` is an equivalence relation over its domain. |
+-----------+-----------------------+---------------------------------------------------+
|``y == x`` |convertible to ``bool``|``==`` is an equivalence relation over its domain. |
+-----------+-----------------------+---------------------------------------------------+
|``x != y`` |convertible to ``bool``|``bool(a==b) != bool(a!=b)`` over its domain. |
+-----------+-----------------------+---------------------------------------------------+
|``y != x`` |convertible to ``bool``|``bool(a==b) != bool(a!=b)`` over its domain. |
+-----------+-----------------------+---------------------------------------------------+
If ``X`` and ``Y`` both model Random Access Traversal Iterator then
the following additional requirements must be met.
+-----------+-----------------------+---------------------+--------------------------------------+
|Expression |Return Type |Operational Semantics|Assertion/ Precondition |
+===========+=======================+=====================+======================================+
|``x < y`` |convertible to ``bool``|``y - x > 0`` |``<`` is a total ordering relation |
+-----------+-----------------------+---------------------+--------------------------------------+
|``y < x`` |convertible to ``bool``|``x - y > 0`` |``<`` is a total ordering relation |
+-----------+-----------------------+---------------------+--------------------------------------+
|``x > y`` |convertible to ``bool``|``y < x`` |``>`` is a total ordering relation |
+-----------+-----------------------+---------------------+--------------------------------------+
|``y > x`` |convertible to ``bool``|``x < y`` |``>`` is a total ordering relation |
+-----------+-----------------------+---------------------+--------------------------------------+
|``x >= y`` |convertible to ``bool``|``!(x < y)`` | |
+-----------+-----------------------+---------------------+--------------------------------------+
|``y >= x`` |convertible to ``bool``|``!(y < x)`` | |
+-----------+-----------------------+---------------------+--------------------------------------+
|``x <= y`` |convertible to ``bool``|``!(x > y)`` | |
+-----------+-----------------------+---------------------+--------------------------------------+
|``y <= x`` |convertible to ``bool``|``!(y > x)`` | |
+-----------+-----------------------+---------------------+--------------------------------------+
|``y - x`` |``Distance`` |``distance(Y(x),y)`` |pre: there exists a value ``n`` of |
| | | |``Distance`` such that ``x + n == y``.|
| | | |``y == x + (y - x)``. |
+-----------+-----------------------+---------------------+--------------------------------------+
|``x - y`` |``Distance`` |``distance(y,Y(x))`` |pre: there exists a value ``n`` of |
| | | |``Distance`` such that ``y + n == x``.|
| | | |``x == y + (x - y)``. |
+-----------+-----------------------+---------------------+--------------------------------------+