From c1e5d7e3318bf0cd597a2f06103886372bed1012 Mon Sep 17 00:00:00 2001
From: Jeremy Siek <jeremy.siek@gmail.com>
Date: Thu, 10 Apr 2003 12:44:20 +0000
Subject: [PATCH] new files

[SVN r1140]
---
 doc/access.png            | Bin 0 -> 11127 bytes
 doc/access2old.png        | Bin 0 -> 42175 bytes
 doc/new-iter-concepts.rst | 654 ++++++++++++++++++++++++++++++++++++++
 doc/oldeqnew.png          | Bin 0 -> 33786 bytes
 doc/traversal.png         | Bin 0 -> 9112 bytes
 5 files changed, 654 insertions(+)
 create mode 100644 doc/access.png
 create mode 100644 doc/access2old.png
 create mode 100644 doc/new-iter-concepts.rst
 create mode 100644 doc/oldeqnew.png
 create mode 100644 doc/traversal.png

diff --git a/doc/access.png b/doc/access.png
new file mode 100644
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diff --git a/doc/new-iter-concepts.rst b/doc/new-iter-concepts.rst
new file mode 100644
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--- /dev/null
+++ b/doc/new-iter-concepts.rst
@@ -0,0 +1,654 @@
+++++++++++++++++++++++
+ New Iterator Concepts
+++++++++++++++++++++++
+
+:Author: David Abrahams, Jeremy Siek, Thomas Witt
+:Contact: dave@boost-consulting.com, jsiek@osl.iu.edu, witt@ive.uni-hannover.de
+:organization: `Boost Consulting`_, Indiana University `Open Systems Lab`_, University of Hanover `Institute for Transport Railway Operation and Construction`_
+:date: $Date$
+
+:copyright: Copyright Dave Abrahams, Jeremy Siek, and Thomas Witt 2003. All rights reserved
+
+.. _`Boost Consulting`: http://www.boost-consulting.com
+.. _`Open Systems Lab`: http://www.osl.iu.edu
+.. _`Institute for Transport Railway Operation and Construction`: http://www.ive.uni-hannover.de
+
+:abstract: We propose a new system of iterator concepts that treat
+           access and positioning independently. This allows the
+           concepts to more closely match the requirements
+           of algorithms and provides better categorizations
+           of iterators that are used in practice.
+          
+.. contents:: Table of Contents
+
+============
+ Motivation
+============
+
+The standard iterator categories and requirements are flawed because
+they use a single hierarchy of concepts to address two orthogonal
+issues: *iterator traversal* and *value access*. The current iterator
+concept hierarchy is geared towards iterator traversal (hence the
+category names), while requirements that address value access sneak in
+at various places. The following table gives a summary of the current
+value access requirements in the iterator categories.
+
++------------------------+-------------------------------------------------------------------------+
+| Output Iterator        |  ``*i = a``                                                             |
++------------------------+-------------------------------------------------------------------------+
+| Input Iterator         | ``*i`` is convertible to ``T``                                          |
++------------------------+-------------------------------------------------------------------------+
+| Forward Iterator       | ``*i`` is ``T&`` (or ``const T&`` once                                  |
+|                        | `issue 200`_ is resolved)                                               |
++------------------------+-------------------------------------------------------------------------+
+| Random Access Iterator | ``i[n]`` is convertible to ``T`` (also ``i[n] = t`` is required for     |
+|                        | mutable iterators once `issue 299`_ is resolved)                        |
++------------------------+-------------------------------------------------------------------------+
+
+.. _issue 200: http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#200
+.. _issue 299: http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#299
+
+
+Because iterator traversal and value access are mixed together in a
+single hierarchy, many useful iterators can not be appropriately
+categorized. For example, ``vector<bool>::iterator`` is almost a
+random access iterator, but the return type is not ``bool&`` (see
+`issue 96`_ and Herb Sutter's paper J16/99-0008 = WG21
+N1185). Therefore, its iterators only meet the requirements of input
+iterator and output iterator. This is so nonintuitive that at least
+one implementation erroneously assigns ``random_access_iterator_tag``
+as its ``iterator_category``. Also, ``vector<bool>`` is not the only
+example of useful iterators that do not return true references: there
+is the often cited example of disk-based collections.
+
+.. _issue 96: http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#96
+
+Another example is a counting iterator, an iterator the returns a
+sequence of integers when incremented and dereferenced (see
+counting_iterator_).  There are two ways to implement this iterator,
+1) return a true reference from ``operator[]`` (a reference to an
+integer data member of the counting iterator) or 2) return the
+``value_type`` or a proxy from ``operator[]``. Option 1) runs into the
+problems discussed in `issue 198`_, the reference will not be valid
+after the iterator is destroyed. Option 2) is therefore a better
+choice, but then we have a counting iterator that cannot be a random
+access iterator.
+
+.. _counting_iterator: http://www.boost.org/libs/utility/counting_iterator.htm
+.. _issue 198: http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#198
+
+Yet another example is a transform iterator, an iterator adaptor that
+applies a unary function object to the dereference value of the
+wrapped iterator (see `transform_iterator`_).  For unary functions
+such as ``times`` the return type of ``operator*`` clearly needs
+to be the ``result_type`` of the function object, which is typically
+not a reference. However, with the current iterator requirements, if
+you wrap ``int*`` with a transform iterator, you do not get a random
+access iterator as expected, but an input iterator.
+
+.. _`transform_iterator`: http://www.boost.org/libs/utility/transform_iterator.htm
+
+A fourth example is found in the vertex and edge iterators of the
+`Boost Graph Library`_. These iterators return vertex and edge
+descriptors, which are lightweight handles created on-the-fly. They
+must be returned by-value. As a result, their current standard
+iterator category is ``input_iterator_tag``, which means that,
+strictly speaking, you could not use these iterators with algorithms
+like ``min_element()``. As a temporary solution, the concept
+`Multi-Pass Input Iterator`_ was introduced to describe the vertex and
+edge descriptors, but as the design notes for concept suggest, a
+better solution is needed.
+
+.. _Boost Graph Library: http://www.boost.org/libs/graph/doc/table_of_contents.html
+.. _Multi-Pass Input Iterator: http://www.boost.org/libs/utility/MultiPassInputIterator.html
+
+In short, there are many useful iterators that do not fit into the
+current standard iterator categories. As a result, the following bad
+things happen:
+
+- Iterators are often miss-categorized. 
+- Algorithm requirements are more strict than necessary, because they can 
+  not separate out the need for random-access from the need for a true reference 
+  return type.
+
+
+========================
+ Impact on the Standard
+========================
+
+The new iterator concepts are backwards compatible with the old
+iterator requirements. Iterators that satisfy the old requirements
+also satisfy appropriate concepts in the new system, and iterators
+modeling the new concepts will automatically satisfy the appropriate
+old requirements.
+
+The algorithms in the standard library benefit from the new iterator
+concepts because the new concepts provide a more accurate way to
+express their type requirements. The result is algorithms that are
+usable in more situations and have fewer type requirements.
+
+Forward Iterator -> Forward Traversal Iterator and Readable Iterator
+  ``find_end, find_first_of, adjacent_find, search, search_n, rotate_copy, lower_bound, upper_bound, equal_range, binary_search, min_element, max_element``
+
+Forward Iterator -> Readable Iterator and Writable Iterator
+  ``iter_swap``
+
+Forward Iterator -> Forward Traversal Iterator and Writable Iterator
+  ``fill, generate``
+
+Forward Iterator -> Forward Traversal Iterator and Swappable Iterator
+  ``swap_ranges, rotate``
+
+Forward Iterator -> Forward Traversal Iterator and Readable Iterator and Writable Iterator
+  ``replace, replace_if, remove, remove_if, unique``
+
+Bidirectional Iterator -> Bidirectional Traversal Iterator and Swappable Iterator
+  ``reverse, partition``
+
+Bidirectional Iterator -> Bidirectional Traversal Iterator and Readable Iterator, Bidirectional Iterator -> Bidirectional Traversal Iterator and Writable Iterator
+  ``copy_backwards``
+
+Bidirectional Iterator -> Bidirectional Traversal Iterator and Swappable Iterator and Readable Iterator
+  ``next_permutation, prev_permutation``
+
+Bidirectional Iterator -> Bidirectional Traversal Iterator and Readable Iterator and Writable Iterator
+  ``stable_partition, inplace_merge``
+
+Bidirectional Iterator -> Bidirectional Traversal Iterator and Readable Iterator
+  ``reverse_copy``
+
+Random Access Iterator -> Random Access Traversal Iterator and Swappable Iterator
+  ``random_shuffle, sort, stable_sort, partial_sort, nth_element, push_heap, pop_heap
+  make_heap, sort_heap``
+
+
+========
+ Design
+========
+
+The iterator requirements are be separated into two hierarchies. One
+set of concepts handles the syntax and semantics of value access:
+
+- Readable Iterator
+- Writable Iterator
+- Swappable Iterator
+- Readable Lvalue Iterator
+- Writable Lvalue Iterator
+
+The refinement relationships among these iterator concepts are given
+in the following diagram.
+
+.. image:: access.png
+
+The access concepts describe requirements related to ``operator*`` and
+``operator->``, including the ``value_type``, ``reference``, and
+``pointer`` associated types.
+
+The other set of concepts handles traversal:
+
+- Incrementable Iterator
+- Single-Pass Iterator
+- Forward Traversal Iterator
+- Bidirectional Traversal Iterator
+- Random Access Traversal Iterator
+
+The refinement relationships for the traversal concepts are in the
+following diagram.
+
+.. image:: traversal.png
+
+In addition to the iterator movement operators, such as
+``operator++``, the traversal concepts also include requirements on
+position comparison such as ``operator==`` and ``operator<``.
+
+The relationship between the new iterator concepts and the old are
+given in the following diagram.
+
+.. image:: oldeqnew.png
+
+Like the old iterator requirements, we provide tags for purposes of
+dispatching. There are two hierarchies of tags, one for the access
+concepts and one for the traversal concepts. We provide an access
+mechanism for mapping iterator types to these new tags. Our design
+opts to reuse ``iterator_traits<Iter>::iterator_category`` as the
+access mechanism. To enable this, a pair of access and traversal tags
+are combined using the new `iterator_tag` class.
+
+::
+
+  template <class AccessTag, class TraversalTag>
+  struct iterator_tag : <appropriate old category>
+  {
+    typedef AccessTag access;
+    typedef TraversalTag traversal;
+  };
+
+The ``iterator_tag`` class template inherits the appropriate iterator
+tag from the old requirements based on the new tags of the
+iterator. The algorithm for determining the old tag from the new tags
+picks the smallest old concept that includes all of the requirements
+of the access and traversal concepts.
+
+We also provide two helper classes that make it convenient to obtain
+the access and traversal tags of an iterator. These helper classes
+work both for iterators whose ``iterator_category`` is
+``iterator_tag`` and also for iterators using the original iterator
+categories.
+
+::
+
+  template <class Iterator> struct access_category { typedef ... type; };
+  template <class Iterator> struct traversal_category { typedef ... type; };
+
+
+The most difficult design decision concerned the ``operator[]``. The
+direct approach for specifying ``operator[]`` would have a return type
+of ``reference``; the same as ``operator*``. However, going in this
+direction would mean that an iterator satisfying the old Random Access
+Iterator requirements would not necessarily be a model of Readable or
+Writable Lvalue Iterator. Instead we have chosen a design that matches
+the resolution of `issue 299`_. So ``operator[]`` is only required to
+return something convertible to the ``value_type`` (for a Readable
+Iterator), and is required to support assignment ``i[n] = t`` (for a
+Writable Iterator).
+
+
+===============
+ Proposed Text
+===============
+
+Addition to [lib.iterator.requirements]
+=======================================
+
+Iterator Value Access Concepts [lib.iterator.value.access]
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+Readable Iterators [lib.readable.iterators]
+-------------------------------------------
+
+A class or built-in type ``X`` models the *Readable Iterator* concept
+for the value type ``T`` if the following expressions are valid and
+respect the stated semantics. ``U`` is the type of any specified
+member of type ``T``.
+
+ +------------------------------------------------------------------------------------------------------------------------------------------------------------+
+ | Readable Iterator Requirements (in addition to CopyConstructible)                                                                                          |
+ +--------------------------------------+---------------------------------------------------+-----------------------------------------------------------------+
+ | Expression                           | Return Type                                       | Assertion/Note/Precondition/Postcondition                       |
+ +======================================+===================================================+=================================================================+
+ | ``iterator_traits<X>::value_type``   | ``T``                                             | Any non-reference, non-cv-qualified type                        |
+ +--------------------------------------+---------------------------------------------------+-----------------------------------------------------------------+
+ | ``iterator_traits<X>::reference``    | Convertible to ``iterator_traits<X>::value_type`` |                                                                 |
+ +--------------------------------------+---------------------------------------------------+-----------------------------------------------------------------+
+ | ``access_category<X>::type``         | Convertible to ``readable_iterator_tag``          |                                                                 |
+ +--------------------------------------+---------------------------------------------------+-----------------------------------------------------------------+
+ | ``*a``                               | ``iterator_traits<X>::reference``                 | pre: ``a`` is dereferenceable. If ``a == b`` then               |
+ |                                      |                                                   | ``*a`` is equivalent to ``*b``                                  |
+ +--------------------------------------+---------------------------------------------------+-----------------------------------------------------------------+
+ | ``a->m``                             | ``U&``                                            | pre: ``(*a).m`` is well-defined.  Equivalent to ``(*a).m``      |
+ +--------------------------------------+---------------------------------------------------+-----------------------------------------------------------------+
+
+
+Writable Iterators [lib.writable.iterators]
+-------------------------------------------
+
+A class or built-in type ``X`` models the *Writable Iterator* concept
+if the following expressions are valid and respect the stated
+semantics.  A type ``T`` belongs to the *set of value types* of ``X``
+if, for an object ``t`` of type ``T``, ``*a = t`` is valid.
+
+ +------------------------------------------------------------------------------------------------------------------------------+
+ | Writable Iterator Requirements (in addition to CopyConstructible)                                                            |
+ +--------------------------------------+------------------------------------------+--------------------------------------------+
+ | Expression                           | Return Type                              |  Assertion/Note/Precondition/Postcondition |
+ +======================================+==========================================+============================================+
+ | ``access_category<X>::type``         | Convertible to ``writable_iterator_tag`` |                                            |
+ +--------------------------------------+------------------------------------------+--------------------------------------------+
+ | ``*a = t``                           |                                          | pre: The type of ``t`` is in the set of    |
+ |                                      |                                          | value types of ``X``                       |
+ +--------------------------------------+------------------------------------------+--------------------------------------------+
+
+
+Swappable Iterators [lib.swappable.iterators]
+---------------------------------------------
+
+A class or built-in type ``X`` models the *Swappable Iterator* concept
+if the following expressions are valid and respect the stated
+semantics.
+
+ +------------------------------------------------------------------------------------------------+
+ | Swappable Iterator Requirements (in addition to CopyConstructible)                             |
+ +------------------------------------+-------------+---------------------------------------------+
+ | Expression                         | Return Type |  Assertion/Note/Precondition/Postcondition  |
+ +====================================+=============+=============================================+
+ | ``iter_swap(a, b)``                | ``void``    |  post: the pointed to values are exchanged  |
+ +------------------------------------+-------------+---------------------------------------------+
+
+[*Note:* An iterator that is a model of the *Readable* and *Writable Iterator* concepts
+  is also a model of *Swappable Iterator*.  *--end note*]
+
+
+Readable Lvalue Iterators [lib.readable.lvalue.iterators]
+---------------------------------------------------------
+
+The *Readable Lvalue Iterator* concept adds the requirement that the
+``reference`` type be a reference to the value type of the iterator.
+
+ +--------------------------------------------------------------------------------------------------------------------------------------------------+
+ | Readable Lvalue Iterator Requirements (in addition to Readable Iterator)                                                                         |
+ +------------------------------------+-------------------------------------------------+-----------------------------------------------------------+
+ | Expression                         | Return Type                                     |  Assertion/Note/Precondition/Postcondition                |
+ +====================================+=================================================+===========================================================+
+ | ``iterator_traits<X>::reference``  | ``T&``                                          | ``T`` is *cv* ``iterator_traits<X>::value_type`` where    |
+ |                                    |                                                 |  *cv* is an optional cv-qualification                     |
+ +------------------------------------+-------------------------------------------------+-----------------------------------------------------------+
+ | ``access_category<X>::type``       | Convertible to ``readable_lvalue_iterator_tag`` |                                                           |
+ +------------------------------------+-------------------------------------------------+-----------------------------------------------------------+
+
+
+Writable Lvalue Iterators [lib.writable.lvalue.iterators]
+---------------------------------------------------------
+
+The *Writable Lvalue Iterator* concept adds the requirement that the
+``reference`` type be a non-const reference to the value type of the
+iterator.
+
+ +------------------------------------------------------------------------------------------------------------------------------------------------------+
+ | Writable Lvalue Iterator Requirements (in addition to Readable Lvalue Iterator)                                                                      |
+ +--------------------------------------+--------------------------------------------------+------------------------------------------------------------+
+ | Expression                           | Return Type                                      | Assertion/Note/Precondition/Postcondition                  |
+ +======================================+==================================================+============================================================+
+ | ``iterator_traits<X>::reference``    | ``iterator_traits<X>::value_type&``              |                                                            |
+ +--------------------------------------+--------------------------------------------------+------------------------------------------------------------+
+ | ``access_category<X>::type``         | Convertible to ``writable_lvalue_iterator_tag``  |                                                            |
+ +--------------------------------------+--------------------------------------------------+------------------------------------------------------------+
+
+
+Iterator Traversal Concepts [lib.iterator.traversal]
+++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+Incrementable Iterators [lib.incrementable.iterators]
+-----------------------------------------------------
+
+A class or built-in type ``X`` models the *Incrementable Iterator*
+concept if the following expressions are valid and respect the stated
+semantics.
+
+
+ +------------------------------------------------------------------------------------------------------------------------------------------------------+
+ | Incrementable Iterator Requirements (in addition to Assignable, Copy Constructible)                                                                  |
+ +--------------------------------------+--------------------------------------------------+------------------------------------------------------------+
+ | Expression                           | Return Type                                      | Assertion/Note/Precondition/Postcondition                  |
+ +======================================+==================================================+============================================================+
+ | ``++r``                              | ``X&``                                           | ``&r == &++r``                                             |
+ +--------------------------------------+--------------------------------------------------+------------------------------------------------------------+
+ | ``r++``                              | convertible to ``const X&``                      | ``{ X tmp = r; ++r; return tmp; }``                        |
+ +--------------------------------------+--------------------------------------------------+------------------------------------------------------------+
+ | ``traversal_category<X>::type``      |                                                  | Convertible to ``incrementable_iterator_tag``              |
+ +--------------------------------------+--------------------------------------------------+------------------------------------------------------------+
+
+
+Single Pass Iterators [lib.single.pass.iterators]
+-------------------------------------------------
+
+A class or built-in type ``X`` models the *Single Pass Iterator*
+concept if the following expressions are valid and respect the stated
+semantics.
+
+ +------------------------------------------------------------------------------------------------------------------------------------------------------+
+ | Single Pass Iterator Requirements (in addition to Incrementable Iterator and Equality Comparable)                                                    |
+ +----------------------------------+-------------------------+-----------------------------------------------------------------------------------------+
+ | Expression                       | Return Type             | Assertion/Note/Precondition/Postcondition/Semantics                                     |
+ +==================================+=========================+=========================================================================================+
+ | ``++r``                          | ``X&``                  | pre: ``r`` is dereferenceable; post: ``r`` is dereferenceable or ``r`` is past-the-end  |
+ +----------------------------------+-------------------------+-----------------------------------------------------------------------------------------+
+ | ``a != b``                       | convertible to ``bool`` | ``!(a == b)``                                                                           |
+ +----------------------------------+-------------------------+-----------------------------------------------------------------------------------------+
+ | ``traversal_category<X>::type``  |                         | Convertible to ``single_pass_iterator_tag``                                             |
+ +------------------------------------------------------------------------------------------------------------------------------------------------------+
+
+
+Forward Traversal Iterators [lib.forward.traversal.iterators]
+-------------------------------------------------------------
+
+A class or built-in type ``X`` models the *Forward Traversal Iterator*
+concept if the following expressions are valid and respect the stated
+semantics.
+
+ +----------------------------------------------------------------------------------------------------------------------------------+
+ | Forward Traversal Iterator Requirements (in addition to Single Pass Iterator)                                                    |
+ +------------------------------------------+--------------+------------------------------------------------------------------------+
+ | Expression                               | Return Type  |   Assertion/Note/Precondition/Postcondition/Semantics                  |
+ +==========================================+==============+========================================================================+
+ | ``++r``                                  | ``X&``       |   ``r == s`` and ``r`` is dereferenceable implies ``++r == ++s.``      |
+ +------------------------------------------+--------------+------------------------------------------------------------------------+
+ | ``iterator_traits<X>::difference_type``  |              |   A signed integral type representing the distance between iterators   |
+ +------------------------------------------+--------------+------------------------------------------------------------------------+
+ | ``traversal_category<X>::type``          |              |   Convertible to ``forward_traversal_iterator_tag``                    |
+ +------------------------------------------+--------------+------------------------------------------------------------------------+
+
+
+Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]
+-------------------------------------------------------------------------
+
+A class or built-in type ``X`` models the *Bidirectional Traversal
+Iterator* concept if the following expressions are valid and respect
+the stated semantics.
+
+   +-------------------------------------------------------------------------------------------------------------+
+   |Bidirectional Traversal Iterator Requirements (in addition to Forward Traversal Iterator)                    |
+   +-----------------------------------------+-------------+-----------------------------------------------------+
+   | Expression                              | Return Type | Assertion/Note/Precondition/Postcondition/Semantics |
+   +=========================================+=============+=====================================================+
+   | ``--r``                                 | ``X&``      |pre: there exists ``s`` such that ``r == ++s``.      |
+   |                                         |             |post: ``s`` is dereferenceable. ``--(++r) == r``.    |
+   |                                         |             |``--r == --s`` implies ``r == s``. ``&r == &--r``.   |
+   +-----------------------------------------+-------------+-----------------------------------------------------+
+   |``r--``                                  |convertible  |``{ X tmp = r; --r; return tmp; }``                  |
+   |                                         |to const     |                                                     |
+   |                                         |``X&``       |                                                     |
+   +-----------------------------------------+-------------+-----------------------------------------------------+
+   | ``traversal_category<X>::type``         |             | Convertible to                                      |
+   |                                         |             | ``bidirectional_traversal_iterator_tag``            |
+   |                                         |             |                                                     |
+   +-----------------------------------------+-------------+-----------------------------------------------------+
+
+
+Random Access Traversal Iterators [lib.random.access.traversal.iterators]
+-------------------------------------------------------------------------
+
+A class or built-in type ``X`` models the *Random Access Traversal
+Iterator* concept if the following expressions are valid and respect
+the stated semantics.
+
+   +------------------------------------------------------------------------------------------------------------------------------------------------+
+   | Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal Iterator)                                                |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   | Expression                     | Return Type                           | Operational Semantics        |   Assertion/Note/Pre/Post-condition    |
+   +================================+=======================================+==============================+========================================+
+   |``r += n``                      | ``X&``                                |``{ Distance m = n; if (m >=  |                                        |
+   |                                |                                       |0) while (m--) ++r; else while|                                        |
+   |                                |                                       |(m++) --r; return r; }``      |                                        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |      ``a + n``, ``n + a``      | ``X``                                 |``{ X tmp = a; return tmp +=  |                                        |
+   |                                |                                       |n; }``                        |                                        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``r -= n``                      | ``X&``                                |``return r += -n``            |                                        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``a - n``                       | ``X``                                 |``{ X tmp = a; return tmp -=  |                                        |
+   |                                |                                       |n; }``                        |                                        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``b - a``                       |``Distance``                           |``a < b ?  distance(a,b) :    |pre: there exists a value ``n`` of      |
+   |                                |                                       |-distance(b,a)``              |``Distance`` such that ``a + n == b``.  |
+   |                                |                                       |                              |``b == a + (b - a)``.                   |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``a[n]``                        |convertible to T                       |``*(a + n)``                  |Not required to return an lvalue        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``a[n] = t``                    |convertible to T                       |``*(a + n) = t``              |Not required to return an lvalue        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``a < b``                       |convertible to ``bool``                |``b - a > 0``                 |``<`` is a total ordering relation      |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``a > b``                       |convertible to ``bool``                |``b < a``                     |``>`` is a total ordering relation      |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``a >= b``                      |convertible to ``bool``                |``!(a < b)``                  |                                        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   |``a <= b``                      |convertible to ``bool``                |``!(a > b)``                  |                                        |
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+   | ``traversal_category<X>::type``|                                       |                              |Convertible to                          |
+   |                                |                                       |                              |``random_access_traversal_iterator_tag``|
+   +--------------------------------+---------------------------------------+------------------------------+----------------------------------------+
+
+
+
+Addition to [lib.iterator.synopsis]
+===================================
+
+::
+
+  // lib.iterator.traits, traits and tags
+  template <class Iterator> struct access_category;
+  template <class Iterator> struct traversal_category;
+
+  template <class AccessTag, class TraversalTag>
+  struct iterator_tag : <appropriate old category> {
+    typedef AccessTag access;
+    typedef TraversalTag traversal;
+  };
+
+  struct readable_iterator_tag { };
+  struct writable_iterator_tag { };
+  struct swappable_iterator_tag { };
+  struct readable_writable_iterator_tag { };
+  struct readable_lvalue_iterator_tag { };
+  struct writable_lvalue_iterator_tag
+    : virtual public readable_writable_iterator_tag,
+      virtual public readable_lvalue_iterator_tag { };
+
+  struct incrementable_iterator_tag { };
+  struct single_pass_iterator_tag : public incrementable_iterator_tag { };
+  struct forward_traversal_tag : public single_pass_iterator_tag { };
+  struct bidirectional_traversal_tag : public forward_traversal_tag { };
+  struct random_access_traversal_tag : bidirectional_traversal_tag { };
+
+  struct null_category_tag { };
+  struct input_output_iterator_tag : input_iterator_tag, output_iterator_tag {};
+
+
+Addition to [lib.iterator.traits]
+=================================
+
+The ``iterator_tag`` class template is an iterator category tag that
+encodes the access and traversal tags in addition to being compatible
+with the original iterator tags. The ``iterator_tag`` class inherits
+from one of the original iterator tags according to the following
+pseudo-code.
+
+::
+
+   inherit-category(access-tag, traversal-tag) {
+     if (access-tag is convertible to readable_lvalue_iterator_tag
+         or access-tag is convertible to writable_lvalue_iterator_tag) {
+       if (traversal-tag is convertible to random_access_traversal_tag)
+         return random_access_iterator_tag;
+       else if (traversal-tag is convertible to bidirectional_traversal_tag)
+         return bidirectional_iterator_tag;
+       else if (traversal-tag is convertible to forward_traversal_tag)
+         return forward_iterator_tag;
+       else
+         return null_category_tag;
+     } else if (access-tag is convertible to readable_writable_iterator_tag
+                and traversal-tag is convertible to single_pass_iterator_tag)
+       return input_output_iterator_tag;
+     else if (access-tag is convertible to readable_iterator_tag
+              and traversal-tag is convertible to single_pass_iterator_tag)
+       return input_iterator_tag;
+     else if (access-tag is convertible to writable_iterator_tag
+              and traversal-tag is convertible to incrementable_iterator_tag)
+       return output_iterator_tag;
+     else
+       return null_category_tag
+   }
+
+
+The ``access_category`` and ``traversal_category`` class templates are
+traits classes. For iterators whose
+``iterator_traits<Iter>::iterator_category`` type is ``iterator_tag``,
+the ``access_category`` and ``traversal_category`` traits access the
+``access`` and ``traversal`` member types within ``iterator_tag``.
+For iterators whose ``iterator_traits<Iter>::iterator_category`` type
+is not ``iterator_tag`` and instead is a tag convertible to one of the
+original tags, an appropriate traversal and access tags are deduced.
+
+::
+
+  template <class Iterator>
+  struct access_category {
+    // pseudo code
+    cat = iterator_traits<Iterator>::iterator_category;
+    if (cat == iterator_tag<Access,Traversal>)
+      return Access;
+    else if (cat is convertible to forward_iterator_tag)
+      if (iterator_traits<Iterator>::reference is a const reference)
+        return readable_lvalue_iterator_tag;
+      else
+        return writable_lvalue_iterator_tag;
+    else if (cat is convertible to input_iterator_tag)
+      return readable_iterator_tag;
+    else if (cat is convertible to output_iterator_tag)
+      return writable_iterator_tag;
+    else
+      return null_category_tag;
+  };
+
+  template <class Iterator>
+  struct traversal_category {
+    // pseudo code
+    cat = iterator_traits<Iterator>::iterator_category;
+    if (cat == iterator_tag<Access,Traversal>)
+      return Traversal;
+    else if (cat is convertible to random_access_iterator_tag)
+      return random_access_traversal_tag;
+    else if (cat is convertible to bidirectional_iterator_tag)
+      return bidirectional_traversal_tag;
+    else if (cat is convertible to forward_iterator_tag)
+      return forward_traversal_tag;
+    else if (cat is convertible to input_iterator_tag)
+      return single_pass_iterator_tag;
+    else if (cat is convertible to output_iterator_tag)
+      return incrementable_iterator_tag;
+    else
+      return null_category_tag;
+  };
+
+The following specializations provide the access and traversal
+categories for pointer types.
+
+::
+
+  template <typename T>
+  struct access_category<const T*>
+  {
+    typedef readable_lvalue_iterator_tag type;
+  };
+  template <typename T>
+  struct access_category<T*>
+  {
+    typedef writable_lvalue_iterator_tag type;
+  };
+
+  template <typename T>
+  struct traversal_category<T*>
+  {
+    typedef random_access_traversal_tag type;
+  };
+
+
+
+..
+ LocalWords:  Abrahams Siek Witt const bool Sutter's WG int UL LI href Lvalue
+ LocalWords:  ReadableIterator WritableIterator SwappableIterator cv pre iter
+ LocalWords:  ConstantLvalueIterator MutableLvalueIterator CopyConstructible
+ LocalWords:  ForwardTraversalIterator BidirectionalTraversalIterator lvalue
+ LocalWords:  RandomAccessTraversalIterator dereferenceable Incrementable tmp
+ LocalWords:  incrementable xxx min prev inplace png oldeqnew AccessTag struct
+ LocalWords:  TraversalTag typename
diff --git a/doc/oldeqnew.png b/doc/oldeqnew.png
new file mode 100644
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diff --git a/doc/traversal.png b/doc/traversal.png
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