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New Iterator Concepts

Author: David Abrahams, Jeremy Siek, Thomas Witt
Contact: dave@boost-consulting.com, jsiek@osl.iu.edu, witt@styleadvisor.com
Organization: Boost Consulting, Indiana University Open Systems Lab, Zephyr Associates, Inc.
Date: 2004-11-01
Number:This is a revised version of n1550=03-0133, which was accepted for Technical Report 1 by the C++ standard committee's library working group. This proposal is a revision of paper n1297, n1477, and n1531.
Copyright: Copyright David Abrahams, Jeremy Siek, and Thomas Witt 2003.
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.

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. As a result, many algorithms with requirements expressed in terms of the iterator categories are too strict. Also, many real-world iterators can not be accurately categorized. A proxy-based iterator with random-access traversal, for example, may only legally have a category of "input iterator", so generic algorithms are unable to take advantage of its random-access capabilities. 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.

Value Access Requirements in Existing 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)

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, the iterators of vector<bool> only meet the requirements of input iterator and output iterator. This is so nonintuitive that the C++ standard contradicts itself on this point. In paragraph 23.2.4/1 it says that a vector is a sequence that supports random access iterators.

Another difficult-to-categorize iterator is the transform iterator, an adaptor which applies a unary function object to the dereferenced value of the some underlying 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. Because random access iterators are required to return lvalues from operator*, if you wrap int* with a transform iterator, you do not get a random access iterator as might be expected, but an input iterator.

A third 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 the concept suggest, a better solution is needed.

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:

Impact on the Standard

This proposal for TR1 is a pure extension. Further, the new iterator concepts are backward-compatible with the old iterator requirements, and old iterators are forward-compatible with the new iterator concepts. That is to say, 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.

Possible (but not proposed) Changes to the Working Paper

The extensions in this paper suggest several changes we might make to the working paper for the next standard. These changes are not a formal part of this proposal for TR1.

Changes to Algorithm Requirements

The algorithms in the standard library could 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.

For the next working paper (but not for TR1), the committee should consider the following changes to the type requirements of algorithms. These changes are phrased as textual substitutions, listing the algorithms to which each textual substitution applies.

Forward Iterator -> Forward Traversal Iterator and Readable Iterator

find_end, adjacent_find, search, search_n, rotate_copy, lower_bound, upper_bound, equal_range, binary_search, min_element, max_element

Forward Iterator (1) -> Single Pass Iterator and Readable Iterator, Forward Iterator (2) -> Forward Traversal Iterator and Readable Iterator

find_first_of

Forward Iterator -> Readable Iterator and Writable Iterator

iter_swap

Forward Iterator -> Single Pass Iterator and Writable Iterator

fill, generate

Forward Iterator -> Forward Traversal Iterator and Swappable Iterator

rotate

Forward Iterator (1) -> Swappable Iterator and Single Pass Iterator, Forward Iterator (2) -> Swappable Iterator and Incrementable Iterator

swap_ranges
Forward Iterator -> Forward Traversal Iterator and Readable Iterator and Writable Iterator
remove, remove_if, unique

Forward Iterator -> Single Pass Iterator and Readable Iterator and Writable Iterator

replace, replace_if
Bidirectional Iterator -> Bidirectional Traversal Iterator and Swappable Iterator
reverse
Bidirectional Iterator -> Bidirectional Traversal Iterator and Readable and Swappable Iterator
partition

Bidirectional Iterator (1) -> Bidirectional Traversal Iterator and Readable Iterator, Bidirectional Iterator (2) -> 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 Readable and Writable Iterator
random_shuffle, sort, stable_sort, partial_sort, nth_element, push_heap, pop_heap make_heap, sort_heap
Input Iterator (2) -> Incrementable Iterator and Readable Iterator
equal, mismatch
Input Iterator (2) -> Incrementable Iterator and Readable Iterator
transform

Deprecations

For the next working paper (but not for TR1), the committee should consider deprecating the old iterator tags, and std::iterator_traits, since it will be superceded by individual traits metafunctions.

vector<bool>

For the next working paper (but not for TR1), the committee should consider reclassifying vector<bool>::iterator as a Random Access Traversal Iterator and Readable Iterator and Writable Iterator.

Design

The iterator requirements are to be separated into two groups. One set of concepts handles the syntax and semantics of value access:

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:

The refinement relationships for the traversal concepts are in the following diagram.

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 reason for the fine grain slicing of the concepts into the Incrementable and Single Pass is to provide concepts that are exact matches with the original input and output iterator requirements.

This proposal also includes a concept for specifying when an iterator is interoperable with another iterator, in the sense that int* is interoperable with int const*.

The relationship between the new iterator concepts and the old are given in the following diagram.

oldeqnew.png

Like the old iterator requirements, we provide tags for purposes of dispatching based on the traversal concepts. The tags are related via inheritance so that a tag is convertible to another tag if the concept associated with the first tag is a refinement of the second tag.

Our design reuses iterator_traits<Iter>::iterator_category to indicate an iterator's traversal capability. To specify capabilities not captured by any old-style iterator category, an iterator designer can use an iterator_category type that is convertible to both the the most-derived old iterator category tag which fits, and the appropriate new iterator traversal tag.

We do not provide tags for the purposes of dispatching based on the access concepts, in part because we could not find a way to automatically infer the right access tags for old-style iterators. An iterator's writability may be dependent on the assignability of its value_type and there's no known way to detect whether an arbitrary type is assignable. Fortunately, the need for dispatching based on access capability is not as great as the need for dispatching based on traversal capability.

A 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 preferred resolution of issue 299: 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]

In the tables below, X is an iterator type, a is a constant object of type X, R is std::iterator_traits<X>::reference, T is std::iterator_traits<X>::value_type, and v is a constant object of type T.

Readable Iterators [lib.readable.iterators]

A class or built-in type X models the Readable Iterator concept for value type T if, in addition to X being Assignable and Copy Constructible, 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 Assignable and Copy Constructible)
Expression Return Type Note/Precondition
iterator_traits<X>::value_type T Any non-reference, non-cv-qualified type
*a Convertible to T
pre: a is dereferenceable. If a == b then *a
is equivalent to *b.
a->m U& pre: 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, in addition to X being Copy Constructible, the following expressions are valid and respect the stated semantics. Writable Iterators have an associated set of value types.

Writable Iterator Requirements (in addition to Copy Constructible)
Expression Return Type Precondition
*a = o   pre: The type of o 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, in addition to X being Copy Constructible, the following expressions are valid and respect the stated semantics.

Swappable Iterator Requirements (in addition to Copy Constructible)
Expression Return Type Postcondition
iter_swap(a, b) void the pointed to values are exchanged

[Note: An iterator that is a model of the Readable Iterator and Writable Iterator concepts is also a model of Swappable Iterator. --end note]

Lvalue Iterators [lib.lvalue.iterators]

The Lvalue Iterator concept adds the requirement that the return type of operator* type be a reference to the value type of the iterator.

Lvalue Iterator Requirements
Expression Return Type Note/Assertion
*a T& T is cv iterator_traits<X>::value_type where cv is an optional cv-qualification. pre: a is dereferenceable.

If X is a Writable Iterator then a == b if and only if *a is the same object as *b. If X is a Readable Iterator then a == b implies *a is the same object as *b.

Iterator Traversal Concepts [lib.iterator.traversal]

In the tables below, X is an iterator type, a and b are constant objects of type X, r and s are mutable objects of type X, T is std::iterator_traits<X>::value_type, and v is a constant object of type T.

Incrementable Iterators [lib.incrementable.iterators]

A class or built-in type X models the Incrementable Iterator concept if, in addition to X being Assignable and Copy Constructible, the following expressions are valid and respect the stated semantics.

Incrementable Iterator Requirements (in addition to Assignable, Copy Constructible)
Expression Return Type Assertion
++r X& &r == &++r
r++    
*r++    
iterator_traversal<X>::type Convertible to incrementable_traversal_tag  

If X is a Writable Iterator then X a(r++); is equivalent to X a(r); ++r; and *r++ = o is equivalent to *r = o; ++r. If X is a Readable Iterator then T z(*r++); is equivalent to T z(*r); ++r;.

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 Operational Semantics Assertion/ Pre-/Post-condition
++r X&   pre: r is dereferenceable; post: r is dereferenceable or r is past-the-end
a == b convertible to bool   == is an equivalence relation over its domain
a != b convertible to bool !(a == b)  
iterator_traversal<X>::type Convertible to single_pass_traversal_tag    

Forward Traversal Iterators [lib.forward.traversal.iterators]

A class or built-in type X models the Forward Traversal Iterator concept if, in addition to X meeting the requirements of Default Constructible and Single Pass Iterator, the following expressions are valid and respect the stated semantics.

Forward Traversal Iterator Requirements (in addition to Default Constructible and Single Pass Iterator)
Expression Return Type Assertion/Note
X u; X& note: u may have a singular value.
++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  
iterator_traversal<X>::type Convertible to forward_traversal_tag  

Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]

A class or built-in type X models the Bidirectional Traversal Iterator concept if, in addition to X meeting the requirements of Forward Traversal Iterator, the following expressions are valid and respect the stated semantics.

Bidirectional Traversal Iterator Requirements (in addition to Forward Traversal Iterator)
Expression Return Type Operational Semantics Assertion/ Pre-/Post-condition
--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 to const X&
{
  X tmp = r;
  --r;
  return tmp;
}
 
iterator_traversal<X>::type Convertible to bidirectional_traversal_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. In the table below, Distance is iterator_traits<X>::difference_type and n represents a constant object of type Distance.

Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal Iterator)
Expression Return Type Operational Semantics Assertion/ Precondition
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) : -distance(b,a) pre: there exists a value n of Distance such that a + n == b. b == a + (b - a).
a[n] convertible to T *(a + n) pre: a is a Readable Iterator
a[n] = v convertible to T *(a + n) = v pre: a is a Writable Iterator
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)  
iterator_traversal<X>::type Convertible to random_access_traversal_tag    

Interoperable Iterators [lib.interoperable.iterators]

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).

Addition to [lib.iterator.synopsis]

// lib.iterator.traits, traits and tags
template <class Iterator> struct is_readable_iterator;
template <class Iterator> struct iterator_traversal;

struct incrementable_traversal_tag { };
struct single_pass_traversal_tag : incrementable_traversal_tag { };
struct forward_traversal_tag : single_pass_traversal_tag { };
struct bidirectional_traversal_tag : forward_traversal_tag { };
struct random_access_traversal_tag : bidirectional_traversal_tag { };

Addition to [lib.iterator.traits]

The is_readable_iterator class template satisfies the UnaryTypeTrait requirements.

Given an iterator type X, is_readable_iterator<X>::value yields true if, for an object a of type X, *a is convertible to iterator_traits<X>::value_type, and false otherwise.

iterator_traversal<X>::type is

category-to-traversal(iterator_traits<X>::iterator_category) 

where category-to-traversal is defined as follows

category-to-traversal(C) =
    if (C is convertible to incrementable_traversal_tag)
        return C;
    else if (C is convertible to random_access_iterator_tag)
        return random_access_traversal_tag;
    else if (C is convertible to bidirectional_iterator_tag)
        return bidirectional_traversal_tag;
    else if (C is convertible to forward_iterator_tag)
        return forward_traversal_tag;
    else if (C is convertible to input_iterator_tag)
        return single_pass_traversal_tag;
    else if (C is convertible to output_iterator_tag)
        return incrementable_traversal_tag;
    else
        the program is ill-formed

Footnotes

The UnaryTypeTrait concept is defined in n1519; the LWG is considering adding the requirement that specializations are derived from their nested ::type.