Document number: | J16/01-0011 = WG21 N1297
Date: | March 21, 2001
Author: | Jeremy Siek, University of Notre Dame
| jsiek@lsc.nd.edu

#
Improved Iterator Categories and Requirements

## Introduction

The standard iterator categories and requirements are flawed because they use a single hierarchy of requirements to address two orthogonal issues: iterator traversal and dereference return type. The current iterator requirement hierarchy is mainly geared towards iterator traversal (hence the category names), while requirements that address dereference return type sneak in at various places. The following table gives a summary of the current dereference return type requirements in the iterator categories.

Table 1. Summary of current dereference return type requirements.

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` (which is odd because the operational semantics say `i[n]` is equivalent to `*(i + n)` which would have a return type of `T&`)

## Examples of useful iterators that do not ``fit''

Because of the mixing of iterator traversal and dereference return type, 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 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.

Another example is a counting iterator, an iterator the returns a sequence of integers when incremented and dereferenced (see `boost::counting_iterator`). There are two ways to implement this iterator, 1) make the `reference` type be a true reference (a reference to an integer data member of the counting iterator) or 2) make the `reference` type be the same as the `value_type`. 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.

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 `boost::transform_iterator`). For unary functions such as `std::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.

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 `std::input_iterator_tag`, which means that, strictly speaking, you could not use these iterators with algorithms like `std::min_element()`. As a temporary solution, we introduced the concept Multi-Pass Input Iterator to describe the vertex and edge descriptors, but as the design notes for 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:

- 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.

## Proposal for new iterator categories and requirements

The iterator requirements should be separated into two hierarchies. One set of concepts handles the return type semantics:

- Readable Iterator
- Writable Iterator
- Swappable Iterator
- Constant Lvalue Iterator
- Mutable Lvalue Iterator

The other set of concepts handles iterator traversal:

- Forward Traversal Iterator
- Bidirectional Traversal Iterator
- Random Access Traversal Iterator

The current Input Iterator and Output Iterator requirements will continue to be used as is. Note that Input Iterator implies Readable Iterator and Output Iterator implies Writable Iterator.

Note: we considered defining a Single-Pass Iterator, which could be combined with Readable or Writable Iterator to replace the Input and Output Iterator requirements. We rejected this idea because there are several differences between Input and Output Iterators that make it hard to merge them: Input Iterator requires Equality Comparable while Output Iterator does not and Input Iterator requires Assignable while Output Iterator does not.

### New categories and traits classes

Each of the new iterator requirements will need a category tag.

    namespace std {

      // Return Type Categories
      struct readable_iterator_tag { };
      struct writable_iterator_tag { };
      struct swappable_iterator_tag { };
      struct mutable_lvalue_iterator_tag : virtual public writable_iterator_tag,
        virtual public readable_iterator_tag { };
      struct constant_lvalue_iterator_tag : public readable_iterator_tag { };

      // Traversal Categories
      struct forward_traversal_tag { };
      struct bidirectional_traversal_tag : public forward_traversal_tag { };
      struct random_access_traversal_tag : public bidirectional_traversal_tag { };

    }

And there will need to be a way to access these category tags using a traits mechanism. Adding new typedefs to `std::iterator_traits` is not an acceptable solution because that would break every existing iterator. Instead, we propose two new traits classes. It is important that these traits classes are backward compatible, that is, they should work with any iterator for which there is a valid definition of `std::iterator_traits`. This can be accomplished by making the default behavior of the traits classes map the `iterator_category` of the iterator to the appropriate return or traversal category. For new iterators, either specializations of these traits classes can be defined, or the iterator can provide nested typedefs, and inherit from `new_iterator_base` (which is just a signal to the traits class that it is a new iterator). As with `std::iterator_traits`, specializations for `T*` are provided.

    namespace std {

      struct new_iterator_base { };

      template <typename Iterator>
      struct return_category
      {
        // Pseudo-code
        if (Iterator inherits from new_iterator_base) {
          typedef typename Iterator::return_category type;
        } else {
          typedef std::iterator_traits<Iterator> OldTraits;
          typedef typename OldTraits::iterator_category Cat;
          if (Cat inherits from std::forward_iterator_tag)
    	if (is-const(T))
    	  typedef boost::constant_lvalue_iterator_tag type;
    	else
    	  typedef boost::mutable_lvalue_iterator_tag type;
          else if (Cat inherits from std::input_iterator_tag)
    	typedef boost::readable_iterator_tag type;
          else if (Cat inherits from std::output_iterator_tag)
    	typedef boost::writable_iterator_tag type;
        }
      };

      template <typename T>
      struct return_category<T*>
      {
        // Pseudo-code
        if (is-const(T))
          typedef boost::constant_lvalue_iterator_tag type;
        else
          typedef boost::mutable_lvalue_iterator_tag type;
      };

      template <typename Iterator>
      struct traversal_category
      {
        // Pseudo-code
        if (Iterator inherits from new_iterator_base) {
          typedef typename Iterator::traversal_category type;
        } else {
          typedef std::iterator_traits<Iterator> OldTraits;
          typedef typename OldTraits::iterator_category Cat;

          if (Cat inherits from std::random_access_iterator_tag)
    	typedef boost::random_access_traversal_tag type;
          else if (Cat inherits from std::bidirectional_iterator_tag)
    	typedef boost::bidirectional_traversal_tag type;
          else if (Cat inherits from std::forward_iterator_tag)
    	typedef boost::forward_traversal_tag type;
        }
      };

      template <typename T>
      struct traversal_category<T*>
      {
        typedef boost::random_access_traversal_tag type;
      };

    }

## Impact on the Standard Algorithms

Many of the standard algorithms place more requirements than necessary on their iterator parameters due to the coarseness of the current iterator categories. By using the new iterator categories a better fit can be achieved, thereby increasing the reusability of the algorithms. These changes will not affect user-code, though they will require changes by standard implementers: dispatching should be based on the new categories, and in places return values may need to be handled more carefully. In particular, uses of `std::swap()` will need to be replaced with `std::iter_swap()`, and `std::iter_swap()` will need to call `std::swap()`.

Table 2. Requirement changes for standard algorithms.

Algorithm | Requirement Change
--- | ---
find_end | Forward Iterator -> Forward Traversal Iterator and Readable Iterator
find_first_of
adjacent_find
search
search_n
rotate_copy
lower_bound
upper_bound
equal_range
binary_search
min_element
max_element
iter_swap | Forward Iterator -> Swappable Iterator
fill | Forward Iterator -> Forward Traversal Iterator and Writable Iterator
generate
swap_ranges | Forward Iterator -> Forward Traversal Iterator and Swappable Iterator
rotate
replace | Forward Iterator -> Forward Traversal Iterator and Readable Iterator and Writable Iterator
replace_if
remove
remove_if
unique
reverse | Bidirectional Iterator -> Bidirectional Traversal Iterator and Swappable Iterator
partition
copy_backwards | Bidirectional Iterator -> Bidirectional Traversal Iterator and Readable Iterator Bidirectional Iterator -> Bidirectional Traversal Iterator and Writable Iterator
next_permutation | Bidirectional Iterator -> Bidirectional Traversal Iterator and Swappable Iterator and Readable Iterator
prev_permutation
stable_partition | Bidirectional Iterator -> Bidirectional Traversal Iterator and Readable Iterator and Writable Iterator
inplace_merge
reverse_copy | Bidirectional Iterator -> Bidirectional Traversal Iterator and Readable Iterator
random_shuffle | Random Access Iterator -> Random Access Traversal Iterator and Swappable Iterator
sort
stable_sort
partial_sort
nth_element
push_heap
pop_heap
make_heap
sort_heap

## The New Iterator Requirements

### Notation

`X` | The iterator type.
`T` | The value type of `X`, i.e., `std::iterator_traits<X>::value_type`.
`x`, `y` | An object of type `X`.
`t` | An object of type `T`.

### Readable Iterator

A Readable Iterator is an iterator that dereferences to produce an rvalue that is convertible to the `value_type` of the iterator.

### Associated Types

Value type | `std::iterator_traits<X>::value_type` | The type of the objects pointed to by the iterator.
Reference type | `std::iterator_traits<X>::reference` | The return type of dereferencing the iterator. This type must be convertible to `T`.
Return Category | `std::return_category<X>::type` | A type convertible to `std::readable_iterator_tag`

### Refinement of

Copy Constructible

### Valid expressions

Name | Expression | Type requirements | Return type
--- | --- | --- | ---
Dereference | `*x` |  | `std::iterator_traits<X>::reference`
Member access | `x->m` | `T` is a type with a member named `m`. | If `m` is a data member, the type of `m`. If `m` is a member function, the return type of `m`.

### Writable Iterator

A Writable Iterator is an iterator that can be used to store a value using the dereference-assignment expression.

### Definitions

If `x` is an Writable Iterator of type `X`, then the expression `*x = a;` stores the value `a` into `x`. Note that `operator=`, like other C++ functions, may be overloaded; it may, in fact, even be a template function. In general, then, `a` may be any of several different types. A type `A` belongs to the set of value types of `X` if, for an object `a` of type `A`, `*x = a;` is well-defined and does not require performing any non-trivial conversions on `a`.

### Associated Types

Return Category | `std::return_category<X>::type` | A type convertible to `std::writable_iterator_tag`

### Refinement of

Copy Constructible

### Valid expressions

Name | Expression | Return type
--- | --- | ---
Dereference assignment | `*x = a` | unspecified

### Swappable Iterator

A Swappable Iterator is an iterator whose dereferenced values can be swapped.

Note: the requirements for Swappable Iterator are dependent on the issues surrounding `std::swap()` being resolved. Here we assume that the issue will be resolved by allowing the overload of `std::swap()` for user-defined types.

Note: Readable Iterator and Writable Iterator combined implies Swappable Iterator because of the fully templated `std::swap()`. However, Swappable Iterator does not imply Readable Iterator nor Writable Iterator.

### Associated Types

Return Category | `std::return_category<X>::type` | A type convertible to `std::swappable_iterator_tag`

### Valid expressions

Of the two valid expressions listed below, only one OR the other is required. If `std::iter_swap()` is overloaded for `X` then `std::swap()` is not required. If `std::iter_swap()` is not overloaded for `X` then the default (fully templated) version is used, which will call `std::swap()` (this means changing the current requirements for `std::iter_swap()`).

Name | Expression | Return type
--- | --- | ---
Iterator Swap | `std::iter_swap(x, y)` | void
Dereference and Swap | `std::swap(*x, *y)` | void

### Constant Lvalue Iterator

A Constant Lvalue Iterator is an iterator that dereferences to produce a const reference to the pointed-to object, i.e., the associated `reference` type is `const T&`. Changing the value of or destroying an iterator that models Constant Lvalue Iterator does not invalidate pointers and references previously obtained from that iterator.

### Refinement of

Readable Iterator

### Associated Types

Reference type | `std::iterator_traits<X>::reference` | The return type of dereferencing the iterator, which must be `const T&`.
Return Category | `std::return_category<X>::type` | A type convertible to `std::constant_lvalue_iterator_tag`

### Mutable Lvalue Iterator

A Mutable Lvalue Iterator is an iterator that dereferences to produce a reference to the pointed-to object. The associated `reference` type is `T&`. Changing the value of or destroying an iterator that models Mutable Lvalue Iterator does not invalidate pointers and references previously obtained from that iterator.

### Refinement of

Readable Iterator, Writable Iterator, and Swappable Iterator.

### Associated Types

Reference type | `std::iterator_traits<X>::reference` | The return type of dereferencing the iterator, which must be `T&`.
Return Category | `std::return_category<X>::type` | A type convertible to `std::mutable_lvalue_iterator_tag`

### Forward Traversal Iterator

The Forward Iterator is an iterator that can be incremented. Also, it is permissible to make multiple passes through the iterator's range.

### Refinement of

Copy Constructible, Assignable, Default Constructible, and Equality Comparable

### Associated types

Difference Type | `std::iterator_traits<X>::difference_type` | A signed integral type used for representing distances between iterators that point into the same range.
Traversal Category | `std::traversal_category<X>::type` | A type convertible to `std::forward_traversal_tag`

### Valid expressions

Name | Expression | Type requirements | Return type
--- | --- | --- | ---
Preincrement | `++i` |  | `X&`
Postincrement | `i++` |  | convertible to `const X&`

### Bidirectional Traversal Iterator

An iterator that can be incremented and decremented.

### Refinement of

Forward Traversal Iterator

### Associated types

Traversal Category | `std::traversal_category<X>::type` | A type convertible to `std::bidirectional_traversal_tag`

### Valid expressions

Name | Expression | Type requirements | Return type
--- | --- | --- | ---
Predecrement | `--i` |  | `X&`
Postdecrement | `i--` |  | convertible to `const X&`

### Random Access Traversal Iterator

An iterator that provides constant-time methods for moving forward and backward in arbitrary-sized steps.

### Refinement of

Bidirectional Traversal Iterator and Less Than Comparable where `<` is a total ordering

### Associated types

Traversal Category | `std::traversal_category<X>::type` | A type convertible to `std::random_access_traversal_tag`

### Valid expressions

Name | Expression | Type requirements | Return type
--- | --- | --- | ---
Iterator addition | `i += n` |  | `X&`
Iterator addition | `i + n` or `n + i` |  | `X`
Iterator subtraction | `i -= n` |  | `X&`
Iterator subtraction | `i - n` |  | `X`
Difference | `i - j` |  | `std::iterator_traits<X>::difference_type`
Element operator | `i[n]` | `X` must also be a model of Readable Iterator. | `std::iterator_traits<X>::reference`
Element assignment | `i[n] = t` | `X` must also be a model of Writable Iterator. | unspecified