# Boost Iterator Adaptor Library

## Introduction

The Iterator Adaptor library allows you transform an arbitrary ``base'' type into a standard-conforming iterator with the behaviors you choose. Doing so is especially easy if the ``base'' type is itself an iterator. The library also supplies several example adaptors which apply specific useful behaviors to arbitrary base iterators.

## Table of Contents

- Header `boost/iterator_adaptors.hpp`
  - Generalized Iterator Adaptor
    - Class template `iterator_adaptor`
    - Template Parameters
    - Named Template Parameters
    - The Policies Class
    - Additional Class Members
    - Example
    - (`const`/non-`const`) Iterator Interactions
    - Challenge
    - Concept Model
    - Declaration Synopsis
    - Notes
  - Specialized Iterator Adaptors
    - Indirect Iterator Adaptor
    - Reverse Iterator Adaptor
    - Transform Iterator Adaptor
    - Projection Iterator Adaptor
    - Filter Iterator Adaptor
- Header `boost/counting_iterator.hpp`
  Counting Iterator Adaptor
- Header `boost/function_output_iterator.hpp`
  Function Output Iterator Adaptor

Dave Abrahams started the library, applying policy class technique and handling const/non-const iterator interactions. He also contributed the `indirect_` and `reverse_` iterator generators, and expanded `counting_iterator_generator` to cover all incrementable types. He edited most of the documentation, sometimes heavily.
Jeremy Siek contributed the transform iterator adaptor, the integer-only version of `counting_iterator_generator`, the function output iterator adaptor, and most of the documentation.
John Potter contributed the `projection_` and `filter_` iterator generators and made some simplifications to the main `iterator_adaptor` template.

## Class template `iterator_adaptor`

Implementing standard conforming iterators is a non-trivial task. There are some fine points such as the interactions between an iterator and its corresponding const_iterator, and there are myriad operators that should be implemented but are easily forgotten or mishandled, such as `operator->()`. Using `iterator_adaptor`, you can easily implement an iterator class, and even more easily extend and adapt existing iterator types. Moreover, it is easy to make a pair of interoperable `const` and `non-const` iterators.

`iterator_adaptor` is declared like this:

    template <class Base, class Policies,
        class ValueOrNamedParams = typename std::iterator_traits<Base>::value_type,
        class ReferenceOrNamedParams = ...(see below),
        class PointerOrNamedParams = ...(see below),
        class CategoryOrNamedParams = typename std::iterator_traits<Base>::iterator_category,
        class DistanceOrNamedParams = typename std::iterator_traits<Base>::difference_type>
    struct iterator_adaptor;

### Template Parameters

Although `iterator_adaptor` takes seven template parameters, defaults have been carefully chosen to minimize the number of parameters you must supply in most cases, especially if `BaseType` is an iterator.

Parameter | Description
--- | ---
`BaseType` | The type being wrapped.
`Policies` | A policy class that supplies core functionality to the resulting iterator. A detailed description can be found below.
`Value` | The `value_type` of the resulting iterator, unless const. If Value is `const X` the `value_type` will be (non-`const`) `X`[1]. If the `value_type` you wish to use is an abstract base class see note [5]. Default: `std::iterator_traits<BaseType>::value_type` [2]
`Reference` | The `reference` type of the resulting iterator, and in particular, the result type of `operator*()`. Default: If `Value` is supplied, `Value&` is used. Otherwise `std::iterator_traits<BaseType>::reference` is used.
`Pointer` | The `pointer` type of the resulting iterator, and in particular, the result type of `operator->()`. Default: If `Value` was supplied, then `Value*`, otherwise `std::iterator_traits<BaseType>::pointer`.
`Category` | The `iterator_category` type for the resulting iterator. Default: `std::iterator_traits<BaseType>::iterator_category`
`Distance` | The `difference_type` for the resulting iterator. Default: `std::iterator_traits<BaseType>::difference_type`
`NamedParams` | A list of named template parameters generated using the `iterator_traits_generator` class (see below).

### Named Template Parameters

With seven template parameters, providing arguments for `iterator_adaptor` in the correct order can be challenging. Also, often times one would like to specify the sixth or seventh template parameter, but use the defaults for the third through fifth. As a solution to these problems we provide a mechanism for naming the last five template parameters, and providing them in any order through the `iterator_traits_generator` class.

>     class iterator_traits_generator
>     {
>     public:
>       template <class Value>
>       struct value_type : public recursive magic { };

>       template <class Reference>
>       struct reference : public recursive magic { };

>       template <class Pointer>
>       struct pointer : public recursive magic { };

>       template <class Distance>
>       struct difference_type : public recursive magic { };

>       template <class Category>
>       struct iterator_category : public recursive magic { };
>     };

The `iterator_traits_generator` is used to create a list of of template arguments. For example, suppose you want to set the `Reference` and `Category` parameters, and use the defaults for the rest. Then you can use the traits generator as follows:

>     iterator_traits_generator::reference<foo>::category<std::input_iterator_tag>

This generated type can then be passed into the `iterator_adaptor` class to replace any of the last five parameters. If you use the traits generator in the ith parameter position, then the parameters i through 7 will use the types specified in the generator. For example, the following adapts `foo_iterator` to create an InputIterator with `reference` type `foo`, and whose other traits are determined according to the defaults described above.

>     iterator_adaptor<foo_iterator, foo_policies,
>         iterator_traits_generator
>         ::reference<foo>
>         ::iterator_category<std::input_iterator_tag>
>     >

### The Policies Class

The main task in using `iterator_adaptor` is creating an appropriate `Policies` class. The `Policies` class will become the functional heart of the resulting iterator, supplying the core operations that determine its behavior. The `iterator_adaptor` template defines all of the operators required of a Random Access Iterator by dispatching to a `Policies` object. Your `Policies` class must implement a subset of the core iterator operations below corresponding to the iterator categories you want it to support.

Core Iterator Operations
`T`: adapted iterator type; `p`: object of type T; `n`: `T::size_type`; `x`: `T::difference_type`; `p1`, `p2`: iterators
Operation | Effects | Implements Operations | Required for Iterator Categories
--- | --- | --- | ---
`initialize` | optionally modify base iterator during iterator construction | constructors | Input/ Output/ Forward/ Bidirectional/ Random Access
`dereference` | returns an element of the iterator's `reference` type | `*p`, `p[n]`
`equal` | tests the iterator for equality | `p1 == p2`, `p1 != p2`
`increment` | increments the iterator | `++p`, `p++`
`decrement` | decrements the iterator | `--p`, `p--` | Bidirectional/ Random Access
`less` | imposes a Strict Weak Ordering relation on iterators | `p1 < p2`, `p1 <= p2`, `p1 > p2`, `p1 >= p2` | Random Access
`distance` | measures the distance between iterators | `p1 - p2`
`advance` | adds an integer offset to iterators | `p + x`, `x + p`, `p += x`, `p - x`, `p -= x`

The library also supplies a "trivial" policy class, `default_iterator_policies`, which implements all seven of the core operations in the usual way. If you wish to create an iterator adaptor that only changes a few of the base type's behaviors, then you can derive your new policy class from `default_iterator_policies` to avoid retyping the usual behaviors. You should also look at `default_iterator_policies` as the ``boilerplate'' for your own policy classes, defining functions with the same interface. This is the definition of `default_iterator_policies`:

>     struct default_iterator_policies
>     {
>       template <class BaseType>
>       void initialize(BaseType&)
>         { }

>       template <class Reference, class BaseType>
>       Reference dereference(type<Reference>, const BaseType& x) const
>         { return *x; }

>       template <class BaseType>
>       static void increment(BaseType& x)
>         { ++x; }

>       template <class BaseType1, class BaseType2>
>       bool equal(BaseType1& x, BaseType2& y) const
>         { return x == y; }

>       template <class BaseType>
>       static void decrement(BaseType& x)
>         { --x; }

>       template <class BaseType, class DifferenceType>
>       static void advance(BaseType& x, DifferenceType n)
>         { x += n; }

>       template <class Difference, class BaseType1, class BaseType2>
>       Difference distance(type<Difference>, BaseType1& x, BaseType2& y) const
>         { return y - x; }

>       template <class BaseType1, class BaseType2>
>       bool less(BaseType1& x, BaseType2& y) const
>         { return x < y; }
>     };

Template member functions are used throughout `default_iterator_policies` so that it can be employed with a wide range of iterators. If we had used concrete types above, we'd have tied the usefulness of `default_iterator_policies` to a particular range of adapted iterators. If you follow the same pattern with your `Policies` classes, you can use them to generate more specialized adaptors along the lines of those supplied by this library.

### Additional Members

In addition to all of the member functions required of a Random Access Iterator, the `iterator_adaptor` class template defines the following members.

`explicit iterator_adaptor(const Base&, const Policies& = Policies())` Construct an adapted iterator from a base object and a policies object. As this constructor is `explicit`, it does not provide for implicit conversions from the `Base` type to the iterator adaptor.
`template <class B, class V, class R, class P> iterator_adaptor(const iterator_adaptor<B,Policies,V,R,P,Category,Distance>&)` This constructor allows for conversion from non-`const` to constant adapted iterators. See below for more details. Requires: `B` is convertible to `Base`.
`base_type base() const;` Return a copy of the base object.

### Example

It is often useful to automatically apply some function to the value returned by dereferencing an iterator. The transform iterator makes it easy to create an iterator adaptor which does just that. Here we will show how easy it is to implement the transform iterator using the `iterator_adaptor` template.

We want to be able to adapt a range of iterators and functions, so the policies class will have a template parameter for the function type and it will have a data member of that type. We know that the function takes one argument and that we'll need to be able to deduce the `result_type` of the function so we can use it for the adapted iterator's `value_type`. AdaptableUnaryFunction is the Concept that fulfills those requirements.

To implement a transform iterator we will only change one of the base iterator's behaviors, so the `transform_iterator_policies` class can inherit the rest from `default_iterator_policies`. We will define the `dereference()` member function, which is used to implement `operator*()` of the adapted iterator. The implementation will dereference the base iterator and apply the function object. The `type<Reference>` parameter is used to convey the appropriate return type. The complete code for `transform_iterator_policies` is:

>       template <class AdaptableUnaryFunction>
>       struct transform_iterator_policies : public default_iterator_policies
>       {
>         transform_iterator_policies() { }

>         transform_iterator_policies(const AdaptableUnaryFunction& f)
>           : m_f(f) { }

>         template <class Reference, class BaseIterator>
>         Reference dereference(type<Reference>, const BaseIterator& i) const
>           { return m_f(*i); }

>         AdaptableUnaryFunction m_f;
>       };

The next step is to use the `iterator_adaptor` template to construct the transform iterator type. The nicest way to package the construction of the transform iterator is to create a type generator. The first template parameter to the generator will be the type of the function object and the second will be the base iterator type. We use `iterator_adaptor` to define the transform iterator type as a nested `typedef` inside the `transform_iterator_generator` class. Because the function may return by-value, we must limit the `iterator_category` to Input Iterator, and the iterator's `reference` type cannot be a true reference (the standard allows this for input iterators), so in this case we can use few of `iterator_adaptor`'s default template arguments.

>     template <class AdaptableUnaryFunction, class Iterator>
>     struct transform_iterator_generator
>     {
>         typedef typename AdaptableUnaryFunction::result_type value_type;
>     public:
>         typedef iterator_adaptor<Iterator,
>             transform_iterator_policies<AdaptableUnaryFunction>,
>             value_type, value_type, value_type*, std::input_iterator_tag>
>           type;
>     };

As a finishing touch, we will create an object generator for the transform iterator. This is a function that makes it more convenient to create a transform iterator.

>     template <class AdaptableUnaryFunction, class Iterator>
>     typename transform_iterator_generator<AdaptableUnaryFunction,Iterator>::type
>     make_transform_iterator(Iterator base,
>                             const AdaptableUnaryFunction& f = AdaptableUnaryFunction())
>     {
>         typedef typename transform_iterator_generator<AdaptableUnaryFunction,
>           Iterator>::type result_t;
>         return result_t(base, f);
>     }

Here is an example that shows how to use a transform iterator to iterate through a range of numbers, multiplying each of them by 2 and printing the result to standard output.

>     #include <functional>
>     #include <algorithm>
>     #include <iostream>
>     #include <boost/iterator_adaptors.hpp>

>     int main(int, char*[])
>     {
>       int x[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
>       const int N = sizeof(x)/sizeof(int);
>       std::cout << "multiplying the array by 2:" << std::endl;
>       std::copy(boost::make_transform_iterator(x, std::bind1st(std::multiplies<int>(), 2)),
>           boost::make_transform_iterator(x + N, std::bind1st(std::multiplies<int>(), 2)),
>           std::ostream_iterator<int>(std::cout, " "));
>       std::cout << std::endl;
>       return 0;
>     }

> This output is:

>     2 4 6 8 10 12 14 16

### Iterator Interactions

C++ allows `const` and non-`const` pointers to interact in the following intuitive ways:

- a non-`const` pointer to `T` can be implicitly converted to a `const` pointer to `T`.
- `const` and non-`const` pointers to `T` can be freely mixed in comparison expressions.
- `const` and non-`const` pointers to `T` can be freely subtracted, in any order.

Getting user-defined iterators to work together that way is nontrivial (see here for an example of where the C++ standard got it wrong), but `iterator_adaptor` can make it easy. The rules are as follows:

- Adapted iterators that share the same `Policies`, `Category`, and `Distance` parameters are called interoperable.
- An adapted iterator can be implicitly converted to any other adapted iterator with which it is interoperable, so long as the `Base` type of the source iterator can be converted to the `Base` type of the target iterator.
- Interoperable iterators can be freely mixed in comparison expressions so long as the `Policies` class has `equal` (and, for random access iterators, `less`) members that can accept both `Base` types in either order.
- Interoperable iterators can be freely mixed in subtraction expressions so long as the `Policies` class has a `distance` member that can accept both `Base` types in either order.

#### Example

The Projection Iterator adaptor is similar to the transform iterator adaptor in that its `operator*()` applies some function to the result of dereferencing the base iterator and then returns the result. The difference is that the function must return a reference to some existing object (for example, a data member within the `value_type` of the base iterator).

The projection_iterator_pair_generator template is a special two-type generator for mutable and constant versions of a projection iterator. It is defined as follows:

>     template <class AdaptableUnaryFunction, class Iterator, class ConstIterator>
>     struct projection_iterator_pair_generator {
>         typedef typename AdaptableUnaryFunction::result_type value_type;
>         typedef projection_iterator_policies<AdaptableUnaryFunction> policies;
>     public:
>         typedef iterator_adaptor<Iterator,policies,value_type> iterator;
>         typedef iterator_adaptor<ConstIterator,policies,value_type,
>             const value_type&,const value_type*> const_iterator;
>     };

It is assumed that the `Iterator` and `ConstIterator` arguments are corresponding mutable and constant iterators.

- Clearly, then, the `projection_iterator_pair_generator`'s `iterator` and `const_iterator` are interoperable, since they share the same `Policies` and since `Category` and `Distance` as supplied by `std::iterator_traits` through the default template parameters to `iterator_adaptor` should be the same.
- Since `Iterator` can presumably be converted to `ConstIterator`, the projection `iterator` will be convertible to the projection `const_iterator`.
- Since `projection_iterator_policies` implements only the `dereference` operation, and inherits all other behaviors from `default_iterator_policies`, which has fully-templatized `equal`, `less`, and `distance` operations, the `iterator` and `const_iterator` can be freely mixed in comparison and subtraction expressions.

### Challenge

There is an unlimited number of ways the `iterator_adaptors` class can be used to create iterators. One interesting exercise would be to re-implement the iterators of `std::list` and `std::slist` using `iterator_adaptors`, where the adapted `Iterator` types would be node pointers.

### Concept Model

Depending on the `Base` and `Policies` template parameters, an `iterator_adaptor` can be a Input Iterator, Forward Iterator, Bidirectional Iterator, or Random Access Iterator.

### Declaration Synopsis

    template <class Base, class Policies,
        class Value = typename std::iterator_traits<Base>::value_type,
        class Reference = ...(see below),
        class Pointer = ...(see below),
        class Category = typename std::iterator_traits<Base>::iterator_category,
        class Distance = typename std::iterator_traits<Base>::difference_type
             >
    struct iterator_adaptor
    {
        typedef Distance difference_type;
        typedef typename boost::remove_const<Value>::type value_type;
        typedef Pointer pointer;
        typedef Reference reference;
        typedef Category iterator_category;
        typedef Base base_type;
        typedef Policies policies_type;

        iterator_adaptor();
        explicit iterator_adaptor(const Base&, const Policies& = Policies());

        base_type base() const;

        template <class B, class V, class R, class P>
        iterator_adaptor(
            const iterator_adaptor<B,Policies,V,R,P,Category,Distance>&);

        reference operator*() const;
        operator_arrow_result_type operator->() const; [3]
        value_type operator[](difference_type n) const; [4]

        iterator_adaptor& operator++();
        iterator_adaptor& operator++(int);
        iterator_adaptor& operator--();
        iterator_adaptor& operator--(int);

        iterator_adaptor& operator+=(difference_type n);
        iterator_adaptor& operator-=(difference_type n);

        iterator_adaptor& operator-(Distance x) const;
    };

    template <class B, class P, class V, class R, class Ptr,
        class C, class D1, class D2>
    iterator_adaptor<B,P,V,R,Ptr,C,D1>
    operator+(iterator_adaptor<B,P,V,R,Ptr,C,D1>, D2);

    template <class B, class P, class V, class R, class Ptr,
        class C, class D1, class D2>
    iterator_adaptor<B,P,V,R,P,C,D1>
    operator+(D2, iterator_adaptor<B,P,V,R,Ptr,C,D1> p);

    template <class B1, class B2, class P, class V1, class V2,
        class R1, class R2, class P1, class P2, class C, class D>
    Distance operator-(const iterator_adaptor<B1,P,V1,R1,P1,C,D>&,
                       const iterator_adaptor<B2,P,V2,R2,P2,C,D>&);

    template <class B1, class B2, class P, class V1, class V2,
        class R1, class R2, class P1, class P2, class C, class D>
    bool operator==(const iterator_adaptor<B1,P,V1,R1,P1,C,D>&,
                    const iterator_adaptor<B2,P,V2,R2,P2,C,D>&);

    // and similarly for operators !=, <, <=, >=, >

### Notes

[1] The standard specifies that the `value_type` of `const` iterators to `T` (e.g. `const T*`) is `non-const T`, while the `pointer` and `reference` types for all Forward Iterators are `const T*` and `const T&`, respectively. Stripping the `const`-ness of `Value` allows you to easily make a `const` iterator adaptor by supplying a `const` type for `Value`, and allowing the defaults for the `Pointer` and `Reference` parameters to take effect. Although compilers that don't support partial specialization won't strip `const` for you, having a `const value_type` is often harmless in practice.

[2] If your compiler does not support partial specialization and the base iterator is a builtin pointer type, you will not be able to use the default for `Value` and will have to specify this type explicitly.

[3] The result type for the `operator->()` depends on the category and value type of the iterator and is somewhat complicated to describe. But be assured, it works in a stardard conforming fashion, providing access to members of the objects pointed to by the iterator.

[4] The result type of `operator[]()` is `value_type` instead of `reference` as might be expected. There are two reasons for this choice. First, the C++ standard only requires that the return type of an arbitrary Random Access Iterator's `operator[]`be ``convertible to T'' (Table 76), so when adapting an arbitrary base iterator we may not have a reference to return. Second, and more importantly, for certain kinds of iterators, returning a reference could cause serious memory problems due to the reference being bound to a temporary object whose lifetime ends inside of the `operator[]`.

[5] The `value_type` of an iterator may not be an abstract base class, however many common uses of iterators never need the `value_type`, only the `reference` type. If you wish to create such an iterator adaptor, use a dummy type such as `char` for the `Value` parameter, and use a reference to your abstract base class for the `Reference` parameter. Note that such an iterator does not fulfill the C++ standards requirements for a Forward Iterator, so you will need to use a less restrictive iterator category such as `std::input_iterator_tag`.

Revised 19 Mar 2001

© Copyright Dave Abrahams and Jeremy Siek 2001. Permission to copy, use, modify, sell and distribute this document is granted provided this copyright notice appears in all copies. This document is provided "as is" without express or implied warranty, and with no claim as to its suitability for any purpose.