1 Revision History

1.1 R2

• Adding extra semantic constraints in the concept concat-indirectly-readable to prevent non-equality-preserving behaviour of operator* and iter_move.

1.2 R1

• Removed the common_range support for underlying ranges that are !common_range && random_access_range && sized_range.

• Introduced extra exposition concepts to simplify the wording that defines concatable.

2 Abstract

This paper proposes views::concat as very briefly introduced in Section 4.7 of [P2214R1]. It is a view factory that takes an arbitrary number of ranges as an argument list, and provides a view that starts at the first element of the first range, ends at the last element of the last range, with all range elements sequenced in between respectively in the order given in the arguments, effectively concatenating, or chaining together the argument ranges.

3 Motivation and Examples

std::vector<int> v1{1,2,3}, v2{4,5}, v3{};
std::array  a{6,7,8};
int s = 9;
std::cout << std::format("[{:n}, {:n}, {:n}, {:n}, {}]\n", 
                v1, v2, v3, a, s); 
// output:  [1, 2, 3, 4, 5, , 6, 7, 8, 9]

std::vector<int> v1{1,2,3}, v2{4,5}, v3{};
std::array  a{6,7,8};
auto s = std::views::single(9);
std::cout << std::format("{}\n", 
                std::views::concat(v1, v2, v3, a, s)); 
// output:  [1, 2, 3, 4, 5, 6, 7, 8, 9]

class Foo;

class Bar{
public:
  const Foo& getFoo() const;
};

class MyClass{
  std::vector<Foo> foos_;
  Bar bar_;
public:
  auto getFoos () const{
    std::vector<std::reference_wrapper<Foo const>> fooRefs;
    fooRefs.reserve(foos_.size() + 1);

    for (auto const& f : foos_) {
      fooRefs.emplace_back(f);
    }
    fooRefs.emplace_back(bar_.getFoo());
    return fooRefs;
  }
};

// user
for(const auto& foo: myClass.getFoos()){
  // `foo` is std::reference_wrapper<Foo const>, not simply a Foo
  // ...
}

class Foo;

class Bar{
public:
  const Foo& getFoo() const;
};

class MyClass{
  std::vector<Foo> foos_;
  Bar bar_;
public:
  auto getFoos () const{
    return std::views::concat(
      foos_,
      std::views::single(std::cref(bar_))
      | std::views::transform(&Bar::getFoo)
    );
  }
};

// user
for(const auto& foo: myClass.getFoos()){
  // use foo, which is Foo const &
}

The first example shows that dealing with multiple ranges require care even in the simplest of cases: The “Before” version manually concatenates all the ranges in a formatting string, but empty ranges aren’t handled and the result contains an extra comma and a space. With concat_view, empty ranges are handled per design, and the construct expresses the intent cleanly and directly.

In the second example, the user has a class composed of fragmented and indirect data. They want to implement a member function that provides a range-like view to all this data sequenced together in some order, and without creating any copies. The “Before” implementation is needlessly complex and creates a temporary container with a potentially problematic indirection in its value type. concat_view based implementation is a neat one-liner.

4 Design

This is a generator factory as described in [P2214R1] Section 4.7. As such, it can not be piped to. It takes the list of ranges to concatenate as arguments to ranges::concat_view constructor, or to ranges::views::concat customization point object.

4.1 concatable-ity of ranges

Adaptability of any given two or more distinct ranges into a sequence that itself models a range, depends on the compatibility of the reference and the value types of these ranges. A precise formulation is made in terms of std::common_reference_t and std::common_type_t, and is captured by the exposition only concept concatable. See Wording. Proposed concat_view is then additionally constrained by this concept. (Note that, this is an improvement over [range-v3] concat_view which lacks such constraints, and fails with hard errors instead.)

4.1.1 reference

The reference type is the common_reference_t of all underlying range’s range_reference_t. In addition, as the result of common_reference_t is not necessarily a reference type, an extra constraint is needed to make sure that each underlying range’s range_reference_t is convertible to that common reference.

4.1.2 value_type

To support the cases where underlying ranges have proxy iterators, such as zip_view, the value_type cannot simply be the remove_cvref_t of the reference type, and it needs to respect underlying ranges’ value_type. Therefore, in this proposal the value_type is defined as the common_type_t of all underlying range’s range_value_t.

4.1.3 range_rvalue_reference_t

To make concat_view’s iterator’s iter_move behave correctly for the cases where underlying iterators customise iter_move, such as zip_view, concat_view has to respect those customizations. Therefore, concat_view requires common_reference_t of all underlying ranges’s range_rvalue_reference_t exist and can be converted to from each underlying range’s range_rvalue_reference_t.

4.1.4 indirectly_readable

In order to make concat_view model input_range, reference, value_type, and range_rvalue_reference_t have to be constrained so that the iterator of the concat_view models indirectly_readable.

4.1.5 Mixing ranges of references with ranges of prvalues

In the following example,

std::vector<std::string> v = ...;
auto r1 = v | std::views::transform([](auto&& s) -> std::string&& {return std::move(s);});
auto r2 = std::views::iota(0, 2)
            | std::views::transform([](auto i){return std::to_string(i)});
auto cv = std::views::concat(r1, r2);
auto it = cv.begin();
*it; // first deref
*it; // second deref

r1 is a range of which range_reference_t is std::string&&, while r2’s range_reference_t is std::string. The common_reference_t between these two references would be std::string. After the “first deref”, even though the result is unused, there is a conversion from std::string&& to std::string when the result of underlying iterator’s operator* is converted to the common_reference_t. This is a move construction and the underlying vector’s element is modified to a moved-from state. Later when the “second deref” is called, the result is a moved-from std::string. This breaks the “equality preserving” requirements.

Similar to operator*, ranges::iter_move has this same issue, and it is more common to run into this problem. For example,

std::vector<std::string> v = ...;
auto r = std::views::iota(0, 2)
           | std::views::transform([](auto i){return std::to_string(i)});
auto cv = std::views::concat(v, r);
auto it = cv.begin();
std::ranges::iter_move(it); // first iter_move
std::ranges::iter_move(it); // second iter_move

v’s range_rvalue_reference_t is std::string&&, and r’s range_rvalue_reference_t is std::string, the common_reference_t between them is std::string. After the first iter_move, the underlying vector’s first element is moved to construct the temporary common_reference_t, aka std::string. As a result, the second iter_move results in a moved-from state std::string. This breaks the “non-modifying” equality-preserving contract in indirectly_readable concept.

A naive solution for this problem is to ban all the usages of mixing ranges of references with ranges of prvalues. However, not all of this kind of mixing are problematic. For example, concating a range of std::string&& with a range of prvalue std::string_view is OK, because converting std::string&& to std::string_view does not modify the std::string&&. In general, it is not possible to detect whether the conversion from T&& to U modifies T&& through syntactic requirements. Therefore, the authors of this paper propose to use the “equality-preserving” semantic requirements of the requires-expression and the notational convention that constant lvalues shall not be modified in a manner observable to equality-preserving as defined in 18.2 [concepts.equality]. See Wording.

4.1.6 Unsupported Cases and Potential Extensions for the Future

Common type and reference based concatable logic is a practical and convenient solution that satisfies the motivation as outlined, and is what the authors propose in this paper. However, there are several potentially important use cases that get left out:

1. Concatenating ranges of different subclasses, into a range of their common base.
2. Concatenating ranges of unrelated types into a range of a user-determined common type, e.g. a std::variant.

Here is an example of the first case where common_reference formulation can manifest a rather counter-intuitive behavior: Let D1 and D2 be two types only related by their common base B, and d1, d2, and b be some range of these types, respectively. concat(b, d1, d2) is a well-formed range of B by the current formulation, suggesting such usage is supported. However, a mere reordering of the sequence, say to concat(d1, d2, b), yields one that is not.

The authors believe that such cases should be supported, but can only be done so via an adaptor that needs at least one explicit type argument at its interface. A future extension may satisfy these use cases, for example a concat_as view, or by even generally via an as view that is a type-generalized version of the as_const view of [P2278R1].

4.2 Zero or one view

• No argument views::concat() is ill-formed. It can not be a views::empty<T> because there is no reasonable way to determine an element type T.
• Single argument views::concat(r) is expression equivalent to views::all(r), which intuitively follows.

4.3 Hidden O(N) time complexity for N adapted ranges

Time complexities as required by the ranges concepts are formally expressed with respect to the total number of elements (the size) of a given range, and not to the statically known parameters of that range. Hence, the complexity of concat_view or its iterators’ operations are documented to be constant time, even though some of these are a linear function of the number of ranges it concatenates which is a statically known parameter of this view.

Some examples of these operations for concat_view are copy, begin and size, and its iterators’ increment, decrement, advance, distance. This characteristic (but not necessarily the specifics) are very much similar to the other n-ary adaptors like zip_view [P2321R2] and cartesian_view [P2374R3].

4.4 Borrowed vs Cheap Iterator

concat_view can be designed to be a borrowed_range, if all the underlying ranges are. However, this requires the iterator implementation to contain a copy of all iterators and sentinels of all underlying ranges at all times (just like that of views::zip [P2321R2]). On the other hand (unlike views::zip), a much cheaper implementation can satisfy all the proposed functionality provided it is permitted to be unconditionally not borrowed. This implementation would maintain only a single active iterator at a time and simply refers to the parent view for the bounds.

Experience shows the borrowed-ness of concat is not a major requirement; and the existing implementation in [range-v3] seems to have picked the cheaper alternative. This paper proposes the same.

4.5 Common Range

concat_view can be common_range if the last underlying range models common_range

4.6 Bidirectional Range

concat_view can model bidirectional_range if the underlying ranges satisfy the following conditions:

• Every underlying range models bidirectional_range
  
• If the iterator is at nth range’s begin position, after operator-- it should go to (n-1)th’s range’s end-1 position. This means, the (n-1)th range has to support either
  • common_range && bidirectional_range, so the position can be reached by --ranges::end(n-1th range), assuming n-1th range is not empty, or
  • random_access_range && sized_range, so the position can be reached by ranges::begin(n-1th range) + (ranges::size(n-1th range) - 1) in constant time, assuming n-1th range is not empty.
  Note that the last underlying range does not have to satisfy this constraint because n-1 can never be the last underlying range. If neither of the two constraints is satisfied, in theory we can cache the end-1 position for every single underlying range inside the concat_view itself. But the authors do not consider this type of ranges as worth supporting bidirectional

In the concat implementation in [range-v3], operator-- is only constrained on all underlying ranges being bidirectional_range on the declaration, but its implementation is using ranges::next(ranges::begin(r), ranges::end(r)) which implicitly requires random access to make the operation constant time. So it went with the second constraint. In this paper, both are supported.

4.7 Random Access Range

concat_view can be random_access_range if all the underlying ranges model random_access_range and sized_range.

4.8 Sized Range

concat_view can be sized_range if all the underlying ranges model sized_range

4.9 Implementation experience

views::concat has been implemented in [range-v3], with equivalent semantics as proposed here. The authors also implemented a version that directly follows the proposed wording below without any issue [ours].

5 Wording

5.1 Addition to <ranges>

Add the following to 26.2 [ranges.syn], header <ranges> synopsis:

// [...]
namespace std::ranges {
  // [...]

  // [range.concat], concat view
  template <input_range... Views>
    requires see below
  class concat_view;

  namespace views {
    inline constexpr unspecified concat = unspecified;
  }

}

5.2 Range adaptor helpers [range.adaptor.helpers]

This paper applies the same following changes as in [P2374R3]. If [P2374R3] is merged into the standard, the changes in this section can be dropped.

New section after Non-propagating cache 26.7.4 [range.nonprop.cache]. Move the definitions of tuple-or-pair, tuple-transform, and tuple-for-each from Class template zip_view 26.7.20.2 [range.zip.view] to this section:

namespace std::ranges {
    template <class... Ts>
    using tuple-or-pair = see below;                     // exposition only

    template<class F, class Tuple>
    constexpr auto tuple-transform(F&& f, Tuple&& tuple) { // exposition only
        return apply([&]<class... Ts>(Ts&&... elements) {
            return tuple-or-pair<invoke_result_t<F&, Ts>...>(
                invoke(f, std::forward<Ts>(elements))...
            );
        }, std::forward<Tuple>(tuple));
    }

    template<class F, class Tuple>
    constexpr void tuple-for-each(F&& f, Tuple&& tuple) { // exposition only
        apply([&]<class... Ts>(Ts&&... elements) {
            (invoke(f, std::forward<Ts>(elements)), ...);
        }, std::forward<Tuple>(tuple));
    }
}

Given some pack of types Ts, the alias template tuple-or-pair is defined as follows:

1. If sizeof...(Ts) is 2, tuple-or-pair<Ts...> denotes pair<Ts...>.
2. Otherwise, tuple-or-pair<Ts...> denotes tuple<Ts...>.

5.3 concat

Add the following subclause to 26.7 [range.adaptors].

24.7.? Concat view [range.concat]

24.7.?.1 Overview [range.concat.overview]

1 concat_view presents a view that concatenates all the underlying ranges.

2 The name views::concat denotes a customization point object (16.3.3.3.6 [customization.point.object]). Given a pack of subexpressions Es..., the expression views::concat(Es...) is expression-equivalent to

• (2.1) views::all(Es...) if Es is a pack with only one element and views::all(Es...) is a well formed expression,
• (2.2) otherwise, concat_view(Es...) if this expression is well formed,
• (2.3) otherwise, ill-formed.

[Example:

std::vector<int> v1{1,2,3}, v2{4,5}, v3{};
std::array  a{6,7,8};
auto s = std::views::single(9);
for(auto&& i : std::views::concat(v1, v2, v3, a, s)){
  std::cout << i << ' '; // prints: 1 2 3 4 5 6 7 8 9 
}

• end example]

24.7.?.2 Class template concat_view [range.concat.view]

namespace std::ranges {

  template <class... Rs>
  using concat-reference-t = common_reference_t<range_reference_t<Rs>...>; // exposition only

  template <class... Rs>
  using concat-value-t = common_type_t<range_value_t<Rs>...>; // exposition only

  template <class... Rs>
  using concat-rvalue-reference-t = common_reference_t<range_rvalue_reference_t<Rs>...>; // exposition only

  template <class... Rs>
  concept concat-indirectly-readable = see below; // exposition only

  template <class... Rs>
  concept concatable = see below;             // exposition only

  template <class... Rs>
  concept concat-random-access =              // exposition only
    ((random_access_range<Rs> && sized_range<Rs>)&&...);

  template <class R>
  concept constant-time-reversible =          // exposition only
    (bidirectional_range<R> && common_range<R>) ||
    (sized_range<R> && random_access_range<R>);

  template <class... Rs>
  concept concat-bidirectional = see below;   // exposition only

  template <input_range... Views>
    requires (view<Views> && ...) && (sizeof...(Views) > 0) &&
              concatable<Views...>
  class concat_view : public view_interface<concat_view<Views...>> {
    tuple<Views...> views_ = tuple<Views...>(); // exposition only

    template <bool Const>
    class iterator;                           // exposition only

  public:
    constexpr concat_view() requires(default_initializable<Views>&&...) = default;

    constexpr explicit concat_view(Views... views);

    constexpr iterator<false> begin() requires(!(simple-view<Views> && ...));

    constexpr iterator<true> begin() const
      requires((range<const Views> && ...) && concatable<const Views...>);

    constexpr auto end() requires(!(simple-view<Views> && ...));

    constexpr auto end() const requires(range<const Views>&&...);

    constexpr auto size() requires(sized_range<Views>&&...);

    constexpr auto size() const requires(sized_range<const Views>&&...);
  };

  template <class... R>
    concat_view(R&&...) -> concat_view<views::all_t<R>...>;
}

template <class... Rs>
concept concat-indirectly-readable = see below;

template <class Ref, class RRef, class It>
concept concat-indirectly-readable-impl = requires (const It it){
  static_cast<Ref>(*it);
  static_cast<RRef>(ranges::iter_move(it));
};

template <class... Rs>
concept concat-indirectly-readable =
  common_reference_with<concat-reference-t<Rs...>&&, 
                        concat-value-t<Rs...>&> &&
  common_reference_with<concat-reference-t<Rs...>&&, 
                        concat-rvalue-reference-t<Rs...>&&> &&
  common_reference_with<concat-rvalue-reference-t<Rs...>&&, 
                        concat-value-t<Rs...> const&> &&
  (concat-indirectly-readable-impl<concat-reference-t<Rs...>, 
                                   concat-rvalue-reference-t<Rs...>, 
                                   iterator_t<Rs>> && ...);

template <class... Rs>
concept concatable = see below;

template <class... Rs>
concept concatable = requires {
  typename concat-reference-t<Rs...>;
  typename concat-value-t<Rs...>;
  typename concat-rvalue-reference-t<Rs...>;
} && concat-indirectly-readable<Rs...>;

template <class... Rs>
concept concat-bidirectional = see below;

constexpr explicit concat_view(Views... views);

constexpr iterator<false> begin() requires(!(simple-view<Views> && ...));
constexpr iterator<true> begin() const
  requires((range<const Views> && ...) && concatable<const Views...>);

iterator<is-const> it{this, in_place_index<0>, ranges::begin(get<0>(views_))};
it.template satisfy<0>();
return it;

constexpr auto end() requires(!(simple-view<Views> && ...));
constexpr auto end() const requires(range<const Views>&&...);

if constexpr (common_range<last-view>) {
    constexpr auto N = sizeof...(Views);
    return iterator<is-const>{this, in_place_index<N - 1>, 
                      ranges::end(get<N - 1>(views_))};
} else {
    return default_sentinel;
}

constexpr auto size() requires(sized_range<Views>&&...);
constexpr auto size() const requires(sized_range<const Views>&&...);

return apply(
    [](auto... sizes) {
        using CT = make_unsigned_t<common_type_t<decltype(sizes)...>>;
        return (CT{0} + ... + CT{sizes});
    },
    tuple-transform(ranges::size, views_));

24.7.?.3 Class concat_view::iterator [range.concat.iterator]

namespace std::ranges{

  template <input_range... Views>
    requires (view<Views> && ...) && (sizeof...(Views) > 0) &&
              concatable<Views...>
  template <bool Const>
  class concat_view<Views...>::iterator {
  
  public:
    using value_type = common_type_t<range_value_t<maybe-const<Const, Views>>...>;
    using difference_type = common_type_t<range_difference_t<maybe-const<Const, Views>>...>;
    using iterator_concept = see below;
    using iterator_category = see below;                  // not always present.

  private:
    using base-iter =                                     // exposition only
      variant<iterator_t<maybe-const<Const, Views>>...>;
    
    maybe-const<Const, concat_view>* parent_ = nullptr;   // exposition only
    base-iter it_ = base-iter();                          // exposition only

    friend class iterator<!Const>;
    friend class concat_view;

    template <std::size_t N>
    constexpr void satisfy();                             // exposition only

    template <std::size_t N>
    constexpr void prev();                                // exposition only

    template <std::size_t N>
    constexpr void advance-fwd(difference_type offset, difference_type steps); // exposition only

    template <std::size_t N>
    constexpr void advance-bwd(difference_type offset, difference_type steps); // exposition only

    template <class... Args>
    explicit constexpr iterator(
                maybe-const<Const, concat_view>* parent,
                Args&&... args) 
        requires constructible_from<base-iter, Args&&...>;  // exposition only

  public:

    iterator() requires(default_initializable<iterator_t<maybe-const<Const, Views>>>&&...) =
        default;

    constexpr iterator(iterator<!Const> i) 
        requires Const &&
        (convertible_to<iterator_t<Views>, iterator_t<maybe-const<Const, Views>>>&&...);

    constexpr decltype(auto) operator*() const;

    constexpr iterator& operator++();

    constexpr void operator++(int);

    constexpr iterator operator++(int) 
        requires(forward_range<maybe-const<Const, Views>>&&...);
    
    constexpr iterator& operator--() 
        requires concat-bidirectional<maybe-const<Const, Views>...>;

    constexpr iterator operator--(int) 
        requires concat-bidirectional<maybe-const<Const, Views>...>

    constexpr iterator& operator+=(difference_type n) 
        requires concat-random-access<maybe-const<Const, Views>...>;

    constexpr iterator& operator-=(difference_type n) 
        requires concat-random-access<maybe-const<Const, Views>...>;

    constexpr decltype(auto) operator[](difference_type n) const
        requires concat-random-access<maybe-const<Const, Views>...>;

    friend constexpr bool operator==(const iterator& x, const iterator& y)
        requires(equality_comparable<iterator_t<maybe-const<Const, Views>>>&&...);

    friend constexpr bool operator==(const iterator& it, default_sentinel_t);

    friend constexpr bool operator<(const iterator& x, const iterator& y)
        requires(random_access_range<maybe-const<Const, Views>>&&...);

    friend constexpr bool operator>(const iterator& x, const iterator& y)
        requires(random_access_range<maybe-const<Const, Views>>&&...);

    friend constexpr bool operator<=(const iterator& x, const iterator& y)
        requires(random_access_range<maybe-const<Const, Views>>&&...);

    friend constexpr bool operator>=(const iterator& x, const iterator& y)
        requires(random_access_range<maybe-const<Const, Views>>&&...);

    friend constexpr auto operator<=>(const iterator& x, const iterator& y)
        requires((random_access_range<maybe-const<Const, Views>> &&
         three_way_comparable<maybe-const<Const, Views>>)&&...);

    friend constexpr iterator operator+(const iterator& it, difference_type n)
        requires concat-random-access<maybe-const<Const, Views>...>;

    friend constexpr iterator operator+(difference_type n, const iterator& it)
        requires concat-random-access<maybe-const<Const, Views>...>;

    friend constexpr iterator operator-(const iterator& it, difference_type n)
        requires concat-random-access<maybe-const<Const, Views>...>;

    friend constexpr difference_type operator-(const iterator& x, const iterator& y) 
        requires concat-random-access<maybe-const<Const, Views>...>;

    friend constexpr difference_type operator-(const iterator& x, default_sentinel_t) 
        requires concat-random-access<maybe-const<Const, Views>...>;

    friend constexpr difference_type operator-(default_sentinel_t, const iterator& x) 
        requires concat-random-access<maybe-const<Const, Views>...>;

    friend constexpr decltype(auto) iter_move(iterator const& it) noexcept(see below);

    friend constexpr void iter_swap(const iterator& x, const iterator& y) noexcept(see below)
        requires see below;
  };

}

1 iterator::iterator_concept is defined as follows:

• (1.1) If concat-random-access<maybe-const<Const, Views>...> is modeled, then iterator_concept denotes random_access_iterator_tag.
• (1.2) Otherwise, if concat-bidirectional<maybe-const<Const, Views>...> is modeled, then iterator_concept denotes bidirectional_iterator_tag.
• (1.3) Otherwise, if (forward_range<maybe-const<Const, Views>> && ...) is modeled, then iterator_concept denotes forward_iterator_tag.
• (1.4) Otherwise, iterator_concept denotes input_iterator_tag.

2 The member typedef-name iterator_category is defined if and only if (forward_range<maybe-const<Const, Views>>&&...) is modeled. In that case, iterator::iterator_category is defined as follows:

• (2.1) If is_lvalue_reference<reference> is false, then iterator_category denotes input_iterator_tag
• (2.2) Otherwise, let Cs denote the pack of types iterator_traits<iterator_t<maybe-const<Const, Views>>>::iterator_category....
  • (2.2.1) If (derived_from<Cs, random_access_iterator_tag> && ...) && concat-random-access<maybe-const<Const, Views>...> is true, iterator_category denotes random_access_iterator_tag.
  • (2.2.2) If (derived_from<Cs, bidirectional_iterator_tag> && ...) && concat-bidirectional<maybe-const<Const, Views>...> is true, iterator_category denotes bidirectional_iterator_tag.
  • (2.2.3) If (derived_from<Cs, forward_iterator_tag> && ...) is true, iterator_category denotes forward_iterator_tag.
  • (2.2.4) Otherwise, iterator_category denotes input_iterator_tag.

template <std::size_t N>
constexpr void satisfy();                             // exposition only

if constexpr (N != (sizeof...(Views) - 1)) {
    if (get<N>(it_) == ranges::end(get<N>(parent_->views_))) {
        it_.template emplace<N + 1>(ranges::begin(get<N + 1>(parent_->views_)));
        satisfy<N + 1>();
    }
}

template <std::size_t N>
constexpr void prev();                                // exposition only

if constexpr (N == 0) {
    --get<0>(it_);
} else {
    if (get<N>(it_) == ranges::begin(get<N>(parent_->views_))) {
        using prev_view = maybe-const<Const, tuple_element_t<N - 1, tuple<Views...>>>;
        if constexpr (common_range<prev_view>) {
            it_.template emplace<N - 1>(ranges::end(get<N - 1>(parent_->views_)));
        } else {
            it_.template emplace<N - 1>(
                ranges::next(ranges::begin(get<N - 1>(parent_->views_)),
                             ranges::size(get<N - 1>(parent_->views_))));
        }
        prev<N - 1>();
    } else {
        --get<N>(it_);
    }
}

template <std::size_t N>
constexpr void advance-fwd(difference_type offset, difference_type steps); // exposition only

if constexpr (N == sizeof...(Views) - 1) {
    get<N>(it_) += steps;
} else {
    auto n_size = ranges::size(get<N>(parent_->views_));
    if (offset + steps < static_cast<difference_type>(n_size)) {
        get<N>(it_) += steps;
    } else {
        it_.template emplace<N + 1>(ranges::begin(get<N + 1>(parent_->views_)));
        advance-fwd<N + 1>(0, offset + steps - n_size);
    }
}

template <std::size_t N>
constexpr void advance-bwd(difference_type offset, difference_type steps); // exposition only

if constexpr (N == 0) {
    get<N>(it_) -= steps;
} else {
    if (offset >= steps) {
        get<N>(it_) -= steps;
    } else {
        it_.template emplace<N - 1>(ranges::begin(get<N - 1>(parent_->views_)) +
                                    ranges::size(get<N - 1>(parent_->views_)));
        advance-bwd<N - 1>(
            static_cast<difference_type>(ranges::size(get<N - 1>(parent_->views_))),
            steps - offset);
    }
}

template <class... Args>
explicit constexpr iterator(
            maybe-const<Const, concat_view>* parent,
            Args&&... args) 
    requires constructible_from<base-iter, Args&&...>; // exposition only

constexpr iterator(iterator<!Const> i) 
    requires Const &&
    (convertible_to<iterator_t<Views>, iterator_t<maybe-const<Const, Views>>>&&...);

constexpr decltype(auto) operator*() const;

using reference = common_reference_t<range_reference_t<maybe-const<Const, Views>>...>;
return std::visit([](auto&& it) -> reference { 
    return *it; }, it_);

constexpr iterator& operator++();

++get<i>(it_);
satisfy<i>();
return *this;

constexpr void operator++(int);

++*this;

constexpr iterator operator++(int) 
    requires(forward_range<maybe-const<Const, Views>>&&...);

auto tmp = *this;
++*this;
return tmp;

constexpr iterator& operator--() 
    requires concat-bidirectional<maybe-const<Const, Views>...>;

prev<i>();
return *this;

constexpr iterator operator--(int) 
    requires concat-bidirectional<maybe-const<Const, Views>...>

auto tmp = *this;
--*this;
return tmp;

constexpr iterator& operator+=(difference_type n) 
    requires concat-random-access<maybe-const<Const, Views>...>;

if(n > 0) {
  advance-fwd<i>(get<i>(it_) - ranges::begin(get<i>(parent_->views_)), n);
} else if (n < 0) {
  advance-bwd<i>(get<i>(it_) - ranges::begin(get<i>(parent_->views_)), -n);
}
return *this;

constexpr iterator& operator-=(difference_type n) 
    requires concat-random-access<maybe-const<Const, Views>...>;

*this += -n;
return *this;

constexpr decltype(auto) operator[](difference_type n) const
    requires concat-random-access<maybe-const<Const, Views>...>;

return *((*this) + n);

friend constexpr bool operator==(const iterator& x, const iterator& y)
    requires(equality_comparable<iterator_t<maybe-const<Const, Views>>>&&...);

return x.it_ == y.it_;

friend constexpr bool operator==(const iterator& it, default_sentinel_t);

constexpr auto last_idx = sizeof...(Views) - 1;
return it.it_.index() == last_idx &&
       get<last_idx>(it.it_) == ranges::end(get<last_idx>(it.parent_->views_));

friend constexpr bool operator<(const iterator& x, const iterator& y)
    requires(random_access_range<maybe-const<Const, Views>>&&...);

return x.it_ < y.it_;

friend constexpr bool operator>(const iterator& x, const iterator& y)
    requires(random_access_range<maybe-const<Const, Views>>&&...);

return y < x;

friend constexpr bool operator<=(const iterator& x, const iterator& y)
    requires(random_access_range<maybe-const<Const, Views>>&&...);

return !(y < x);

friend constexpr bool operator>=(const iterator& x, const iterator& y)
    requires(random_access_range<maybe-const<Const, Views>>&&...);

return !(x < y);

friend constexpr auto operator<=>(const iterator& x, const iterator& y)
    requires((random_access_range<maybe-const<Const, Views>> &&
     three_way_comparable<maybe-const<Const, Views>>)&&...);

return x.it_ <=> y.it_;

friend constexpr iterator operator+(const iterator& it, difference_type n)
    requires concat-random-access<maybe-const<Const, Views>...>;

return iterator{it} += n;

friend constexpr iterator operator+(difference_type n, const iterator& it)
    requires concat-random-access<maybe-const<Const, Views>...>;

return it + n;

friend constexpr iterator operator-(const iterator& it, difference_type n)
    requires concat-random-access<maybe-const<Const, Views>...>;

return iterator{it} -= n;

friend constexpr difference_type operator-(const iterator& x, const iterator& y) 
    requires concat-random-access<maybe-const<Const, Views>...>;

friend constexpr difference_type operator-(const iterator& x, default_sentinel_t) 
    requires concat-random-access<maybe-const<Const, Views>...>;

return -(dx + s);

friend constexpr difference_type operator-(default_sentinel_t, const iterator& x) 
    requires concat-random-access<maybe-const<Const, Views>...>;

return -(x - default_sentinel);

friend constexpr decltype(auto) iter_move(iterator const& it) noexcept(see below);

return std::visit(
    [](auto const& i) ->
        common_reference_t<range_rvalue_reference_t<maybe-const<Const, Views>>...> { 
        return ranges::iter_move(i);
    },
    it.it_);

((is_nothrow_invocable_v<decltype(ranges::iter_move), 
                           const iterator_t<maybe-const<Const, Views>>&> &&
  is_nothrow_convertible_v<range_rvalue_reference_t<maybe-const<Const, Views>>,
                             common_reference_t<range_rvalue_reference_t<
                               maybe-const<Const, Views>>...>>) &&...)

friend constexpr void iter_swap(const iterator& x, const iterator& y) noexcept(see below)
    requires see below;

std::visit(ranges::iter_swap, x.it_, y.it_);

5.4 Feature Test Macro

Add the following macro definition to 17.3.2 [version.syn], header <version> synopsis, with the value selected by the editor to reflect the date of adoption of this paper:

#define __cpp_lib_ranges_concat  20XXXXL // also in <ranges>

6 References