Boost.Hana: Sequence

| Boost.Hana 1.5.0 Your standard library for metaprogramming |

Variables
Sequence
Concepts

## Description

The `Sequence` concept represents generic index-based sequences.

Compared to other abstract concepts, the Sequence concept is very specific. It represents generic index-based sequences. The reason why such a specific concept is provided is because there are a lot of models that behave exactly the same while being implemented in wildly different ways. It is useful to regroup all those data types under the same umbrella for the purpose of generic programming.

In fact, models of this concept are not only similar. They are actually isomorphic, in a sense that we define below, which is a fancy way of rigorously saying that they behave exactly the same to an external observer.

## Minimal complete definition

`Iterable`, `Foldable`, and `make`

The `Sequence` concept does not provide basic methods that could be used as a minimal complete definition; instead, it borrows methods from other concepts and add laws to them. For this reason, it is necessary to specialize the `Sequence` metafunction in Hana's namespace to tell Hana that a type is indeed a `Sequence`. Explicitly specializing the `Sequence` metafunction can be seen like a seal saying "this data type satisfies the additional laws of a `Sequence`", since those can't be checked by Hana automatically.

## Laws

The laws for being a `Sequence` are simple, and their goal is to restrict the semantics that can be associated to the functions provided by other concepts. First, a `Sequence` must be a finite `Iterable` (thus a `Foldable` too). Secondly, for a `Sequence` tag `S`, `make<S>(x1, ..., xn)` must be an object of tag `S` and whose linearization is `[x1, ..., xn]`. This basically ensures that objects of tag `S` are equivalent to their linearization, and that they can be created from such a linearization (with `make`).

While it would be possible in theory to handle infinite sequences, doing so complicates the implementation of many algorithms. For simplicity, the current version of the library only handles finite sequences. However, note that this does not affect in any way the potential for having infinite `Searchable`s and `Iterable`s.

## Refined concepts

1. `Comparable` (definition provided automatically)
   Two `Sequence`s are equal if and only if they contain the same number of elements and their elements at any given index are equal.
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/assert.hpp>
   #include <boost/hana/equal.hpp>
   #include <boost/hana/not_equal.hpp>
   #include <boost/hana/tuple.hpp>
   namespace hana = boost::hana;
   static_assert(hana::make_tuple(1, 2, 3) == hana::make_tuple(1, 2, 3), "");
   BOOST_HANA_CONSTANT_CHECK(hana::make_tuple(1, 2, 3) != hana::make_tuple(1, 2, 3, 4));
   int main() { }
2. `Orderable` (definition provided automatically)
   `Sequence`s are ordered using the traditional lexicographical ordering.
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/less.hpp>
   #include <boost/hana/tuple.hpp>
   namespace hana = boost::hana;
   static_assert(hana::make_tuple(1, 2, 3) < hana::make_tuple(2, 3, 4), "");
   static_assert(hana::make_tuple(1, 2, 3) < hana::make_tuple(1, 2, 3, 4), "");
   int main() { }
3. `Functor` (definition provided automatically)
   `Sequence`s implement `transform` as the mapping of a function over each element of the sequence. This is somewhat equivalent to what `std::transform` does to ranges of iterators. Also note that mapping a function over an empty sequence returns an empty sequence and never applies the function, as would be expected.
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/assert.hpp>
   #include <boost/hana/equal.hpp>
   #include <boost/hana/transform.hpp>
   #include <boost/hana/tuple.hpp>
   #include <sstream>
   #include <string>
   namespace hana = boost::hana;
   auto to_string = [](auto x) {
   std::ostringstream ss;
   ss << x;
   return ss.str();
   };
   int main() {
   BOOST_HANA_RUNTIME_CHECK(
   hana::transform(hana::make_tuple(1, '2', "345", std::string{"67"}), to_string) ==
   hana::make_tuple("1", "2", "345", "67")
   );
   }
4. `Applicative` (definition provided automatically)
   First, `lift`ing a value into a `Sequence` is the same as creating a singleton sequence containing that value. Second, applying a sequence of functions to a sequence of values will apply each function to all the values in the sequence, and then return a list of all the results. In other words,
   ap([f1, ..., fN], [x1, ..., xM]) == [
   f1(x1), ..., f1(xM),
   ...
   fN(x1), ..., fN(xM)
   ]
   Example:
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/ap.hpp>
   #include <boost/hana/equal.hpp>
   #include <boost/hana/ext/std/tuple.hpp>
   #include <boost/hana/functional/flip.hpp>
   #include <boost/hana/lift.hpp>
   #include <boost/hana/pair.hpp>
   #include <boost/hana/tuple.hpp>
   #include <tuple>
   namespace hana = boost::hana;
   static_assert(hana::lift<hana::tuple_tag>('x') == hana::make_tuple('x'), "");
   static_assert(hana::equal(hana::lift<hana::ext::std::tuple_tag>('x'), std::make_tuple('x')), "");
   constexpr auto f = hana::make_pair;
   constexpr auto g = hana::flip(hana::make_pair);
   static_assert(
   hana::ap(hana::make_tuple(f, g), hana::make_tuple(1, 2, 3), hana::make_tuple('a', 'b'))
   ==
   hana::make_tuple(
   f(1, 'a'), f(1, 'b'), f(2, 'a'), f(2, 'b'), f(3, 'a'), f(3, 'b'),
   g(1, 'a'), g(1, 'b'), g(2, 'a'), g(2, 'b'), g(3, 'a'), g(3, 'b')
   )
   , "");
   int main() { }
5. `Monad` (definition provided automatically)
   First, `flaten`ning a `Sequence` takes a sequence of sequences and concatenates them to get a larger sequence. In other words,
   flatten([[a1, ..., aN], ..., [z1, ..., zM]]) == [
   a1, ..., aN, ..., z1, ..., zM
   ]
   This acts like a `std::tuple_cat` function, except it receives a sequence of sequences instead of a variadic pack of sequences to flatten.
   Example:
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/equal.hpp>
   #include <boost/hana/flatten.hpp>
   #include <boost/hana/tuple.hpp>
   namespace hana = boost::hana;
   static_assert(
   hana::flatten(hana::make_tuple(
   hana::make_tuple(1, 2),
   hana::make_tuple(3, 4),
   hana::make_tuple(hana::make_tuple(5, 6))
   ))
   == hana::make_tuple(1, 2, 3, 4, hana::make_tuple(5, 6))
   , "");
   int main() { }
   Also note that the model of `Monad` for `Sequence`s can be seen as modeling nondeterminism. A nondeterministic computation can be modeled as a function which returns a sequence of possible results. In this line of thought, `chain`ing a sequence of values into such a function will return a sequence of all the possible output values, i.e. a sequence of all the values applied to all the functions in the sequences.
   Example:
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/assert.hpp>
   #include <boost/hana/chain.hpp>
   #include <boost/hana/equal.hpp>
   #include <boost/hana/for_each.hpp>
   #include <boost/hana/traits.hpp>
   #include <boost/hana/tuple.hpp>
   #include <boost/hana/type.hpp>
   #include <type_traits>
   #include <utility>
   namespace hana = boost::hana;
   // Using the `tuple` Monad, we generate all the possible combinations of
   // cv-qualifiers and reference qualifiers. Then, we use the `optional`
   // Monad to make sure that our generic function can be called with
   // arguments of any of those types.
   // cv_qualifiers : type -> tuple(type)
   auto cv_qualifiers = [](auto t) {
   return hana::make_tuple(
   t,
   hana::traits::add_const(t),
   hana::traits::add_volatile(t),
   hana::traits::add_volatile(hana::traits::add_const(t))
   );
   };
   // ref_qualifiers : type -> tuple(type)
   auto ref_qualifiers = [](auto t) {
   return hana::make_tuple(
   hana::traits::add_lvalue_reference(t),
   hana::traits::add_rvalue_reference(t)
   );
   };
   auto possible_args = cv_qualifiers(hana::type_c<int>) | ref_qualifiers;
   BOOST_HANA_CONSTANT_CHECK(
   possible_args == hana::make_tuple(
   hana::type_c<int&>,
   hana::type_c<int&&>,
   hana::type_c<int const&>,
   hana::type_c<int const&&>,
   hana::type_c<int volatile&>,
   hana::type_c<int volatile&&>,
   hana::type_c<int const volatile&>,
   hana::type_c<int const volatile&&>
   )
   );
   struct some_function {
   template <typename T>
   void operator()(T&&) const { }
   };
   int main() {
   hana::for_each(possible_args, [](auto t) {
   using T = typename decltype(t)::type;
   static_assert(decltype(hana::is_valid(some_function{})(std::declval<T>())){},
   "some_function should be callable with any type of argument");
   });
   }
6. `MonadPlus` (definition provided automatically)
   `Sequence`s are models of the `MonadPlus` concept by considering the empty sequence as the unit of `concat`, and sequence concatenation as `concat`.
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/append.hpp>
   #include <boost/hana/assert.hpp>
   #include <boost/hana/concat.hpp>
   #include <boost/hana/empty.hpp>
   #include <boost/hana/equal.hpp>
   #include <boost/hana/tuple.hpp>
   #include <string>
   namespace hana = boost::hana;
   using namespace std::string_literals;
   BOOST_HANA_CONSTANT_CHECK(hana::empty<hana::tuple_tag>() == hana::make_tuple());
   static_assert(hana::append(hana::make_tuple(1, '2', 3.3), nullptr)
   == hana::make_tuple(1, '2', 3.3, nullptr), "");
   int main() {
   BOOST_HANA_RUNTIME_CHECK(
   hana::concat(hana::make_tuple(1, '2', 3.3), hana::make_tuple("abcdef"s)) ==
   hana::make_tuple(1, '2', 3.3, "abcdef"s)
   );
   }
7. `Foldable`
   The model of `Foldable` for `Sequence`s is uniquely determined by the model of `Iterable`.
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/assert.hpp>
   #include <boost/hana/fold_left.hpp>
   #include <boost/hana/tuple.hpp>
   #include <sstream>
   namespace hana = boost::hana;
   auto to_string = [](auto x) {
   std::ostringstream ss;
   ss << x;
   return ss.str();
   };
   auto show = [](auto x, auto y) {
   return "(" + to_string(x) + " + " + to_string(y) + ")";
   };
   int main() {
   BOOST_HANA_RUNTIME_CHECK(
   hana::fold_left(hana::make_tuple(2, "3", '4'), "1", show) == "(((1 + 2) + 3) + 4)"
   );
   }
8. `Iterable`
   The model of `Iterable` for `Sequence`s corresponds to iteration over each element of the sequence, in order. This model is not provided automatically, and it is in fact part of the minimal complete definition for the `Sequence` concept.
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/assert.hpp>
   #include <boost/hana/drop_front.hpp>
   #include <boost/hana/equal.hpp>
   #include <boost/hana/front.hpp>
   #include <boost/hana/is_empty.hpp>
   #include <boost/hana/tuple.hpp>
   namespace hana = boost::hana;
   static_assert(hana::front(hana::make_tuple(1, '2', 3.3)) == 1, "");
   static_assert(hana::drop_front(hana::make_tuple(1, '2', 3.3)) == hana::make_tuple('2', 3.3), "");
   BOOST_HANA_CONSTANT_CHECK(!hana::is_empty(hana::make_tuple(1, '2', 3.3)));
   BOOST_HANA_CONSTANT_CHECK(hana::is_empty(hana::make_tuple()));
   int main() { }
9. `Searchable` (definition provided automatically)
   Searching through a `Sequence` is equivalent to just searching through a list of the values it contains. The keys and the values on which the search is performed are both the elements of the sequence.
   // Copyright Louis Dionne 2013-2017
   // Distributed under the Boost Software License, Version 1.0.
   // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   #include <boost/hana/assert.hpp>
   #include <boost/hana/contains.hpp>
   #include <boost/hana/core/is_a.hpp>
   #include <boost/hana/equal.hpp>
   #include <boost/hana/find_if.hpp>
   #include <boost/hana/optional.hpp>
   #include <boost/hana/tuple.hpp>
   #include <string>
   namespace hana = boost::hana;
   using namespace std::string_literals;
   int main() {
   BOOST_HANA_RUNTIME_CHECK(
   hana::find_if(hana::make_tuple(1, '2', 3.3, "abc"s), hana::is_a<std::string>) == hana::just("abc"s)
   );
   BOOST_HANA_RUNTIME_CHECK(
   "abc"s ^hana::in^ hana::make_tuple(1, '2', 3.3, "abc"s)
   );
   }

## Concrete models

`hana::tuple`

## Variables
constexpr auto | boost::hana::cartesian_product
| Computes the cartesian product of a sequence of sequences.Given a sequence of sequences, `cartesian_product` returns a new sequence of sequences containing the cartesian product of the original sequences. For this method to finish, a finite number of finite sequences must be provided. More...
constexpr auto | boost::hana::drop_back
| Drop the last `n` elements of a finite sequence, and return the rest.Given a finite `Sequence` `xs` with a linearization of `[x1, ..., xm]` and a non-negative `IntegralConstant` `n`, `drop_back(xs, n)` is a sequence with the same tag as `xs` whose linearization is `[x1, ..., xm-n]`. If `n` is not given, it defaults to an `IntegralConstant` with a value equal to `1`. More...
constexpr auto | boost::hana::group
| Group adjacent elements of a sequence that all respect a binary predicate, by default equality.Given a finite Sequence and an optional predicate (by default `equal`), `group` returns a sequence of subsequences representing groups of adjacent elements that are "equal" with respect to the predicate. In other words, the groups are such that the predicate is satisfied when it is applied to any two adjacent elements in that group. The sequence returned by `group` is such that the concatenation of its elements is equal to the original sequence, which is equivalent to saying that the order of the elements is not changed. More...
constexpr insert_t | boost::hana::insert {}
| Insert a value at a given index in a sequence.Given a sequence, an index and an element to insert, `insert` inserts the element at the given index. More...
constexpr auto | boost::hana::insert_range
| Insert several values at a given index in a sequence.Given a sequence, an index and any `Foldable` containing elements to insert, `insert_range` inserts the elements in the `Foldable` at the given index of the sequence. More...
constexpr auto | boost::hana::intersperse
| Insert a value between each pair of elements in a finite sequence.Given a finite `Sequence` `xs` with a linearization of `[x1, x2, ..., xn]`, `intersperse(xs, z)` is a new sequence with a linearization of `[x1, z, x2, z, x3, ..., xn-1, z, xn]`. In other words, it inserts the `z` element between every pair of elements of the original sequence. If the sequence is empty or has a single element, `intersperse` returns the sequence as-is. In all cases, the sequence must be finite. More...
constexpr auto | boost::hana::partition
| Partition a sequence based on a `predicate`.Specifically, returns an unspecified `Product` whose first element is a sequence of the elements satisfying the predicate, and whose second element is a sequence of the elements that do not satisfy the predicate. More...
constexpr auto | boost::hana::permutations
| Return a sequence of all the permutations of the given sequence.Specifically, `permutations(xs)` is a sequence whose elements are permutations of the original sequence `xs`. The permutations are not guaranteed to be in any specific order. Also note that the number of permutations grows very rapidly as the length of the original sequence increases. The growth rate is `O(length(xs)!)`; with a sequence `xs` of length only 8, `permutations(xs)` contains over 40 000 elements! More...
constexpr auto | boost::hana::remove_at
| Remove the element at a given index from a sequence.`remove_at` returns a new sequence identical to the original, except that the element at the given index is removed. Specifically, `remove_at([x0, ..., xn-1, xn, xn+1, ..., xm], n)` is a new sequence equivalent to `[x0, ..., xn-1, xn+1, ..., xm]`. More...
template<std::size_t n>
constexpr auto | boost::hana::remove_at_c
| Equivalent to `remove_at`; provided for convenience. More...
constexpr auto | boost::hana::remove_range
| Remove the elements inside a given range of indices from a sequence.`remove_range` returns a new sequence identical to the original, except that elements at indices in the provided range are removed. Specifically, `remove_range([x0, ..., xn], from, to)` is a new sequence equivalent to `[x0, ..., x_from-1, x_to, ..., xn]`. More...
template<std::size_t from, std::size_t to>
constexpr auto | boost::hana::remove_range_c
| Equivalent to `remove_range`; provided for convenience. More...
constexpr auto | boost::hana::reverse
| Reverse a sequence.Specifically, `reverse(xs)` is a new sequence containing the same elements as `xs`, except in reverse order. More...
constexpr auto | boost::hana::scan_left
| Fold a Sequence to the left and return a list containing the successive reduction states.Like `fold_left`, `scan_left` reduces a sequence to a single value using a binary operation. However, unlike `fold_left`, it builds up a sequence of the intermediary results computed along the way and returns that instead of only the final reduction state. Like `fold_left`, `scan_left` can be used with or without an initial reduction state. More...
constexpr auto | boost::hana::scan_right
| Fold a Sequence to the right and return a list containing the successive reduction states.Like `fold_right`, `scan_right` reduces a sequence to a single value using a binary operation. However, unlike `fold_right`, it builds up a sequence of the intermediary results computed along the way and returns that instead of only the final reduction state. Like `fold_right`, `scan_right` can be used with or without an initial reduction state. More...
constexpr auto | boost::hana::slice
| Extract the elements of a `Sequence` at the given indices.Given an arbitrary sequence of `indices`, `slice` returns a new sequence of the elements of the original sequence that appear at those indices. In other words,. More...
template<std::size_t from, std::size_t to>
constexpr auto | boost::hana::slice_c
| Shorthand to `slice` a contiguous range of elements.`slice_c` is simply a shorthand to slice a contiguous range of elements. In particular, `slice_c<from, to>(xs)` is equivalent to `slice(xs, range_c<std::size_t, from, to>)`, which simply slices all the elements of `xs` contained in the half-open interval delimited by `[from, to)`. Like for `slice`, the indices used with `slice_c` are 0-based and they must be in the bounds of the sequence being sliced. More...
constexpr auto | boost::hana::sort
| Sort a sequence, optionally based on a custom `predicate`.Given a Sequence and an optional predicate (by default `less`), `sort` returns a new sequence containing the same elements as the original, except they are ordered in such a way that if `x` comes before `y` in the sequence, then either `predicate(x, y)` is true, or both `predicate(x, y)` and `predicate(y, x)` are false. More...
constexpr auto | boost::hana::span
| Returns a `Product` containing the longest prefix of a sequence satisfying a predicate, and the rest of the sequence.The first component of the returned `Product` is a sequence for which all elements satisfy the given predicate. The second component of the returned `Product` is a sequence containing the remainder of the argument. Both or either sequences may be empty, depending on the input argument. More specifically,. More...
constexpr auto | boost::hana::take_back
| Returns the last `n` elements of a sequence, or the whole sequence if the sequence has less than `n` elements.Given a `Sequence` `xs` and an `IntegralConstant` `n`, `take_back(xs, n)` is a new sequence containing the last `n` elements of `xs`, in the same order. If `length(xs) <= n`, the whole sequence is returned and no error is triggered. More...
template<std::size_t n>
constexpr auto | boost::hana::take_back_c
| Equivalent to `take_back`; provided for convenience. More...
constexpr auto | boost::hana::take_front
| Returns the first `n` elements of a sequence, or the whole sequence if the sequence has less than `n` elements.Given a `Sequence` `xs` and an `IntegralConstant` `n`, `take_front(xs, n)` is a new sequence containing the first `n` elements of `xs`, in the same order. If `length(xs) <= n`, the whole sequence is returned and no error is triggered. More...
template<std::size_t n>
constexpr auto | boost::hana::take_front_c
| Equivalent to `take_front`; provided for convenience. More...
constexpr auto | boost::hana::take_while
| Take elements from a sequence while the `predicate` is satisfied.Specifically, `take_while` returns a new sequence containing the longest prefix of `xs` in which all the elements satisfy the given predicate. More...
template<typename S >
constexpr auto | boost::hana::unfold_left
| Dual operation to `fold_left` for sequences.While `fold_left` reduces a structure to a summary value from the left, `unfold_left` builds a sequence from a seed value and a function, starting from the left. More...
template<typename S >
constexpr auto | boost::hana::unfold_right
| Dual operation to `fold_right` for sequences.While `fold_right` reduces a structure to a summary value from the right, `unfold_right` builds a sequence from a seed value and a function, starting from the right. More...
constexpr auto | boost::hana::unique
| Removes all consecutive duplicate elements from a Sequence.Given a `Sequence` and an optional binary predicate, `unique` returns a new sequence containing only the first element of every subrange of the original sequence whose elements are all equal. In other words, it turns a sequence of the form `[a, a, b, c, c, c, d, d, d, a]` into a sequence `[a, b, c, d, a]`. The equality of two elements is determined by the provided `predicate`, or by `equal` if no `predicate` is provided. More...
constexpr auto | boost::hana::zip
| Zip one sequence or more.Given `n` sequences `s1, ..., sn`, `zip` produces a sequence whose `i`-th element is a tuple of `(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip` produces a sequence of the form. More...
constexpr auto | boost::hana::zip_shortest
| Zip one sequence or more.Given `n` sequences `s1, ..., sn`, `zip_shortest` produces a sequence whose `i`-th element is a tuple of `(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip_shortest` produces a sequence of the form. More...
constexpr auto | boost::hana::zip_shortest_with
| Zip one sequence or more with a given function.Given a `n`-ary function `f` and `n` sequences `s1, ..., sn`, `zip_shortest_with` produces a sequence whose `i`-th element is `f(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip_shortest_with` produces a sequence of the form. More...
constexpr auto | boost::hana::zip_with
| Zip one sequence or more with a given function.Given a `n`-ary function `f` and `n` sequences `s1, ..., sn`, `zip_with` produces a sequence whose `i`-th element is `f(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip_with` produces a sequence of the form. More...

## Variable Documentation

constexpr auto boost::hana::cartesian_product

`#include <boost/hana/fwd/cartesian_product.hpp>`

Initial value:
= [](auto&& xs) {
return tag-dispatched;
}

Computes the cartesian product of a sequence of sequences.Given a sequence of sequences, `cartesian_product` returns a new sequence of sequences containing the cartesian product of the original sequences. For this method to finish, a finite number of finite sequences must be provided.

Note
  All the sequences must have the same tag, and that tag must also match that of the top-level sequence.

## Signature

Given a `Sequence` `S(T)`, the signature is

\[ \mathtt{cartesian\_product} : S(S(T)) \to S(S(T)) \]

Parameters

  xs | A sequence of sequences of which the cartesian product is computed.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/cartesian_product.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
namespace hana = boost::hana;
constexpr auto tuples = hana::make_tuple(
hana::make_tuple(1, 2, 3),
hana::make_tuple('a', 'b'),
hana::make_tuple(hana::type_c<int>, hana::type_c<char>)
);
constexpr auto prod = hana::make_tuple(
hana::make_tuple(1, 'a', hana::type_c<int>),
hana::make_tuple(1, 'a', hana::type_c<char>),
hana::make_tuple(1, 'b', hana::type_c<int>),
hana::make_tuple(1, 'b', hana::type_c<char>),
hana::make_tuple(2, 'a', hana::type_c<int>),
hana::make_tuple(2, 'a', hana::type_c<char>),
hana::make_tuple(2, 'b', hana::type_c<int>),
hana::make_tuple(2, 'b', hana::type_c<char>),
hana::make_tuple(3, 'a', hana::type_c<int>),
hana::make_tuple(3, 'a', hana::type_c<char>),
hana::make_tuple(3, 'b', hana::type_c<int>),
hana::make_tuple(3, 'b', hana::type_c<char>)
);
static_assert(hana::cartesian_product(tuples) == prod, "");
int main() { }

constexpr auto boost::hana::drop_back

`#include <boost/hana/fwd/drop_back.hpp>`

Initial value:
= [](auto&& xs[, auto const& n]) {
return tag-dispatched;
}

Drop the last `n` elements of a finite sequence, and return the rest.Given a finite `Sequence` `xs` with a linearization of `[x1, ..., xm]` and a non-negative `IntegralConstant` `n`, `drop_back(xs, n)` is a sequence with the same tag as `xs` whose linearization is `[x1, ..., xm-n]`. If `n` is not given, it defaults to an `IntegralConstant` with a value equal to `1`.

In case `length(xs) <= n`, `drop_back` will simply drop the whole sequence without failing, thus returning an empty sequence.

Parameters

  xs | The sequence from which elements are dropped.
  n | A non-negative `IntegralConstant` representing the number of elements to be dropped from the end of the sequence. If `n` is not given, it defaults to an `IntegralConstant` with a value equal to `1`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/drop_back.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
constexpr auto xs = hana::make_tuple(0, '1', 2.0);
static_assert(hana::drop_back(xs, hana::size_c<0>) == xs, "");
static_assert(hana::drop_back(xs, hana::size_c<1>) == hana::make_tuple(0, '1'), "");
static_assert(hana::drop_back(xs, hana::size_c<2>) == hana::make_tuple(0), "");
BOOST_HANA_CONSTANT_CHECK(hana::drop_back(xs, hana::size_c<3>) == hana::make_tuple());
BOOST_HANA_CONSTANT_CHECK(hana::drop_back(xs, hana::size_c<4>) == hana::make_tuple());
static_assert(hana::drop_back(xs) == hana::make_tuple(0, '1'), "");
int main() { }

constexpr auto boost::hana::group

`#include <boost/hana/fwd/group.hpp>`

Initial value:
= [](auto&& xs[, auto&& predicate]) {
return tag-dispatched;
}

Group adjacent elements of a sequence that all respect a binary predicate, by default equality.Given a finite Sequence and an optional predicate (by default `equal`), `group` returns a sequence of subsequences representing groups of adjacent elements that are "equal" with respect to the predicate. In other words, the groups are such that the predicate is satisfied when it is applied to any two adjacent elements in that group. The sequence returned by `group` is such that the concatenation of its elements is equal to the original sequence, which is equivalent to saying that the order of the elements is not changed.

If no predicate is provided, adjacent elements in the sequence must all be compile-time `Comparable`.

## Signature

Given a Sequence `s` with tag `S(T)`, an `IntegralConstant` `Bool` holding a value of type `bool`, and a predicate \( pred : T \times T \to Bool \), `group` has the following signatures. For the variant with a provided predicate,

\[ \mathtt{group} : S(T) \times (T \times T \to Bool) \to S(S(T)) \]

for the variant without a custom predicate, `T` is required to be Comparable. The signature is then

\[ \mathtt{group} : S(T) \to S(S(T)) \]

Parameters

  xs | The sequence to split into groups.
  predicate | A binary function called as `predicate(x, y)`, where `x` and `y` are adjacent elements in the sequence, whether both elements should be in the same group (subsequence) of the result. In the current version of the library, the result returned by `predicate` must be an `IntegralConstant` holding a value of a type convertible to `bool`. Also, `predicate` has to define an equivalence relation as defined by the `Comparable` concept. When this predicate is not provided, it defaults to `equal`, which requires the comparison of any two adjacent elements in the sequence to return a boolean `IntegralConstant`.

## Syntactic sugar (`group.by`)

`group` can be called in a third way, which provides a nice syntax especially when working with the `comparing` combinator:

group.by(predicate, xs) == group(xs, predicate)
group.by(predicate) == group(-, predicate)

where `group(-, predicate)` denotes the partial application of `group` to `predicate`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/comparing.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/group.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/length.hpp>
#include <boost/hana/range.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
namespace hana = boost::hana;
// group without a predicate
BOOST_HANA_CONSTANT_CHECK(
hana::group(hana::make_tuple(hana::int_c<1>, hana::long_c<1>, hana::type_c<int>, hana::char_c<'x'>, hana::char_c<'x'>))
== hana::make_tuple(
hana::make_tuple(hana::int_c<1>, hana::long_c<1>),
hana::make_tuple(hana::type_c<int>),
hana::make_tuple(hana::char_c<'x'>, hana::char_c<'x'>)
)
);
// group with a predicate
constexpr auto tuples = hana::make_tuple(
hana::range_c<int, 0, 1>,
hana::range_c<int, 0, 2>,
hana::range_c<int, 1, 3>,
hana::range_c<int, 2, 6>
);
BOOST_HANA_CONSTANT_CHECK(
hana::group(tuples, hana::comparing(hana::length))
== hana::make_tuple(
hana::make_tuple(
hana::range_c<int, 0, 1>
),
hana::make_tuple(
hana::range_c<int, 0, 2>,
hana::range_c<int, 1, 3>
),
hana::make_tuple(
hana::range_c<int, 2, 6>
)
)
);
// group.by is syntactic sugar
static_assert(
hana::group.by(hana::comparing(hana::typeid_),
hana::make_tuple(1, 2, 3, 'x', 'y', 4.4, 5.5))
== hana::make_tuple(
hana::make_tuple(1, 2, 3),
hana::make_tuple('x', 'y'),
hana::make_tuple(4.4, 5.5)
)
, "");
int main() { }

constexpr auto boost::hana::insert {}
| related

`#include <boost/hana/fwd/insert.hpp>`

Insert a value at a given index in a sequence.Given a sequence, an index and an element to insert, `insert` inserts the element at the given index.

Parameters

  xs | The sequence in which a value should be inserted.
  n | The index at which an element should be inserted. This must be a non-negative `Constant` of an integral type, and it must also be true that `n < length(xs)` if `xs` is a finite sequence.
  element | The element to insert in the sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/insert.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/tuple.hpp>
#include <string>
namespace hana = boost::hana;
using namespace hana::literals;
using namespace std::literals;
int main() {
auto xs = hana::make_tuple("Hello"s, "world!"s);
BOOST_HANA_RUNTIME_CHECK(
hana::insert(xs, 1_c, " "s) == hana::make_tuple("Hello"s, " "s, "world!"s)
);
}

constexpr auto boost::hana::insert_range

`#include <boost/hana/fwd/insert_range.hpp>`

Initial value:
= [](auto&& xs, auto&& n, auto&& elements) {
return tag-dispatched;
}

Insert several values at a given index in a sequence.Given a sequence, an index and any `Foldable` containing elements to insert, `insert_range` inserts the elements in the `Foldable` at the given index of the sequence.

Parameters

  xs | The sequence in which values should be inserted.
  n | The index at which elements should be inserted. This must be a non-negative `Constant` of an integral type, and it must also be true that `n < length(xs)` if `xs` is a finite sequence.
  elements | A `Foldable` containing elements to insert in the sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/insert_range.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/tuple.hpp>
#include <string>
namespace hana = boost::hana;
using namespace hana::literals;
using namespace std::literals;
int main() {
auto xs = hana::make_tuple("Hello"s, "world!"s);
BOOST_HANA_RUNTIME_CHECK(
hana::insert_range(xs, 1_c, hana::make_tuple(1, 2, 3)) == hana::make_tuple("Hello"s, 1, 2, 3, "world!"s)
);
}

constexpr auto boost::hana::intersperse

`#include <boost/hana/fwd/intersperse.hpp>`

Initial value:
= [](auto&& xs, auto&& z) {
return tag-dispatched;
}

Insert a value between each pair of elements in a finite sequence.Given a finite `Sequence` `xs` with a linearization of `[x1, x2, ..., xn]`, `intersperse(xs, z)` is a new sequence with a linearization of `[x1, z, x2, z, x3, ..., xn-1, z, xn]`. In other words, it inserts the `z` element between every pair of elements of the original sequence. If the sequence is empty or has a single element, `intersperse` returns the sequence as-is. In all cases, the sequence must be finite.

Parameters

  xs | The sequence in which a value is interspersed.
  z | The value to be inserted between every pair of elements of the sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/intersperse.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(hana::intersperse(hana::make_tuple(1, '2', 3.3), 'x') == hana::make_tuple(1, 'x', '2', 'x', 3.3), "");
BOOST_HANA_CONSTANT_CHECK(hana::intersperse(hana::make_tuple(), 'x') == hana::make_tuple());
int main() { }

constexpr auto boost::hana::partition

`#include <boost/hana/fwd/partition.hpp>`

Initial value:
= [](auto&& xs, auto&& predicate) {
return tag-dispatched;
}

Partition a sequence based on a `predicate`.Specifically, returns an unspecified `Product` whose first element is a sequence of the elements satisfying the predicate, and whose second element is a sequence of the elements that do not satisfy the predicate.

## Signature

Given a Sequence `S(T)`, an `IntegralConstant` `Bool` holding a value of type `bool`, and a predicate \( T \to Bool \), `partition` has the following signature:

\[ \mathtt{partition} : S(T) \times (T \to Bool) \to S(T) \times S(T) \]

Parameters

  xs | The sequence to be partitioned.
  predicate | A function called as `predicate(x)` for each element `x` in the sequence, and returning whether `x` should be added to the sequence in the first component or in the second component of the resulting pair. In the current version of the library, `predicate` must return an `IntegralConstant` holding a value convertible to `bool`.

## Syntactic sugar (`partition.by`)

`partition` can be called in an alternate way, which provides a nice syntax in some cases where the predicate is short:

partition.by(predicate, xs) == partition(xs, predicate)
partition.by(predicate) == partition(-, predicate)

where `partition(-, predicate)` denotes the partial application of `partition` to `predicate`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/ext/std/integral_constant.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/mod.hpp>
#include <boost/hana/not_equal.hpp>
#include <boost/hana/pair.hpp>
#include <boost/hana/partition.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <type_traits>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(
hana::partition(hana::tuple_c<int, 1, 2, 3, 4, 5, 6, 7>, [](auto x) {
return x % hana::int_c<2> != hana::int_c<0>;
})
==
hana::make_pair(
hana::tuple_c<int, 1, 3, 5, 7>,
hana::tuple_c<int, 2, 4, 6>
)
);
BOOST_HANA_CONSTANT_CHECK(
hana::partition(hana::tuple_t<void, int, float, char, double>, hana::trait<std::is_floating_point>)
==
hana::make_pair(
hana::tuple_t<float, double>,
hana::tuple_t<void, int, char>
)
);
// partition.by is syntactic sugar
BOOST_HANA_CONSTANT_CHECK(
hana::partition.by(hana::trait<std::is_floating_point>,
hana::tuple_t<void, int, float, char, double>)
==
hana::make_pair(
hana::tuple_t<float, double>,
hana::tuple_t<void, int, char>
)
);
int main() { }

constexpr auto boost::hana::permutations

`#include <boost/hana/fwd/permutations.hpp>`

Initial value:
= [](auto&& xs) {
return tag-dispatched;
}

Return a sequence of all the permutations of the given sequence.Specifically, `permutations(xs)` is a sequence whose elements are permutations of the original sequence `xs`. The permutations are not guaranteed to be in any specific order. Also note that the number of permutations grows very rapidly as the length of the original sequence increases. The growth rate is `O(length(xs)!)`; with a sequence `xs` of length only 8, `permutations(xs)` contains over 40 000 elements!

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/all_of.hpp>
#include <boost/hana/assert.hpp>
#include <boost/hana/config.hpp>
#include <boost/hana/contains.hpp>
#include <boost/hana/functional/curry.hpp>
#include <boost/hana/permutations.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTEXPR_LAMBDA auto is_permutation_of = hana::curry<2>([](auto xs, auto perm) {
return hana::contains(hana::permutations(xs), perm);
});
int main() {
BOOST_HANA_CONSTEXPR_CHECK(
hana::all_of(
hana::make_tuple(
hana::make_tuple('1', 2, 3.0),
hana::make_tuple('1', 3.0, 2),
hana::make_tuple(2, '1', 3.0),
hana::make_tuple(2, 3.0, '1'),
hana::make_tuple(3.0, '1', 2),
hana::make_tuple(3.0, 2, '1')
),
is_permutation_of(hana::make_tuple('1', 2, 3.0))
)
);
}

constexpr auto boost::hana::remove_at

`#include <boost/hana/fwd/remove_at.hpp>`

Initial value:
= [](auto&& xs, auto const& n) {
return tag-dispatched;
}

Remove the element at a given index from a sequence.`remove_at` returns a new sequence identical to the original, except that the element at the given index is removed. Specifically, `remove_at([x0, ..., xn-1, xn, xn+1, ..., xm], n)` is a new sequence equivalent to `[x0, ..., xn-1, xn+1, ..., xm]`.

Note
  The behavior is undefined if the index is out of the bounds of the sequence.

Parameters

  xs | A sequence from which an element is to be removed.
  n | An non-negative `IntegralConstant` representing the index of the element to be removed from the sequence. The behavior is undefined if that index is not in the bounds of the sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/remove_at.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
constexpr auto xs = hana::make_tuple(0, '1', 2.2, 3u);
static_assert(hana::remove_at(xs, hana::size_c<2>) == hana::make_tuple(0, '1', 3u), "");
int main() { }
template<std::size_t n>

constexpr auto boost::hana::remove_at_c

`#include <boost/hana/fwd/remove_at.hpp>`

Initial value:
= [](auto&& xs) {
return hana::remove_at(forwarded(xs), hana::size_c<n>);
}
boost::hana::remove_at
constexpr auto remove_at
Remove the element at a given index from a sequence.remove_at returns a new sequence identical to the...
Definition: remove_at.hpp:46

Equivalent to `remove_at`; provided for convenience.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/remove_at.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
constexpr auto xs = hana::make_tuple(0, '1', 2.2, 3u);
static_assert(hana::remove_at_c<2>(xs) == hana::make_tuple(0, '1', 3u), "");
int main() { }

constexpr auto boost::hana::remove_range

`#include <boost/hana/fwd/remove_range.hpp>`

Initial value:
= [](auto&& xs, auto const& from, auto const& to) {
return tag-dispatched;
}
boost::hana::to
constexpr auto to
Converts an object from one data type to another.
Definition: to.hpp:97

Remove the elements inside a given range of indices from a sequence.`remove_range` returns a new sequence identical to the original, except that elements at indices in the provided range are removed. Specifically, `remove_range([x0, ..., xn], from, to)` is a new sequence equivalent to `[x0, ..., x_from-1, x_to, ..., xn]`.

Note
  The behavior is undefined if the range contains any index out of the bounds of the sequence.

Parameters

  xs | A sequence from which elements are removed.
  [from,to) | An half-open interval of `IntegralConstant`s representing the indices of the elements to be removed from the sequence. The `IntegralConstant`s in the half-open interval must be non-negative and in the bounds of the sequence. The half-open interval must also be valid, meaning that `from <= to`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/remove_range.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
constexpr auto xs = hana::make_tuple(0, '1', 2.2, 3u, 4, 5.5);
static_assert(hana::remove_range(xs, hana::size_c<2>, hana::size_c<4>) == hana::make_tuple(0, '1', 4, 5.5), "");
int main() { }
template<std::size_t from, std::size_t to>

constexpr auto boost::hana::remove_range_c

`#include <boost/hana/fwd/remove_range.hpp>`

Initial value:
= [](auto&& xs) {
return hana::remove_range(forwarded(xs), hana::size_c<from>, hana::size_c<to>);
}
boost::hana::remove_range
constexpr auto remove_range
Remove the elements inside a given range of indices from a sequence.remove_range returns a new sequen...
Definition: remove_range.hpp:49

Equivalent to `remove_range`; provided for convenience.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/remove_range.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
constexpr auto xs = hana::make_tuple(0, '1', 2.2, 3u, 4, 5.5);
static_assert(hana::remove_range_c<2, 4>(xs) == hana::make_tuple(0, '1', 4, 5.5), "");
int main() { }

constexpr auto boost::hana::reverse

`#include <boost/hana/fwd/reverse.hpp>`

Initial value:
= [](auto&& xs) {
return tag-dispatched;
}

Reverse a sequence.Specifically, `reverse(xs)` is a new sequence containing the same elements as `xs`, except in reverse order.

Parameters

  xs | The sequence to reverse.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/reverse.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(hana::reverse(hana::make_tuple(1, '2', 3.3)) == hana::make_tuple(3.3, '2', 1), "");
int main() { }

constexpr auto boost::hana::scan_left

`#include <boost/hana/fwd/scan_left.hpp>`

Initial value:
= [](auto&& xs[, auto&& state], auto const& f) {
return tag-dispatched;
}

Fold a Sequence to the left and return a list containing the successive reduction states.Like `fold_left`, `scan_left` reduces a sequence to a single value using a binary operation. However, unlike `fold_left`, it builds up a sequence of the intermediary results computed along the way and returns that instead of only the final reduction state. Like `fold_left`, `scan_left` can be used with or without an initial reduction state.

When the sequence is empty, two things may arise. If an initial state was provided, a singleton list containing that state is returned. Otherwise, if no initial state was provided, an empty list is returned. In particular, unlike for `fold_left`, using `scan_left` on an empty sequence without an initial state is not an error.

More specifically, `scan_left([x1, ..., xn], state, f)` is a sequence whose `i`th element is equivalent to `fold_left([x1, ..., xi], state, f)`. The no-state variant is handled in an analogous way. For illustration, consider this left fold on a short sequence:

fold_left([x1, x2, x3], state, f) == f(f(f(state, x1), x2), x3)

The analogous sequence generated with `scan_left` will be

scan_left([x1, x2, x3], state, f) == [
state,
f(state, x1),
f(f(state, x1), x2),
f(f(f(state, x1), x2), x3)
]

Similarly, consider this left fold (without an initial state) on a short sequence:

fold_left([x1, x2, x3, x4], f) == f(f(f(x1, x2), x3), x4)

The analogous sequence generated with `scan_left` will be

scan_left([x1, x2, x3, x4], f) == [
x1,
f(x1, x2),
f(f(x1, x2), x3),
f(f(f(x1, x2), x3), x4)
]

Parameters

  xs | The sequence to scan from the left.
  state | The (optional) initial reduction state.
  f | A binary function called as `f(state, x)`, where `state` is the result accumulated so far and `x` is an element in the sequence. If no initial state is provided, `f` is called as `f(x1, x2)`, where `x1` and `x2` are both elements of the sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/scan_left.hpp>
#include <boost/hana/tuple.hpp>
#include <sstream>
namespace hana = boost::hana;
auto to_string = [](auto x) {
std::ostringstream ss;
ss << x;
return ss.str();
};
auto f = [](auto state, auto element) {
return "f(" + to_string(state) + ", " + to_string(element) + ")";
};
int main() {
// with initial state
BOOST_HANA_RUNTIME_CHECK(hana::scan_left(hana::make_tuple(2, "3", '4'), 1, f) == hana::make_tuple(
1,
"f(1, 2)",
"f(f(1, 2), 3)",
"f(f(f(1, 2), 3), 4)"
));
// without initial state
BOOST_HANA_RUNTIME_CHECK(hana::scan_left(hana::make_tuple(1, "2", '3'), f) == hana::make_tuple(
1,
"f(1, 2)",
"f(f(1, 2), 3)"
));
}

constexpr auto boost::hana::scan_right

`#include <boost/hana/fwd/scan_right.hpp>`

Initial value:
= [](auto&& xs[, auto&& state], auto const& f) {
return tag-dispatched;
}

Fold a Sequence to the right and return a list containing the successive reduction states.Like `fold_right`, `scan_right` reduces a sequence to a single value using a binary operation. However, unlike `fold_right`, it builds up a sequence of the intermediary results computed along the way and returns that instead of only the final reduction state. Like `fold_right`, `scan_right` can be used with or without an initial reduction state.

When the sequence is empty, two things may arise. If an initial state was provided, a singleton list containing that state is returned. Otherwise, if no initial state was provided, an empty list is returned. In particular, unlike for `fold_right`, using `scan_right` on an empty sequence without an initial state is not an error.

More specifically, `scan_right([x1, ..., xn], state, f)` is a sequence whose `i`th element is equivalent to `fold_right([x1, ..., xi], state, f)`. The no-state variant is handled in an analogous way. For illustration, consider this right fold on a short sequence:

fold_right([x1, x2, x3], state, f) == f(x1, f(x2, f(x3, state)))

The analogous sequence generated with `scan_right` will be

scan_right([x1, x2, x3], state, f) == [
f(x1, f(x2, f(x3, state))),
f(x2, f(x3, state)),
f(x3, state),
state
]

Similarly, consider this right fold (without an initial state) on a short sequence:

fold_right([x1, x2, x3, x4], f) == f(x1, f(x2, f(x3, x4)))

The analogous sequence generated with `scan_right` will be

scan_right([x1, x2, x3, x4], f) == [
f(x1, f(x2, f(x3, x4))),
f(x2, f(x3, x4)),
f(x3, x4),
x4
]

Parameters

  xs | The sequence to scan from the right.
  state | The (optional) initial reduction state.
  f | A binary function called as `f(x, state)`, where `state` is the result accumulated so far and `x` is an element in the sequence. When no initial state is provided, `f` is called as `f(x1, x2)`, where `x1` and `x2` are elements of the sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/scan_right.hpp>
#include <boost/hana/tuple.hpp>
#include <sstream>
namespace hana = boost::hana;
auto to_string = [](auto x) {
std::ostringstream ss;
ss << x;
return ss.str();
};
auto f = [](auto element, auto state) {
return "f(" + to_string(element) + ", " + to_string(state) + ")";
};
int main() {
// with initial state
BOOST_HANA_RUNTIME_CHECK(hana::scan_right(hana::make_tuple(1, "2", '3'), 4, f) == hana::make_tuple(
"f(1, f(2, f(3, 4)))",
"f(2, f(3, 4))",
"f(3, 4)",
4
));
// without initial state
BOOST_HANA_RUNTIME_CHECK(hana::scan_right(hana::make_tuple(1, "2", '3'), f) == hana::make_tuple(
"f(1, f(2, 3))",
"f(2, 3)",
'3'
));
}

constexpr auto boost::hana::slice

`#include <boost/hana/fwd/slice.hpp>`

Initial value:
= [](auto&& xs, auto&& indices) {
return tag-dispatched;
}

Extract the elements of a `Sequence` at the given indices.Given an arbitrary sequence of `indices`, `slice` returns a new sequence of the elements of the original sequence that appear at those indices. In other words,.

slice([x1, ..., xn], [i1, ..., ik]) == [x_i1, ..., x_ik]

The indices do not have to be ordered or contiguous in any particular way, but they must not be out of the bounds of the sequence. It is also possible to specify the same index multiple times, in which case the element at this index will be repeatedly included in the resulting sequence.

Parameters

  xs | The sequence from which a subsequence is extracted.
  indices | A compile-time `Foldable` containing non-negative `IntegralConstant`s representing the indices. The indices are 0-based, and they must all be in bounds of the `xs` sequence. Note that any `Foldable` will really do (no need for an `Iterable`, for example); the linearization of the `indices` is used to determine the order of the elements included in the slice.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/core/to.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/filter.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/length.hpp>
#include <boost/hana/mod.hpp>
#include <boost/hana/range.hpp>
#include <boost/hana/slice.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
namespace hana = boost::hana;
using namespace hana::literals;
// Slice a contiguous range
constexpr auto xs = hana::make_tuple(0, '1', 2.2, 3_c, hana::type_c<float>);
static_assert(
hana::slice(xs, hana::tuple_c<std::size_t, 1, 2, 3>) ==
hana::make_tuple('1', 2.2, 3_c)
, "");
// A more complex example with a non-contiguous range
constexpr auto letters = hana::to_tuple(hana::range_c<char, 'a', 'z'>);
constexpr auto indices = hana::to_tuple(hana::make_range(hana::size_c<0>, hana::length(letters)));
auto even_indices = hana::filter(indices, [](auto n) {
return n % hana::size_c<2> == hana::size_c<0>;
});
BOOST_HANA_CONSTANT_CHECK(
hana::slice(letters, even_indices) == hana::tuple_c<char,
'a', 'c', 'e', 'g', 'i', 'k', 'm', 'o', 'q', 's', 'u', 'w', 'y'
>
);
int main() { }
template<std::size_t from, std::size_t to>

constexpr auto boost::hana::slice_c

`#include <boost/hana/fwd/slice.hpp>`

Initial value:
= [](auto&& xs) {
return hana::slice(forwarded(xs), hana::range_c<std::size_t, from, to>);
}
boost::hana::slice
constexpr auto slice
Extract the elements of a Sequence at the given indices.Given an arbitrary sequence of indices...
Definition: slice.hpp:53

Shorthand to `slice` a contiguous range of elements.`slice_c` is simply a shorthand to slice a contiguous range of elements. In particular, `slice_c<from, to>(xs)` is equivalent to `slice(xs, range_c<std::size_t, from, to>)`, which simply slices all the elements of `xs` contained in the half-open interval delimited by `[from, to)`. Like for `slice`, the indices used with `slice_c` are 0-based and they must be in the bounds of the sequence being sliced.

Template Parameters

  from | The index of the first element in the slice.
  to | One-past the index of the last element in the slice. It must hold that `from <= to`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/slice.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
namespace hana = boost::hana;
static_assert(
hana::slice_c<1, 3>(hana::make_tuple(1, '2', 3.3, hana::type_c<float>))
==
hana::make_tuple('2', 3.3)
, "");
int main() { }

constexpr auto boost::hana::sort

`#include <boost/hana/fwd/sort.hpp>`

Initial value:
= [](auto&& xs[, auto&& predicate]) {
return tag-dispatched;
}

Sort a sequence, optionally based on a custom `predicate`.Given a Sequence and an optional predicate (by default `less`), `sort` returns a new sequence containing the same elements as the original, except they are ordered in such a way that if `x` comes before `y` in the sequence, then either `predicate(x, y)` is true, or both `predicate(x, y)` and `predicate(y, x)` are false.

Also note that the sort is guaranteed to be stable. Hence, if `x` comes before `y` in the original sequence and both `predicate(x, y)` and `predicate(y, x)` are false, then `x` will come before `y` in the resulting sequence.

If no predicate is provided, the elements in the sequence must all be compile-time `Orderable`.

## Signature

Given a `Sequence` `S(T)`, a boolean `IntegralConstant` `Bool` and a binary predicate \( T \times T \to Bool \), `sort` has the following signatures. For the variant with a provided predicate,

\[ \mathtt{sort} : S(T) \times (T \times T \to Bool) \to S(T) \]

for the variant without a custom predicate, `T` is required to be `Orderable`. The signature is then

\[ \mathtt{sort} : S(T) \to S(T) \]

Parameters

  xs | The sequence to sort.
  predicate | A function called as `predicate(x, y)` for two elements `x` and `y` of the sequence, and returning a boolean `IntegralConstant` representing whether `x` is to be considered less than `y`, i.e. whether `x` should appear before `y` in the resulting sequence. More specifically, `predicate` must define a strict weak ordering on the elements of the sequence. When the predicate is not specified, this defaults to `less`. In the current version of the library, the predicate has to return an `IntegralConstant` holding a value convertible to a `bool`.

## Syntactic sugar (`sort.by`)

`sort` can be called in a third way, which provides a nice syntax especially when working with the `ordering` combinator:

sort.by(predicate, xs) == sort(xs, predicate)
sort.by(predicate) == sort(-, predicate)

where `sort(-, predicate)` denotes the partial application of `sort` to `predicate`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/front.hpp>
#include <boost/hana/greater.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/negate.hpp>
#include <boost/hana/ordering.hpp>
#include <boost/hana/sort.hpp>
#include <boost/hana/tuple.hpp>
#include <string>
namespace hana = boost::hana;
using namespace hana::literals;
using namespace std::literals;
// sort without a predicate
BOOST_HANA_CONSTANT_CHECK(
hana::sort(hana::make_tuple(1_c, -2_c, 3_c, 0_c)) ==
hana::make_tuple(-2_c, 0_c, 1_c, 3_c)
);
// sort with a predicate
BOOST_HANA_CONSTANT_CHECK(
hana::sort(hana::make_tuple(1_c, -2_c, 3_c, 0_c), hana::greater) ==
hana::make_tuple(3_c, 1_c, 0_c, -2_c)
);
int main() {
// sort.by is syntactic sugar
auto tuples = hana::make_tuple(
hana::make_tuple(2_c, 'x', nullptr),
hana::make_tuple(1_c, "foobar"s, hana::int_c<4>)
);
BOOST_HANA_RUNTIME_CHECK(
hana::sort.by(hana::ordering(hana::front), tuples)
== hana::make_tuple(
hana::make_tuple(1_c, "foobar"s, hana::int_c<4>),
hana::make_tuple(2_c, 'x', nullptr)
)
);
}

constexpr auto boost::hana::span

`#include <boost/hana/fwd/span.hpp>`

Initial value:
= [](auto&& xs, auto&& predicate) {
return tag-dispatched;
}

Returns a `Product` containing the longest prefix of a sequence satisfying a predicate, and the rest of the sequence.The first component of the returned `Product` is a sequence for which all elements satisfy the given predicate. The second component of the returned `Product` is a sequence containing the remainder of the argument. Both or either sequences may be empty, depending on the input argument. More specifically,.

span(xs, predicate) == make_pair(take_while(xs, predicate),
drop_while(xs, predicate))

except that `make_pair` may be an arbitrary `Product`.

## Signature

Given a `Sequence` `S(T)`, a `Logical` `Bool` and a predicate \( T \to Bool \), `span` has the following signature:

\[ \mathtt{span} : S(T) \times (T \to Bool) \to S(T) \times S(T) \]

Parameters

  xs | The sequence to break into two parts.
  predicate | A function called as `predicate(x)`, where `x` is an element of the sequence, and returning a `Logical. In the current implementation of the library,`predicate`has to return a compile-time`Logical`.

## Syntactic sugar (`span.by`)

`span` can be called in an alternate way, which provides a nice syntax in some cases where the predicate is short:

span.by(predicate, xs) == span(xs, predicate)
span.by(predicate) == span(-, predicate)

where `span(-, predicate)` denotes the partial application of `span` to `predicate`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/less.hpp>
#include <boost/hana/pair.hpp>
#include <boost/hana/span.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
constexpr auto xs = hana::make_tuple(hana::int_c<1>, hana::int_c<2>, hana::int_c<3>, hana::int_c<4>);
BOOST_HANA_CONSTANT_CHECK(
hana::span(xs, hana::less.than(hana::int_c<3>))
==
hana::make_pair(hana::make_tuple(hana::int_c<1>, hana::int_c<2>),
hana::make_tuple(hana::int_c<3>, hana::int_c<4>))
);
BOOST_HANA_CONSTANT_CHECK(
hana::span(xs, hana::less.than(hana::int_c<0>))
==
hana::make_pair(hana::make_tuple(), xs)
);
BOOST_HANA_CONSTANT_CHECK(
hana::span(xs, hana::less.than(hana::int_c<5>))
==
hana::make_pair(xs, hana::make_tuple())
);
// span.by is syntactic sugar
BOOST_HANA_CONSTANT_CHECK(
hana::span.by(hana::less.than(hana::int_c<3>), xs)
==
hana::make_pair(hana::make_tuple(hana::int_c<1>, hana::int_c<2>),
hana::make_tuple(hana::int_c<3>, hana::int_c<4>))
);
int main() { }

constexpr auto boost::hana::take_back

`#include <boost/hana/fwd/take_back.hpp>`

Initial value:
= [](auto&& xs, auto const& n) {
return tag-dispatched;
}

Returns the last `n` elements of a sequence, or the whole sequence if the sequence has less than `n` elements.Given a `Sequence` `xs` and an `IntegralConstant` `n`, `take_back(xs, n)` is a new sequence containing the last `n` elements of `xs`, in the same order. If `length(xs) <= n`, the whole sequence is returned and no error is triggered.

Parameters

  xs | The sequence to take the elements from.
  n | A non-negative `IntegralConstant` representing the number of elements to keep in the resulting sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/take_back.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(hana::take_back(hana::make_tuple(1, '2', 3.3), hana::size_c<0>) == hana::make_tuple());
static_assert(hana::take_back(hana::make_tuple(1, '2', 3.3), hana::size_c<1>) == hana::make_tuple(3.3), "");
static_assert(hana::take_back(hana::make_tuple(1, '2', 3.3), hana::size_c<2>) == hana::make_tuple('2', 3.3), "");
static_assert(hana::take_back(hana::make_tuple(1, '2', 3.3), hana::size_c<3>) == hana::make_tuple(1, '2', 3.3), "");
static_assert(hana::take_back(hana::make_tuple(1, '2', 3.3), hana::size_c<4>) == hana::make_tuple(1, '2', 3.3), "");
int main() { }
template<std::size_t n>

constexpr auto boost::hana::take_back_c

`#include <boost/hana/fwd/take_back.hpp>`

Initial value:
= [](auto&& xs) {
return hana::take_back(forwarded(xs), hana::size_c<n>);
}
boost::hana::take_back
constexpr auto take_back
Returns the last n elements of a sequence, or the whole sequence if the sequence has less than n elem...
Definition: take_back.hpp:42

Equivalent to `take_back`; provided for convenience.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/take_back.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(hana::take_back_c<2>(hana::make_tuple(1, '2', 3.3)) == hana::make_tuple('2', 3.3), "");
int main() { }

constexpr auto boost::hana::take_front

`#include <boost/hana/fwd/take_front.hpp>`

Initial value:
= [](auto&& xs, auto const& n) {
return tag-dispatched;
}

Returns the first `n` elements of a sequence, or the whole sequence if the sequence has less than `n` elements.Given a `Sequence` `xs` and an `IntegralConstant` `n`, `take_front(xs, n)` is a new sequence containing the first `n` elements of `xs`, in the same order. If `length(xs) <= n`, the whole sequence is returned and no error is triggered.

Parameters

  xs | The sequence to take the elements from.
  n | A non-negative `IntegralConstant` representing the number of elements to keep in the resulting sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/take_front.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(hana::take_front(hana::make_tuple(1, '2', 3.3), hana::size_c<0>) == hana::make_tuple());
static_assert(hana::take_front(hana::make_tuple(1, '2', 3.3), hana::size_c<1>) == hana::make_tuple(1), "");
static_assert(hana::take_front(hana::make_tuple(1, '2', 3.3), hana::size_c<2>) == hana::make_tuple(1, '2'), "");
static_assert(hana::take_front(hana::make_tuple(1, '2', 3.3), hana::size_c<3>) == hana::make_tuple(1, '2', 3.3), "");
static_assert(hana::take_front(hana::make_tuple(1, '2', 3.3), hana::size_c<4>) == hana::make_tuple(1, '2', 3.3), "");
int main() { }
template<std::size_t n>

constexpr auto boost::hana::take_front_c

`#include <boost/hana/fwd/take_front.hpp>`

Initial value:
= [](auto&& xs) {
return hana::take_front(forwarded(xs), hana::size_c<n>);
}
boost::hana::take_front
constexpr auto take_front
Returns the first n elements of a sequence, or the whole sequence if the sequence has less than n ele...
Definition: take_front.hpp:42

Equivalent to `take_front`; provided for convenience.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/take_front.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(hana::take_front_c<2>(hana::make_tuple(1, '2', 3.3)) == hana::make_tuple(1, '2'), "");
int main() { }

constexpr auto boost::hana::take_while

`#include <boost/hana/fwd/take_while.hpp>`

Initial value:
= [](auto&& xs, auto&& predicate) {
return tag-dispatched;
}

Take elements from a sequence while the `predicate` is satisfied.Specifically, `take_while` returns a new sequence containing the longest prefix of `xs` in which all the elements satisfy the given predicate.

Parameters

  xs | The sequence to take elements from.
  predicate | A function called as `predicate(x)`, where `x` is an element of the sequence, and returning a `Logical` representing whether `x` should be included in the resulting sequence. In the current version of the library, `predicate` has to return a `Constant Logical`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/less.hpp>
#include <boost/hana/take_while.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
using namespace hana::literals;
BOOST_HANA_CONSTANT_CHECK(
hana::take_while(hana::tuple_c<int, 0, 1, 2, 3>, hana::less.than(2_c))
==
hana::tuple_c<int, 0, 1>
);
int main() { }
template<typename S >

constexpr auto boost::hana::unfold_left

`#include <boost/hana/fwd/unfold_left.hpp>`

Initial value:
= [](auto&& state, auto&& f) {
return tag-dispatched;
}

Dual operation to `fold_left` for sequences.While `fold_left` reduces a structure to a summary value from the left, `unfold_left` builds a sequence from a seed value and a function, starting from the left.

## Signature

Given a `Sequence` `S`, an initial value `state` of tag `I`, an arbitrary Product `P` and a function \( f : I \to P(I, T) \), `unfold_left<S>` has the following signature:

\[ \mathtt{unfold\_left}_S : I \times (I \to P(I, T)) \to S(T) \]

Template Parameters

  S | The tag of the sequence to build up.

Parameters

  state | An initial value to build the sequence from.
  f | A function called as `f(state)`, where `state` is an initial value, and returning `nothing` if it is done producing the sequence. otherwise, `just(make<P>(state, x))`, where `state` is the new initial value used in the next call to `f`, `x` is an element to be appended to the resulting sequence, and `P` is an arbitrary `Product`.

## Fun fact

In some cases, `unfold_left` can undo a `fold_left` operation:

unfold_left<S>(fold_left(xs, state, f), g) == xs

if the following holds

g(f(x, y)) == just(make_pair(x, y))
g(state) == nothing

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/if.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/minus.hpp>
#include <boost/hana/optional.hpp>
#include <boost/hana/pair.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/unfold_left.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(
hana::unfold_left<hana::tuple_tag>(hana::int_c<10>, [](auto x) {
return hana::if_(x == hana::int_c<0>,
hana::nothing,
hana::just(hana::make_pair(x - hana::int_c<1>, x))
);
})
==
hana::tuple_c<int, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10>
);
int main() { }
template<typename S >

constexpr auto boost::hana::unfold_right

`#include <boost/hana/fwd/unfold_right.hpp>`

Initial value:
= [](auto&& state, auto&& f) {
return tag-dispatched;
}

Dual operation to `fold_right` for sequences.While `fold_right` reduces a structure to a summary value from the right, `unfold_right` builds a sequence from a seed value and a function, starting from the right.

## Signature

Given a `Sequence` `S`, an initial value `state` of tag `I`, an arbitrary Product `P` and a function \( f : I \to P(T, I) \), `unfold_right<S>` has the following signature:

\[ \mathtt{unfold\_right}_S : I \times (I \to P(T, I)) \to S(T) \]

Template Parameters

  S | The tag of the sequence to build up.

Parameters

  state | An initial value to build the sequence from.
  f | A function called as `f(state)`, where `state` is an initial value, and returning `nothing` if it is done producing the sequence. otherwise, `just(make<P>(x, state))`, where `state` is the new initial value used in the next call to `f`, `x` is an element to be prepended to the resulting sequence, and `P` is an arbitrary `Product`.

## Fun fact

In some cases, `unfold_right` can undo a `fold_right` operation:

unfold_right<S>(fold_right(xs, state, f), g) == xs

if the following holds

g(f(x, y)) == just(make_pair(x, y))
g(state) == nothing

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/if.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/minus.hpp>
#include <boost/hana/optional.hpp>
#include <boost/hana/pair.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/unfold_right.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(
hana::unfold_right<hana::tuple_tag>(hana::int_c<10>, [](auto x) {
return hana::if_(x == hana::int_c<0>,
hana::nothing,
hana::just(hana::make_pair(x, x - hana::int_c<1>))
);
})
==
hana::tuple_c<int, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1>
);
int main() { }

constexpr auto boost::hana::unique

`#include <boost/hana/fwd/unique.hpp>`

Initial value:
= [](auto&& xs[, auto&& predicate]) {
return tag-dispatched;
}

Removes all consecutive duplicate elements from a Sequence.Given a `Sequence` and an optional binary predicate, `unique` returns a new sequence containing only the first element of every subrange of the original sequence whose elements are all equal. In other words, it turns a sequence of the form `[a, a, b, c, c, c, d, d, d, a]` into a sequence `[a, b, c, d, a]`. The equality of two elements is determined by the provided `predicate`, or by `equal` if no `predicate` is provided.

## Signature

Given a `Sequence` `S(T)`, a `Logical` `Bool` and a binary predicate \( T \times T \to Bool \), `unique` has the following signature:

\[ \mathtt{unique} : S(T) \times (T \times T \to Bool) \to S(T) \]

Parameters

  xs | The sequence from which to remove consecutive duplicates.
  predicate | A function called as `predicate(x, y)`, where `x` and `y` are adjacent elements of the sequence, and returning a `Logical` representing whether `x` and `y` should be considered equal. `predicate` should define an equivalence relation over the elements of the sequence. In the current implementation of the library, `predicate` has to return a compile-time `Logical`. This parameter is optional; it defaults to `equal` if it is not provided, which then requires the elements of the sequence to be compile-time `Comparable`.

## Syntactic sugar (`unique.by`)

`unique` can be called in an alternate way, which provides a nice syntax, especially in conjunction with the `comparing` combinator:

unique.by(predicate, xs) == unique(xs, predicate)
unique.by(predicate) == unique(-, predicate)

where `unique(-, predicate)` denotes the partial application of `unique` to `predicate`.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/comparing.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <boost/hana/unique.hpp>
#include <string>
namespace hana = boost::hana;
using namespace std::literals;
// unique without a predicate
constexpr auto types = hana::tuple_t<int, float, float, char, int, int, int, double>;
BOOST_HANA_CONSTANT_CHECK(
hana::unique(types) == hana::tuple_t<int, float, char, int, double>
);
int main() {
// unique with a predicate
auto objects = hana::make_tuple(1, 2, "abc"s, 'd', "efg"s, "hij"s, 3.4f);
BOOST_HANA_RUNTIME_CHECK(
hana::unique(objects, [](auto const& t, auto const& u) {
return hana::typeid_(t) == hana::typeid_(u);
})
== hana::make_tuple(1, "abc"s, 'd', "efg"s, 3.4f)
);
// unique.by is syntactic sugar
BOOST_HANA_RUNTIME_CHECK(
hana::unique.by(hana::comparing(hana::typeid_), objects) ==
hana::make_tuple(1, "abc"s, 'd', "efg"s, 3.4f)
);
}

constexpr auto boost::hana::zip

`#include <boost/hana/fwd/zip.hpp>`

Initial value:
= [](auto&& x1, ..., auto&& xn) {
return tag-dispatched;
}

Zip one sequence or more.Given `n` sequences `s1, ..., sn`, `zip` produces a sequence whose `i`-th element is a tuple of `(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip` produces a sequence of the form.

[
make_tuple(s1[0], ..., sn[0]),
make_tuple(s1[1], ..., sn[1]),
...
make_tuple(s1[M], ..., sn[M])
]

where `M` is the length of the sequences, which are all assumed to have the same length. Assuming the sequences to all have the same size allows the library to perform some optimizations. To zip sequences that may have different lengths, `zip_shortest` should be used instead. Also note that it is an error to provide no sequence at all, i.e. `zip` expects at least one sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/zip.hpp>
namespace hana = boost::hana;
static_assert(
hana::zip(hana::make_tuple(1, 'a'), hana::make_tuple(2, 3.3))
==
hana::make_tuple(hana::make_tuple(1, 2), hana::make_tuple('a', 3.3))
, "");
int main() { }

constexpr auto boost::hana::zip_shortest

`#include <boost/hana/fwd/zip_shortest.hpp>`

Initial value:
= [](auto&& x1, ..., auto&& xn) {
return tag-dispatched;
}

Zip one sequence or more.Given `n` sequences `s1, ..., sn`, `zip_shortest` produces a sequence whose `i`-th element is a tuple of `(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip_shortest` produces a sequence of the form.

[
make_tuple(s1[0], ..., sn[0]),
make_tuple(s1[1], ..., sn[1]),
...
make_tuple(s1[M], ..., sn[M])
]

where `M` is the length of the shortest sequence. Hence, the returned sequence stops when the shortest input sequence is exhausted. If you know that all the sequences you are about to zip have the same length, you should use `zip` instead, since it can be more optimized. Also note that it is an error to provide no sequence at all, i.e. `zip_shortest` expects at least one sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/zip_shortest.hpp>
namespace hana = boost::hana;
static_assert(
hana::zip_shortest(hana::make_tuple(1, 'a'), hana::make_tuple(2, 3.3), hana::make_tuple(3, 'c', "ignored"))
==
hana::make_tuple(hana::make_tuple(1, 2, 3), hana::make_tuple('a', 3.3, 'c'))
, "");
int main() { }

constexpr auto boost::hana::zip_shortest_with

`#include <boost/hana/fwd/zip_shortest_with.hpp>`

Initial value:
= [](auto&& f, auto&& x1, ..., auto&& xn) {
return tag-dispatched;
}

Zip one sequence or more with a given function.Given a `n`-ary function `f` and `n` sequences `s1, ..., sn`, `zip_shortest_with` produces a sequence whose `i`-th element is `f(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip_shortest_with` produces a sequence of the form.

[
f(s1[0], ..., sn[0]),
f(s1[1], ..., sn[1]),
...
f(s1[M], ..., sn[M])
]

where `M` is the length of the shortest sequence. Hence, the returned sequence stops when the shortest input sequence is exhausted. If you know that all the sequences you are about to zip have the same length, you should use `zip_with` instead, since it can be more optimized. Also note that it is an error to provide no sequence at all, i.e. `zip_shortest_with` expects at least one sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/mult.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/zip_shortest_with.hpp>
namespace hana = boost::hana;
static_assert(
hana::zip_shortest_with(hana::mult, hana::make_tuple(1, 2, 3, 4), hana::make_tuple(5, 6, 7, 8, "ignored"))
==
hana::make_tuple(5, 12, 21, 32)
, "");
int main() { }

constexpr auto boost::hana::zip_with

`#include <boost/hana/fwd/zip_with.hpp>`

Initial value:
= [](auto&& f, auto&& x1, ..., auto&& xn) {
return tag-dispatched;
}

Zip one sequence or more with a given function.Given a `n`-ary function `f` and `n` sequences `s1, ..., sn`, `zip_with` produces a sequence whose `i`-th element is `f(s1[i], ..., sn[i])`, where `sk[i]` denotes the `i`-th element of the `k`-th sequence. In other words, `zip_with` produces a sequence of the form.

[
f(s1[0], ..., sn[0]),
f(s1[1], ..., sn[1]),
...
f(s1[M], ..., sn[M])
]

where `M` is the length of the sequences, which are all assumed to have the same length. Assuming the sequences to all have the same size allows the library to perform some optimizations. To zip sequences that may have different lengths, `zip_shortest_with` should be used instead. Also note that it is an error to provide no sequence at all, i.e. `zip_with` expects at least one sequence.

## Example

// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/ext/std/tuple.hpp>
#include <boost/hana/mult.hpp>
#include <boost/hana/transform.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <boost/hana/unpack.hpp>
#include <boost/hana/zip_with.hpp>
#include <tuple>
#include <type_traits>
#include <utility>
namespace hana = boost::hana;
// Basic usage:
static_assert(
hana::zip_with(hana::mult, hana::make_tuple(1, 2, 3, 4), hana::make_tuple(5, 6, 7, 8))
==
hana::make_tuple(5, 12, 21, 32)
, "");
// Example of computing a tuple of all the common types of several tuples:
template<typename... Ts>
using common_tuple_t = typename decltype(
hana::unpack(
hana::zip_with(
hana::metafunction<std::common_type>,
hana::transform(std::declval<Ts>(), hana::decltype_)...
),
hana::template_<std::tuple>
)
)::type;
static_assert(std::is_same<
common_tuple_t<
std::tuple<bool, int, unsigned>,
std::tuple<char, long, long>,
std::tuple<int, long long, double>
>,
std::tuple<int, long long, double>
>::value, "");
int main() { }