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/*!
@file
Forward declares `boost::hana::sum`.
@copyright Louis Dionne 2013-2016
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
*/
#ifndef BOOST_HANA_FWD_SUM_HPP
#define BOOST_HANA_FWD_SUM_HPP
#include <boost/hana/config.hpp>
#include <boost/hana/core/when.hpp>
#include <boost/hana/fwd/integral_constant.hpp>
BOOST_HANA_NAMESPACE_BEGIN
//! Compute the sum of the numbers of a structure.
//! @ingroup group-Foldable
//!
//! More generally, `sum` will take any foldable structure containing
//! objects forming a Monoid and reduce them using the Monoid's binary
//! operation. The initial state for folding is the identity of the
//! Monoid. It is sometimes necessary to specify the Monoid to use;
//! this is possible by using `sum<M>`. If no Monoid is specified,
//! the structure will use the Monoid formed by the elements it contains
//! (if it knows it), or `integral_constant_tag<int>` otherwise. Hence,
//! @code
//! sum<M>(xs) = fold_left(xs, zero<M or inferred Monoid>(), plus)
//! sum<> = sum<integral_constant_tag<int>>
//! @endcode
//!
//! For numbers, this will just compute the sum of the numbers in the
//! `xs` structure.
//!
//!
//! @note
//! The elements of the structure are not actually required to be in the
//! same Monoid, but it must be possible to perform `plus` on any two
//! adjacent elements of the structure, which requires each pair of
//! adjacent element to at least have a common Monoid embedding. The
//! meaning of "adjacent" as used here is that two elements of the
//! structure `x` and `y` are adjacent if and only if they are adjacent
//! in the linearization of that structure, as documented by the Iterable
//! concept.
//!
//!
//! Why must we sometimes specify the `Monoid` by using `sum<M>`?
//! -------------------------------------------------------------
//! This is because sequence tags like `tuple_tag` are not parameterized
//! (by design). Hence, we do not know what kind of objects are in the
//! sequence, so we can't know a `0` value of which type should be
//! returned when the sequence is empty. Therefore, the type of the
//! `0` to return in the empty case must be specified explicitly. Other
//! foldable structures like `hana::range`s will ignore the suggested
//! Monoid because they know the tag of the objects they contain. This
//! inconsistent behavior is a limitation of the current design with
//! non-parameterized tags, but we have no good solution for now.
//!
//!
//! Example
//! -------
//! @include example/sum.cpp
#ifdef BOOST_HANA_DOXYGEN_INVOKED
constexpr auto sum = see documentation;
#else
template <typename T, typename = void>
struct sum_impl : sum_impl<T, when<true>> { };
template <typename M>
struct sum_t;
template <typename M = integral_constant_tag<int>>
constexpr sum_t<M> sum{};
#endif
BOOST_HANA_NAMESPACE_END
#endif // !BOOST_HANA_FWD_SUM_HPP
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