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