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cppdraft/alg/fold.md
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cppdraft/alg/fold.md
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[alg.fold]
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# 26 Algorithms library [[algorithms]](./#algorithms)
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## 26.6 Non-modifying sequence operations [[alg.nonmodifying]](alg.nonmodifying#alg.fold)
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### 26.6.18 Fold [alg.fold]
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[ð](#lib:fold_left)
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`template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_iterator [iterator.concept.input]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_for [iterator.concept.sentinel]")<I> S, class T = iter_value_t<I>,
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[indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<T, I> F>
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constexpr auto ranges::fold_left(I first, S last, T init, F f);
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template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R, class T = range_value_t<R>,
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[indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<T, iterator_t<R>> F>
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constexpr auto ranges::fold_left(R&& r, T init, F f);
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`
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[1](#1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6188)
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*Returns*: ranges::fold_left_with_iter(std::move(first), last, std::move(init), f).value
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[ð](#lib:fold_left_first)
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`template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_iterator [iterator.concept.input]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_for [iterator.concept.sentinel]")<I> S,
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[indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<iter_value_t<I>, I> F>
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requires [constructible_from](concept.constructible#concept:constructible_from "18.4.11 Concept constructible_from [concept.constructible]")<iter_value_t<I>, iter_reference_t<I>>
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constexpr auto ranges::fold_left_first(I first, S last, F f);
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template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R, [indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<range_value_t<R>, iterator_t<R>> F>
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requires [constructible_from](concept.constructible#concept:constructible_from "18.4.11 Concept constructible_from [concept.constructible]")<range_value_t<R>, range_reference_t<R>>
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constexpr auto ranges::fold_left_first(R&& r, F f);
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`
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[2](#2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6207)
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*Returns*: ranges::fold_left_first_with_iter(std::move(first), last, f).value
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[ð](#lib:fold_right)
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`template<[bidirectional_iterator](iterator.concept.bidir#concept:bidirectional_iterator "24.3.4.12 Concept bidirectional_iterator [iterator.concept.bidir]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_for [iterator.concept.sentinel]")<I> S, class T = iter_value_t<I>,
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[indirectly-binary-right-foldable](algorithm.syn#concept:indirectly-binary-right-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<T, I> F>
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constexpr auto ranges::fold_right(I first, S last, T init, F f);
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template<[bidirectional_range](range.refinements#concept:bidirectional_range "25.4.6 Other range refinements [range.refinements]") R, class T = range_value_t<R>,
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[indirectly-binary-right-foldable](algorithm.syn#concept:indirectly-binary-right-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<T, iterator_t<R>> F>
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constexpr auto ranges::fold_right(R&& r, T init, F f);
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`
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[3](#3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6225)
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*Effects*: Equivalent to:using U = decay_t<invoke_result_t<F&, iter_reference_t<I>, T>>;if (first == last)return U(std::move(init));
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I tail = ranges::next(first, last);
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U accum = invoke(f, *--tail, std::move(init));while (first != tail) accum = invoke(f, *--tail, std::move(accum));return accum;
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[ð](#lib:fold_right_last)
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`template<[bidirectional_iterator](iterator.concept.bidir#concept:bidirectional_iterator "24.3.4.12 Concept bidirectional_iterator [iterator.concept.bidir]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_for [iterator.concept.sentinel]")<I> S,
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[indirectly-binary-right-foldable](algorithm.syn#concept:indirectly-binary-right-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<iter_value_t<I>, I> F>
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requires [constructible_from](concept.constructible#concept:constructible_from "18.4.11 Concept constructible_from [concept.constructible]")<iter_value_t<I>, iter_reference_t<I>>
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constexpr auto ranges::fold_right_last(I first, S last, F f);
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template<[bidirectional_range](range.refinements#concept:bidirectional_range "25.4.6 Other range refinements [range.refinements]") R,
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[indirectly-binary-right-foldable](algorithm.syn#concept:indirectly-binary-right-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<range_value_t<R>, iterator_t<R>> F>
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requires [constructible_from](concept.constructible#concept:constructible_from "18.4.11 Concept constructible_from [concept.constructible]")<range_value_t<R>, range_reference_t<R>>
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constexpr auto ranges::fold_right_last(R&& r, F f);
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`
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[4](#4)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6253)
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Let U bedecltype(ranges::fold_right(first, last, iter_value_t<I>(*first), f))[.](#4.sentence-1)
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[5](#5)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6257)
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*Effects*: Equivalent to:if (first == last)return optional<U>();
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I tail = ranges::prev(ranges::next(first, std::move(last)));return optional<U>(in_place,
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ranges::fold_right(std::move(first), tail, iter_value_t<I>(*tail), std::move(f)));
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[ð](#lib:fold_left_with_iter)
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`template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_iterator [iterator.concept.input]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_for [iterator.concept.sentinel]")<I> S, class T = iter_value_t<I>,
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[indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<T, I> F>
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constexpr see below ranges::fold_left_with_iter(I first, S last, T init, F f);
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template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R, class T = range_value_t<R>,
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[indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<T, iterator_t<R>> F>
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constexpr see below ranges::fold_left_with_iter(R&& r, T init, F f);
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`
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[6](#6)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6280)
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Let U be decay_t<invoke_result_t<F&, T, iter_reference_t<I>>>[.](#6.sentence-1)
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[7](#7)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6283)
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*Effects*: Equivalent to:if (first == last)return {std::move(first), U(std::move(init))};
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U accum = invoke(f, std::move(init), *first);for (++first; first != last; ++first) accum = invoke(f, std::move(accum), *first);return {std::move(first), std::move(accum)};
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[8](#8)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6295)
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*Remarks*: The return type isfold_left_with_iter_result<I, U> for the first overload andfold_left_with_iter_result<borrowed_iterator_t<R>, U> for the second overload[.](#8.sentence-1)
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[ð](#lib:fold_left_first_with_iter)
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`template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_iterator [iterator.concept.input]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_for [iterator.concept.sentinel]")<I> S,
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[indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<iter_value_t<I>, I> F>
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requires [constructible_from](concept.constructible#concept:constructible_from "18.4.11 Concept constructible_from [concept.constructible]")<iter_value_t<I>, iter_reference_t<I>>
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constexpr see below ranges::fold_left_first_with_iter(I first, S last, F f);
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template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R, [indirectly-binary-left-foldable](algorithm.syn#concept:indirectly-binary-left-foldable "26.4 Header <algorithm> synopsis [algorithm.syn]")<range_value_t<R>, iterator_t<R>> F>
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requires [constructible_from](concept.constructible#concept:constructible_from "18.4.11 Concept constructible_from [concept.constructible]")<range_value_t<R>, range_reference_t<R>>
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constexpr see below ranges::fold_left_first_with_iter(R&& r, F f);
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`
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[9](#9)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6315)
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Let U bedecltype(ranges::fold_left(std::move(first), last, iter_value_t<I>(*first), f))
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[10](#10)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6321)
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*Effects*: Equivalent to:if (first == last)return {std::move(first), optional<U>()};
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optional<U> init(in_place, *first);for (++first; first != last; ++first)*init = invoke(f, std::move(*init), *first);return {std::move(first), std::move(init)};
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[11](#11)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L6333)
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*Remarks*: The return type isfold_left_first_with_iter_result<I, optional<U>> for the first overload andfold_left_first_with_iter_result<borrowed_iterator_t<R>, optional<U>> for the second overload[.](#11.sentence-1)
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