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Diffstat (limited to 'boost/hana/fwd/monadic_fold_right.hpp')
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diff --git a/boost/hana/fwd/monadic_fold_right.hpp b/boost/hana/fwd/monadic_fold_right.hpp new file mode 100644 index 0000000000..692eacbdf4 --- /dev/null +++ b/boost/hana/fwd/monadic_fold_right.hpp @@ -0,0 +1,106 @@ +/*! +@file +Forward declares `boost::hana::monadic_fold_right`. + +@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_MONADIC_FOLD_RIGHT_HPP +#define BOOST_HANA_FWD_MONADIC_FOLD_RIGHT_HPP + +#include <boost/hana/config.hpp> +#include <boost/hana/core/when.hpp> + + +BOOST_HANA_NAMESPACE_BEGIN + //! Monadic right-fold of a structure with a binary operation and an + //! optional initial reduction state. + //! @ingroup group-Foldable + //! + //! @note + //! This assumes the reader to be accustomed to non-monadic right-folds as + //! explained by `hana::fold_right`, and to have read the [primer] + //! (@ref monadic-folds) on monadic folds. + //! + //! `monadic_fold_right<M>` is a right-associative monadic fold. Given a + //! structure containing `x1, ..., xn`, a function `f` and an optional + //! initial state, `monadic_fold_right<M>` applies `f` as follows + //! @code + //! // with state + //! (f(x1, -) | (f(x2, -) | (f(x3, -) | (... | f(xn, state))))) + //! + //! // without state + //! (f(x1, -) | (f(x2, -) | (f(x3, -) | (... | f(xn-1, xn))))) + //! @endcode + //! + //! where `f(xk, -)` denotes the partial application of `f` to `xk`, + //! and `|` is just the operator version of the monadic `chain`. + //! It is worth noting that the order in which the binary function should + //! expect its arguments is reversed from `monadic_fold_left<M>`. + //! + //! When the structure is empty, one of two things may happen. If an + //! initial state was provided, it is lifted to the given Monad and + //! returned as-is. Otherwise, if the no-state version of the function + //! was used, an error is triggered. When the stucture contains a single + //! element and the no-state version of the function was used, that + //! single element is lifted into the given Monad and returned as is. + //! + //! + //! Signature + //! --------- + //! Given a `Monad` `M`, a `Foldable` `F`, an initial state of tag `S`, + //! and a function @f$ f : T \times S \to M(S) @f$, the signatures of + //! `monadic_fold_right<M>` are + //! \f[ + //! \mathtt{monadic\_fold\_right}_M : + //! F(T) \times S \times (T \times S \to M(S)) \to M(S) + //! \f] + //! + //! for the version with an initial state, and + //! \f[ + //! \mathtt{monadic\_fold\_right}_M : + //! F(T) \times (T \times T \to M(T)) \to M(T) + //! \f] + //! + //! for the version without an initial state. + //! + //! @tparam M + //! The Monad representing the monadic context in which the fold happens. + //! The return type of `f` must be in that Monad. + //! + //! @param xs + //! The structure to fold. + //! + //! @param state + //! The initial value used for folding. If the structure is empty, this + //! value is lifted in to the `M` Monad and then returned as-is. + //! + //! @param f + //! A binary function called as `f(x, state)`, where `state` is the result + //! accumulated so far and `x` is an element in the structure. The + //! function must return its result inside the `M` Monad. + //! + //! + //! Example + //! ------- + //! @include example/monadic_fold_right.cpp +#ifdef BOOST_HANA_DOXYGEN_INVOKED + template <typename M> + constexpr auto monadic_fold_right = [](auto&& xs[, auto&& state], auto&& f) -> decltype(auto) { + return tag-dispatched; + }; +#else + template <typename T, typename = void> + struct monadic_fold_right_impl : monadic_fold_right_impl<T, when<true>> { }; + + template <typename M> + struct monadic_fold_right_t; + + template <typename M> + constexpr monadic_fold_right_t<M> monadic_fold_right{}; +#endif +BOOST_HANA_NAMESPACE_END + +#endif // !BOOST_HANA_FWD_MONADIC_FOLD_RIGHT_HPP |