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/*! @file Forward declares `boost::hana::monadic_fold_left`. Copyright Louis Dionne 2013-2022 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_LEFT_HPP #define BOOST_HANA_FWD_MONADIC_FOLD_LEFT_HPP #include #include namespace boost { namespace hana { //! Monadic left-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 left-folds as //! explained by `hana::fold_left`, and to have read the [primer] //! (@ref monadic-folds) on monadic folds. //! //! `monadic_fold_left` is a left-associative monadic fold. Given a //! `Foldable` with linearization `[x1, ..., xn]`, a function `f` and an //! optional initial state, `monadic_fold_left` applies `f` as follows: //! @code //! // with state //! ((((f(state, x1) | f(-, x2)) | f(-, x3)) | ...) | f(-, xn)) //! //! // without state //! ((((f(x1, x2) | f(-, x3)) | f(-, x4)) | ...) | f(-, xn)) //! @endcode //! //! where `f(-, xk)` denotes the partial application of `f` to `xk`, and //! `|` is just the operator version of the monadic `chain`. //! //! 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 : S \times T \to M(S) @f$, the signatures of //! `monadic_fold_left` are //! \f[ //! \mathtt{monadic\_fold\_left}_M : //! F(T) \times S \times (S \times T \to M(S)) \to M(S) //! \f] //! //! for the version with an initial state, and //! \f[ //! \mathtt{monadic\_fold\_left}_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(state, x)`, 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_left.cpp #ifdef BOOST_HANA_DOXYGEN_INVOKED template constexpr auto monadic_fold_left = [](auto&& xs[, auto&& state], auto&& f) -> decltype(auto) { return tag-dispatched; }; #else template struct monadic_fold_left_impl : monadic_fold_left_impl> { }; template struct monadic_fold_left_t { template constexpr decltype(auto) operator()(Xs&& xs, State&& state, F&& f) const; template constexpr decltype(auto) operator()(Xs&& xs, F&& f) const; }; template BOOST_HANA_INLINE_VARIABLE constexpr monadic_fold_left_t monadic_fold_left{}; #endif }} // end namespace boost::hana #endif // !BOOST_HANA_FWD_MONADIC_FOLD_LEFT_HPP