ceph/src/boost/boost/hana/fwd/monadic_fold_right.hpp

   1 /*!
   2 @file
   3 Forward declares `boost::hana::monadic_fold_right`.
   4
   5 @copyright Louis Dionne 2013-2017
   6 Distributed under the Boost Software License, Version 1.0.
   7 (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
   8  */
   9
  10 #ifndef BOOST_HANA_FWD_MONADIC_FOLD_RIGHT_HPP
  11 #define BOOST_HANA_FWD_MONADIC_FOLD_RIGHT_HPP
  12
  13 #include <boost/hana/config.hpp>
  14 #include <boost/hana/core/when.hpp>
  15
  16
  17 BOOST_HANA_NAMESPACE_BEGIN
  18     //! Monadic right-fold of a structure with a binary operation and an
  19     //! optional initial reduction state.
  20     //! @ingroup group-Foldable
  21     //!
  22     //! @note
  23     //! This assumes the reader to be accustomed to non-monadic right-folds as
  24     //! explained by `hana::fold_right`, and to have read the [primer]
  25     //! (@ref monadic-folds) on monadic folds.
  26     //!
  27     //! `monadic_fold_right<M>` is a right-associative monadic fold. Given a
  28     //! structure containing `x1, ..., xn`, a function `f` and an optional
  29     //! initial state, `monadic_fold_right<M>` applies `f` as follows
  30     //! @code
  31     //!     // with state
  32     //!     (f(x1, -) | (f(x2, -) | (f(x3, -) | (... | f(xn, state)))))
  33     //!
  34     //!     // without state
  35     //!     (f(x1, -) | (f(x2, -) | (f(x3, -) | (... | f(xn-1, xn)))))
  36     //! @endcode
  37     //!
  38     //! where `f(xk, -)` denotes the partial application of `f` to `xk`,
  39     //! and `|` is just the operator version of the monadic `chain`.
  40     //! It is worth noting that the order in which the binary function should
  41     //! expect its arguments is reversed from `monadic_fold_left<M>`.
  42     //!
  43     //! When the structure is empty, one of two things may happen. If an
  44     //! initial state was provided, it is lifted to the given Monad and
  45     //! returned as-is. Otherwise, if the no-state version of the function
  46     //! was used, an error is triggered. When the stucture contains a single
  47     //! element and the no-state version of the function was used, that
  48     //! single element is lifted into the given Monad and returned as is.
  49     //!
  50     //!
  51     //! Signature
  52     //! ---------
  53     //! Given a `Monad` `M`, a `Foldable` `F`, an initial state of tag `S`,
  54     //! and a function @f$ f : T \times S \to M(S) @f$, the signatures of
  55     //! `monadic_fold_right<M>` are
  56     //! \f[
  57     //!     \mathtt{monadic\_fold\_right}_M :
  58     //!         F(T) \times S \times (T \times S \to M(S)) \to M(S)
  59     //! \f]
  60     //!
  61     //! for the version with an initial state, and
  62     //! \f[
  63     //!     \mathtt{monadic\_fold\_right}_M :
  64     //!         F(T) \times (T \times T \to M(T)) \to M(T)
  65     //! \f]
  66     //!
  67     //! for the version without an initial state.
  68     //!
  69     //! @tparam M
  70     //! The Monad representing the monadic context in which the fold happens.
  71     //! The return type of `f` must be in that Monad.
  72     //!
  73     //! @param xs
  74     //! The structure to fold.
  75     //!
  76     //! @param state
  77     //! The initial value used for folding. If the structure is empty, this
  78     //! value is lifted in to the `M` Monad and then returned as-is.
  79     //!
  80     //! @param f
  81     //! A binary function called as `f(x, state)`, where `state` is the result
  82     //! accumulated so far and `x` is an element in the structure. The
  83     //! function must return its result inside the `M` Monad.
  84     //!
  85     //!
  86     //! Example
  87     //! -------
  88     //! @include example/monadic_fold_right.cpp
  89 #ifdef BOOST_HANA_DOXYGEN_INVOKED
  90     template <typename M>
  91     constexpr auto monadic_fold_right = [](auto&& xs[, auto&& state], auto&& f) -> decltype(auto) {
  92         return tag-dispatched;
  93     };
  94 #else
  95     template <typename T, typename = void>
  96     struct monadic_fold_right_impl : monadic_fold_right_impl<T, when<true>> { };
  97
  98     template <typename M>
  99     struct monadic_fold_right_t {
 100         template <typename Xs, typename State, typename F>
 101         constexpr decltype(auto) operator()(Xs&& xs, State&& state, F&& f) const;
 102
 103         template <typename Xs, typename F>
 104         constexpr decltype(auto) operator()(Xs&& xs, F&& f) const;
 105     };
 106
 107     template <typename M>
 108     constexpr monadic_fold_right_t<M> monadic_fold_right{};
 109 #endif
 110 BOOST_HANA_NAMESPACE_END
 111
 112 #endif // !BOOST_HANA_FWD_MONADIC_FOLD_RIGHT_HPP