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+/*=============================================================================
+ Copyright (c) 2014 Paul Fultz II
+ fix.h
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+==============================================================================*/
+
+#ifndef BOOST_HOF_GUARD_FUNCTION_FIX_H
+#define BOOST_HOF_GUARD_FUNCTION_FIX_H
+
+/// fix
+/// ===
+///
+/// Description
+/// -----------
+///
+/// The `fix` function adaptor implements a fixed-point combinator. This can be
+/// used to write recursive functions.
+///
+/// When using `constexpr`, a function can recurse to a depth that is defined by
+/// `BOOST_HOF_RECURSIVE_CONSTEXPR_DEPTH`(default is 16). There is no limitiation on
+/// recursion depth for non-constexpr functions. In addition, due to the
+/// eagerness of `constexpr` to instantiation templates, in some cases, an
+/// explicit return type must be specified in order to avoid reaching the
+/// recursion limits of the compiler. This can be accomplished using
+/// [`boost::hof::result`](/include/boost/hof/result):
+///
+/// int r = boost::hof::result<int>(factorial)(5);
+///
+/// Synopsis
+/// --------
+///
+/// template<class F>
+/// constexpr fix_adaptor<F> fix(F f);
+///
+/// Semantics
+/// ---------
+///
+/// assert(fix(f)(xs...) == f(fix(f), xs...));
+///
+/// Requirements
+/// ------------
+///
+/// F must be:
+///
+/// * [ConstFunctionObject](ConstFunctionObject)
+/// * MoveConstructible
+///
+/// Example
+/// -------
+///
+/// #include <boost/hof.hpp>
+/// #include <cassert>
+///
+/// int main() {
+/// auto factorial = boost::hof::fix(
+/// [](auto recurse, auto x) -> decltype(x) {
+/// return x == 0 ? 1 : x * recurse(x-1);
+/// }
+/// );
+/// int r = boost::hof::result<int>(factorial)(5);
+/// assert(r == 5*4*3*2*1);
+/// }
+///
+/// References
+/// ----------
+///
+/// * [Fixed-point combinator](https://en.wikipedia.org/wiki/Fixed-point_combinator)
+/// * [Recursive](Recursive)
+///
+
+#include <boost/hof/always.hpp>
+#include <boost/hof/detail/callable_base.hpp>
+#include <boost/hof/reveal.hpp>
+#include <boost/hof/detail/delegate.hpp>
+#include <boost/hof/detail/move.hpp>
+#include <boost/hof/detail/make.hpp>
+#include <boost/hof/detail/static_const_var.hpp>
+#include <boost/hof/indirect.hpp>
+#include <boost/hof/result.hpp>
+#include <boost/hof/detail/recursive_constexpr_depth.hpp>
+
+
+namespace boost { namespace hof {
+
+namespace detail{
+
+template<class F>
+struct compute_indirect_ref
+{ typedef indirect_adaptor<const F*> type; };
+
+template<class F>
+struct compute_indirect_ref<indirect_adaptor<F*>>
+{ typedef indirect_adaptor<F*> type; };
+
+template<class F>
+constexpr indirect_adaptor<const F*> make_indirect_ref(const F& f) noexcept
+{
+ return indirect_adaptor<const F*>(&f);
+}
+
+template<class F>
+constexpr indirect_adaptor<const F*> make_indirect_ref(const indirect_adaptor<F*>& f) noexcept
+{
+ return f;
+}
+
+template<class F, class=void>
+struct fix_result
+{
+ template<class... Ts>
+ struct apply
+ {
+ typedef decltype(std::declval<F>()(std::declval<Ts>()...)) type;
+ };
+};
+
+template<class F>
+struct fix_result<F, typename holder<
+ typename F::result_type
+>::type>
+{
+ template<class...>
+ struct apply
+ {
+ typedef typename F::result_type type;
+ };
+
+};
+
+template<class F, class Result, int N>
+struct fix_adaptor_base : F
+{
+ BOOST_HOF_INHERIT_CONSTRUCTOR(fix_adaptor_base, F);
+
+ typedef typename compute_indirect_ref<F>::type base_ref_type;
+ typedef fix_adaptor_base<base_ref_type, Result, N-1> derived;
+
+
+ template<class... Ts>
+ constexpr const F& base_function(Ts&&... xs) const noexcept
+ {
+ return boost::hof::always_ref(*this)(xs...);
+ }
+
+ template<class... Ts>
+ constexpr derived derived_function(Ts&&... xs) const noexcept
+ {
+ return derived(boost::hof::detail::make_indirect_ref(this->base_function(xs...)));
+ }
+
+ struct fix_failure
+ {
+ template<class Failure>
+ struct apply
+ {
+ template<class... Ts>
+ struct of
+ : Failure::template of<derived, Ts...>
+ {};
+ };
+ };
+
+ struct failure
+ : failure_map<fix_failure, F>
+ {};
+
+
+ BOOST_HOF_RETURNS_CLASS(fix_adaptor_base);
+
+ template<class... Ts>
+ constexpr BOOST_HOF_SFINAE_RESULT(const F&, id_<derived>, id_<Ts>...)
+ operator()(Ts&&... xs) const BOOST_HOF_SFINAE_RETURNS
+ (
+ BOOST_HOF_MANGLE_CAST(const F&)(BOOST_HOF_CONST_THIS->base_function(xs...))
+ (
+ BOOST_HOF_MANGLE_CAST(derived)(BOOST_HOF_CONST_THIS->derived_function(xs...)),
+ BOOST_HOF_FORWARD(Ts)(xs)...
+ )
+ );
+};
+
+template<class F, class Result>
+struct fix_adaptor_base<F, Result, 0> : F
+{
+ BOOST_HOF_INHERIT_CONSTRUCTOR(fix_adaptor_base, F);
+
+ template<class... Ts>
+ const F& base_function(Ts&&...) const noexcept
+ {
+ return *this;
+ }
+
+ struct fix_failure
+ {
+ template<class Failure>
+ struct apply
+ {
+ template<class... Ts>
+ struct of
+ : Failure::template of<fix_adaptor_base, Ts...>
+ {};
+ };
+ };
+
+ struct failure
+ : failure_map<fix_failure, F>
+ {};
+
+
+ BOOST_HOF_RETURNS_CLASS(fix_adaptor_base);
+
+ template<class... Ts>
+ typename Result::template apply<fix_adaptor_base, Ts...>::type
+ operator()(Ts&&... xs) const
+ {
+ return this->base_function(xs...)(*this, BOOST_HOF_FORWARD(Ts)(xs)...);
+ }
+};
+}
+
+template<class F>
+struct fix_adaptor : detail::fix_adaptor_base<F, detail::fix_result<F>, BOOST_HOF_RECURSIVE_CONSTEXPR_DEPTH>
+{
+ typedef fix_adaptor fit_rewritable1_tag;
+ typedef detail::fix_adaptor_base<F, detail::fix_result<F>, BOOST_HOF_RECURSIVE_CONSTEXPR_DEPTH> base;
+ BOOST_HOF_INHERIT_CONSTRUCTOR(fix_adaptor, base);
+};
+
+template<class Result, class F>
+struct result_adaptor<Result, fix_adaptor<F>>
+: fix_adaptor<result_adaptor<Result, F>>
+{
+ typedef fix_adaptor<result_adaptor<Result, F>> base;
+ BOOST_HOF_INHERIT_CONSTRUCTOR(result_adaptor, base)
+};
+
+BOOST_HOF_DECLARE_STATIC_VAR(fix, detail::make<fix_adaptor>);
+
+}} // namespace boost::hof
+
+#endif