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