meta.hpp

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//
// Meta library
//
//  Copyright Eric Niebler 2014-2015
//
//  Use, modification and distribution is subject to 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)
//
// Project home: https://github.com/ericniebler/meta
//

#ifndef META_HPP
#define META_HPP

#include <cstddef>
#include <initializer_list>
#include <type_traits>
#include <utility>
#include <meta/meta_fwd.hpp>

#if defined(__clang__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunknown-pragmas"
#pragma GCC diagnostic ignored "-Wpragmas"
#pragma GCC diagnostic ignored "-Wdocumentation-deprecated-sync"
#endif
























namespace meta
{
    inline namespace v1
    {

        namespace detail
        {
            template <typename T>
            constexpr T *_nullptr_v()
            {
                return nullptr;
            }
        } // namespace detail

        struct nil_
        {
        };

        template <typename T>
        using _t = typename T::type;

#if defined(__cpp_variable_templates) || defined(META_DOXYGEN_INVOKED)
        template <typename T>
        constexpr typename T::type::value_type _v = T::type::value;
#endif

        namespace lazy
        {
            template <typename T>
            using _t = defer<_t, T>;
        }

        template <std::size_t N>
        using size_t = std::integral_constant<std::size_t, N>;

        template <bool B>
        using bool_ = std::integral_constant<bool, B>;

        template <int I>
        using int_ = std::integral_constant<int, I>;

        template <char Ch>
        using char_ = std::integral_constant<char, Ch>;

        // Math operations
        template <typename T>
        using inc = std::integral_constant<decltype(T::type::value + 1), T::type::value + 1>;

        template <typename T>
        using dec = std::integral_constant<decltype(T::type::value - 1), T::type::value - 1>;

        template <typename T, typename U>
        using plus = std::integral_constant<decltype(T::type::value + U::type::value),
                                            T::type::value + U::type::value>;

        template <typename T, typename U>
        using minus = std::integral_constant<decltype(T::type::value - U::type::value),
                                             T::type::value - U::type::value>;

        template <typename T, typename U>
        using multiplies = std::integral_constant<decltype(T::type::value * U::type::value),
                                                  T::type::value * U::type::value>;

        template <typename T, typename U>
        using divides = std::integral_constant<decltype(T::type::value / U::type::value),
                                               T::type::value / U::type::value>;

        template <typename T>
        using negate = std::integral_constant<decltype(-T::type::value), -T::type::value>;

        template <typename T, typename U>
        using modulus = std::integral_constant<decltype(T::type::value % U::type::value),
                                               T::type::value % U::type::value>;

        template <typename T, typename U>
        using equal_to = bool_<T::type::value == U::type::value>;

        template <typename T, typename U>
        using not_equal_to = bool_<T::type::value != U::type::value>;

        template <typename T, typename U>
        using greater = bool_<(T::type::value > U::type::value)>;

        template <typename T, typename U>
        using less = bool_<(T::type::value < U::type::value)>;

        template <typename T, typename U>
        using greater_equal = bool_<(T::type::value >= U::type::value)>;

        template <typename T, typename U>
        using less_equal = bool_<(T::type::value <= U::type::value)>;

        template <typename T, typename U>
        using bit_and = std::integral_constant<decltype(T::type::value & U::type::value),
                                               T::type::value & U::type::value>;

        template <typename T, typename U>
        using bit_or = std::integral_constant<decltype(T::type::value | U::type::value),
                                              T::type::value | U::type::value>;

        template <typename T, typename U>
        using bit_xor = std::integral_constant<decltype(T::type::value ^ U::type::value),
                                               T::type::value ^ U::type::value>;

        template <typename T>
        using bit_not = std::integral_constant<decltype(~T::type::value), ~T::type::value>;

        namespace lazy
        {
            template <typename T>
            using inc = defer<inc, T>;

            template <typename T>
            using dec = defer<dec, T>;

            template <typename T, typename U>
            using plus = defer<plus, T, U>;

            template <typename T, typename U>
            using minus = defer<minus, T, U>;

            template <typename T, typename U>
            using multiplies = defer<multiplies, T, U>;

            template <typename T, typename U>
            using divides = defer<divides, T, U>;

            template <typename T>
            using negate = defer<negate, T>;

            template <typename T, typename U>
            using modulus = defer<modulus, T, U>;

            template <typename T, typename U>
            using equal_to = defer<equal_to, T, U>;

            template <typename T, typename U>
            using not_equal_to = defer<not_equal_to, T, U>;

            template <typename T, typename U>
            using greater = defer<greater, T, U>;

            template <typename T, typename U>
            using less = defer<less, T, U>;

            template <typename T, typename U>
            using greater_equal = defer<greater_equal, T, U>;

            template <typename T, typename U>
            using less_equal = defer<less_equal, T, U>;

            template <typename T, typename U>
            using bit_and = defer<bit_and, T, U>;

            template <typename T, typename U>
            using bit_or = defer<bit_or, T, U>;

            template <typename T, typename U>
            using bit_xor = defer<bit_xor, T, U>;

            template <typename T>
            using bit_not = defer<bit_not, T>;
        }

        template <typename F, typename... Args>
        using invoke = typename F::template invoke<Args...>;

        namespace lazy
        {
            template <typename F, typename... Args>
            using invoke = defer<invoke, F, Args...>;
        }

        template <typename T>
        struct id
        {
        private:
            // Redirect through a class template for compilers that have not
            // yet implemented CWG 1558:
            // <http://www.open-std.org/jtc1/sc22/wg21/docs/cwg_defects.html#1558>
            template <typename...>
            struct impl
            {
                using type = T;
            };

        public:
            using type = T;

            template <typename... Ts>
            using invoke = _t<impl<Ts...>>;
        };

        template <typename T>
        using id_t = _t<id<T>>;

        namespace lazy
        {
            template <typename T>
            using id = defer<id, T>;
        }

        template <typename... Ts>
        using void_ = invoke<id<void>, Ts...>;

        namespace detail
        {
            template <typename, typename = void>
            struct is_trait_
            {
                using type = std::false_type;
            };

            template <typename T>
            struct is_trait_<T, void_<typename T::type>>
            {
                using type = std::true_type;
            };

            template <typename, typename = void>
            struct is_callable_
            {
                using type = std::false_type;
            };

            template <typename T>
            struct is_callable_<T, void_<quote<T::template invoke>>>
            {
                using type = std::true_type;
            };

            template <template <typename...> class, typename, typename = void>
            struct defer_
            {
            };

            template <template <typename...> class C, typename... Ts>
            struct defer_<C, list<Ts...>, void_<C<Ts...>>>
            {
                using type = C<Ts...>;
            };

            template <typename T, template <T...> class, typename, typename = void>
            struct defer_i_
            {
            };

            template <typename T, template <T...> class C, T... Is>
            struct defer_i_<T, C, integer_sequence<T, Is...>, void_<C<Is...>>>
            {
                using type = C<Is...>;
            };
        } // namespace detail

        template <typename T>
        using is_trait = _t<detail::is_trait_<T>>;

        template <typename T>
        using is_callable = _t<detail::is_callable_<T>>;

        // defer
        template <template <typename...> class C, typename... Ts>
        struct defer : detail::defer_<C, list<Ts...>>
        {
        };

        // defer_i
        template <typename T, template <T...> class C, T... Is>
        struct defer_i : detail::defer_i_<T, C, integer_sequence<T, Is...>>
        {
        };

        // defer_trait
        template <template <typename...> class C, typename... Ts>
        using defer_trait = lazy::_t<defer<C, Ts...>>;

        // defer_trait_i
        template <typename T, template <T...> class C, T... Is>
        using defer_trait_i = lazy::_t<defer_i<T, C, Is...>>;

        template <class T>
        using sizeof_ = meta::size_t<sizeof(T)>;

        template <class T>
        using alignof_ = meta::size_t<alignof(T)>;

        namespace lazy
        {
            template <typename T>
            using sizeof_ = defer<sizeof_, T>;

            template <typename T>
            using alignof_ = defer<alignof_, T>;
        }

        namespace detail
        {
            template <typename, template <typename...> class>
            struct is_ : std::false_type
            {
            };

            template <typename... Ts, template <typename...> class C>
            struct is_<C<Ts...>, C> : std::true_type
            {
            };
        }

        template <typename T, template <typename...> class C>
        using is = _t<detail::is_<T, C>>;

        template <typename... Fs>
        struct compose
        {
        };

        template <typename F0>
        struct compose<F0>
        {
            template <typename... Ts>
            using invoke = invoke<F0, Ts...>;
        };

        template <typename F0, typename... Fs>
        struct compose<F0, Fs...>
        {
            template <typename... Ts>
            using invoke = invoke<F0, invoke<compose<Fs...>, Ts...>>;
        };

        namespace lazy
        {
            template <typename... Fns>
            using compose = defer<compose, Fns...>;
        }

        template <template <typename...> class C>
        struct quote
        {
            // Indirection through defer here needed to avoid Core issue 1430
            // http://open-std.org/jtc1/sc22/wg21/docs/cwg_active.html#1430
            template <typename... Ts>
            using invoke = _t<defer<C, Ts...>>;
        };

        template <typename T, template <T...> class C>
        struct quote_i
        {
            // Indirection through defer_i here needed to avoid Core issue 1430
            // http://open-std.org/jtc1/sc22/wg21/docs/cwg_active.html#1430
            template <typename... Ts>
            using invoke = _t<defer_i<T, C, Ts::type::value...>>;
        };

    #if __GNUC__ == 4 && __GNUC_MINOR__ <= 8 && \
        !defined(__clang__) && !defined(META_DOXYGEN_INVOKED)
        template <template <typename...> class C>
        struct quote_trait
        {
            template <typename... Ts>
            using invoke = _t<invoke<quote<C>, Ts...>>;
        };

        template <typename T, template <T...> class C>
        struct quote_trait_i
        {
            template <typename... Ts>
            using invoke = _t<invoke<quote_i<T, C>, Ts...>>;
        };
    #else
        // clang-format off
        template <template <typename...> class C>
        using quote_trait = compose<quote<_t>, quote<C>>;

        template <typename T, template <T...> class C>
        using quote_trait_i = compose<quote<_t>, quote_i<T, C>>;
        // clang-format on
    #endif

        template <typename F, typename... Ts>
        struct bind_front
        {
            template <typename... Us>
            using invoke = invoke<F, Ts..., Us...>;
        };

        template <typename F, typename... Us>
        struct bind_back
        {
            template <typename... Ts>
            using invoke = invoke<F, Ts..., Us...>;
        };

        namespace lazy
        {
            template <typename Fn, typename... Ts>
            using bind_front = defer<bind_front, Fn, Ts...>;

            template <typename Fn, typename... Ts>
            using bind_back = defer<bind_back, Fn, Ts...>;
        }

        namespace extension
        {
            template <typename F, typename List>
            struct apply
            {
            };

            template <typename F, typename Ret, typename... Args>
            struct apply<F, Ret(Args...)> : lazy::invoke<F, Ret, Args...>
            {
            };

            template <typename F, template <typename...> class T, typename... Ts>
            struct apply<F, T<Ts...>> : lazy::invoke<F, Ts...>
            {
            };

            template <typename F, typename T, T... Is>
            struct apply<F, integer_sequence<T, Is...>>
                : lazy::invoke<F, std::integral_constant<T, Is>...>
            {
            };
        }

        template <typename C, typename List>
        using apply = _t<extension::apply<C, List>>;

        namespace lazy
        {
            template <typename F, typename List>
            using apply = defer<apply, F, List>;
        }

        template <typename F, typename Q = quote<list>>
        using curry = compose<F, Q>;

        template <typename F>
        using uncurry = bind_front<quote<apply>, F>;

        namespace lazy
        {
            template <typename F, typename Q = quote<list>>
            using curry = defer<curry, F, Q>;

            template <typename F>
            using uncurry = defer<uncurry, F>;
        }

        template <typename F>
        struct flip
        {
        private:
            template <typename... Ts>
            struct impl
            {
            };
            template <typename A, typename B, typename... Ts>
            struct impl<A, B, Ts...> : lazy::invoke<F, B, A, Ts...>
            {
            };

        public:
            template <typename... Ts>
            using invoke = _t<impl<Ts...>>;
        };

        namespace lazy
        {
            template <typename F>
            using flip = defer<flip, F>;
        }

        namespace detail
        {
            template <typename...>
            struct on_
            {
            };
            template <typename F, typename... Gs>
            struct on_<F, Gs...>
            {
                template <typename... Ts>
                using invoke = invoke<F, invoke<compose<Gs...>, Ts>...>;
            };
        }

        template <typename... Fs>
        using on = detail::on_<Fs...>;

        namespace lazy
        {
            template <typename F, typename G>
            using on = defer<on, F, G>;
        }

        // if_
        namespace detail
        {
            template <typename...>
            struct _if_
            {
            };

            template <typename If>
            struct _if_<If> : std::enable_if<If::type::value>
            {
            };

            template <typename If, typename Then>
            struct _if_<If, Then> : std::enable_if<If::type::value, Then>
            {
            };

            template <typename If, typename Then, typename Else>
            struct _if_<If, Then, Else> : std::conditional<If::type::value, Then, Else>
            {
            };
        } // namespace detail

        template <typename... Args>
        using if_ = _t<detail::_if_<Args...>>;

        template <bool If, typename... Args>
        using if_c = _t<detail::_if_<bool_<If>, Args...>>;

        namespace lazy
        {
            template <typename... Args>
            using if_ = defer<if_, Args...>;

            template <bool If, typename... Args>
            using if_c = if_<bool_<If>, Args...>;
        }

        namespace detail
        {
            template <typename... Bools>
            struct _and_;

            template <>
            struct _and_<> : std::true_type
            {
            };

            template <typename Bool, typename... Bools>
            struct _and_<Bool, Bools...>
                : if_c<!Bool::type::value, std::false_type, _and_<Bools...>>
            {
            };

            template <typename... Bools>
            struct _or_;

            template <>
            struct _or_<> : std::false_type
            {
            };

            template <typename Bool, typename... Bools>
            struct _or_<Bool, Bools...> : if_c<Bool::type::value, std::true_type, _or_<Bools...>>
            {
            };
        } // namespace detail

        template <bool Bool>
        using not_c = bool_<!Bool>;

        template <typename Bool>
        using not_ = not_c<Bool::type::value>;

#if (__GNUC__ == 5) && (__GNUC_MINOR__ == 1) && !defined(__clang__)
        // Alternative formulation of and_c to workaround
        // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=66405
        template <bool... Bools>
        using and_c = std::is_same<integer_sequence<bool, true, Bools...>,
                                   integer_sequence<bool, Bools..., true>>;
#else
        template <bool... Bools>
        using and_c = std::is_same<integer_sequence<bool, Bools...>,
                                   integer_sequence<bool, (Bools || true)...>>;
#endif

        template <typename... Bools>
        using strict_and = and_c<Bools::type::value...>;

        template <typename... Bools>
        using and_ = _t<detail::_and_<Bools...>>;

        template <bool... Bools>
        using or_c = not_<std::is_same<integer_sequence<bool, Bools...>,
                                       integer_sequence<bool, (Bools && false)...>>>;

        template <typename... Bools>
        using strict_or = or_c<Bools::type::value...>;

        template <typename... Bools>
        using or_ = _t<detail::_or_<Bools...>>;

        namespace lazy
        {
            template <typename... Bools>
            using and_ = defer<and_, Bools...>;

            template <typename... Bools>
            using or_ = defer<or_, Bools...>;

            template <typename Bool>
            using not_ = defer<not_, Bool>;

            template <typename... Bools>
            using strict_and = defer<strict_and, Bools...>;

            template <typename... Bools>
            using strict_or = defer<strict_or, Bools...>;
        }

        // fold
        namespace detail
        {
            template <typename, typename, typename, typename = void>
            struct fold_
            {
            };

            template <typename State, typename Fun>
            struct fold_<list<>, State, Fun>
            {
                using type = State;
            };

            template <typename Head, typename... List, typename State, typename Fun>
            struct fold_<list<Head, List...>, State, Fun, void_<invoke<Fun, State, Head>>>
                : fold_<list<List...>, invoke<Fun, State, Head>, Fun>
            {
            };
        } // namespace detail

        template <typename List, typename State, typename Fun>
        using fold = _t<detail::fold_<List, State, Fun>>;

        template <typename List, typename State, typename Fun>
        using accumulate = fold<List, State, Fun>;

        namespace lazy
        {
            template <typename List, typename State, typename Fun>
            using fold = defer<fold, List, State, Fun>;

            template <typename List, typename State, typename Fun>
            using accumulate = defer<accumulate, List, State, Fun>;
        }

        // reverse_fold
        namespace detail
        {
            template <typename, typename, typename, typename = void>
            struct reverse_fold_
            {
            };

            template <typename State, typename Fun>
            struct reverse_fold_<list<>, State, Fun>
            {
                using type = State;
            };

            template <typename Head, typename... List, typename State, typename Fun>
            struct reverse_fold_<list<Head, List...>, State, Fun,
                                 void_<_t<reverse_fold_<list<List...>, State, Fun>>>>
                : lazy::invoke<Fun, _t<reverse_fold_<list<List...>, State, Fun>>, Head>
            {
            };
        } // namespace detail

        template <typename List, typename State, typename Fun>
        using reverse_fold = _t<detail::reverse_fold_<List, State, Fun>>;

        namespace lazy
        {
            template <typename List, typename State, typename Fun>
            using reverse_fold = defer<reverse_fold, List, State, Fun>;
        }

        // npos
        using npos = meta::size_t<std::size_t(-1)>;

        // list
        template <typename... Ts>
        struct list
        {
            using type = list;
            static constexpr std::size_t size() noexcept { return sizeof...(Ts); }
        };

        // size
        template <typename List>
        using size = meta::size_t<List::size()>;

        namespace lazy
        {
            template <typename List>
            using size = defer<size, List>;
        }

        // concat
        namespace detail
        {
            template <typename... Lists>
            struct concat_
            {
            };

            template <>
            struct concat_<>
            {
                using type = list<>;
            };

            template <typename... List1>
            struct concat_<list<List1...>>
            {
                using type = list<List1...>;
            };

            template <typename... List1, typename... List2>
            struct concat_<list<List1...>, list<List2...>>
            {
                using type = list<List1..., List2...>;
            };

            template <typename... List1, typename... List2, typename... List3>
            struct concat_<list<List1...>, list<List2...>, list<List3...>>
            {
                using type = list<List1..., List2..., List3...>;
            };

            template <typename... List1, typename... List2, typename... List3, typename... Rest>
            struct concat_<list<List1...>, list<List2...>, list<List3...>, Rest...>
                : concat_<list<List1..., List2..., List3...>, Rest...>
            {
            };
        } // namespace detail

        template <typename... Lists>
        using concat = _t<detail::concat_<Lists...>>;

        namespace lazy
        {
            template <typename... Lists>
            using concat = defer<concat, Lists...>;
        }

        template <typename ListOfLists>
        using join = apply<quote<concat>, ListOfLists>;

        namespace lazy
        {
            template <typename ListOfLists>
            using join = defer<join, ListOfLists>;
        }

        // repeat_n
        namespace detail
        {
            template <std::size_t N, typename T>
            struct repeat_n_c_
            {
                using type = concat<_t<repeat_n_c_<N / 2, T>>, _t<repeat_n_c_<N / 2, T>>,
                                    _t<repeat_n_c_<N % 2, T>>>;
            };

            template <typename T>
            struct repeat_n_c_<0, T>
            {
                using type = list<>;
            };

            template <typename T>
            struct repeat_n_c_<1, T>
            {
                using type = list<T>;
            };
        } // namespace detail

        template <typename N, typename T = void>
        using repeat_n = _t<detail::repeat_n_c_<N::type::value, T>>;

        template <std::size_t N, typename T = void>
        using repeat_n_c = _t<detail::repeat_n_c_<N, T>>;

        namespace lazy
        {
            template <typename N, typename T = void>
            using repeat_n = defer<repeat_n, N, T>;
        }

        // at
        namespace detail
        {
            template <typename VoidPtrs>
            struct at_impl_;

            template <typename... VoidPtrs>
            struct at_impl_<list<VoidPtrs...>>
            {
                static nil_ eval(...);

                template <typename T, typename... Us>
                static T eval(VoidPtrs..., T *, Us *...);
            };

            template <typename List, typename N>
            struct at_
            {
            };

            template <typename... Ts, typename N>
            struct at_<list<Ts...>, N>
                : decltype(at_impl_<repeat_n<N, void *>>::eval(detail::_nullptr_v<id<Ts>>()...))
            {
            };
        } // namespace detail

        // at
        template <typename List, typename N>
        using at = _t<detail::at_<List, N>>;

        template <typename List, std::size_t N>
        using at_c = at<List, meta::size_t<N>>;

        namespace lazy
        {
            template <typename List, typename N>
            using at = defer<at, List, N>;
        }

        // drop
        namespace detail
        {
            template <typename VoidPtrs>
            struct drop_impl_
            {
                static nil_ eval(...);
            };

            template <typename... VoidPtrs>
            struct drop_impl_<list<VoidPtrs...>>
            {
                static nil_ eval(...);

                template <typename... Ts>
                static id<list<Ts...>> eval(VoidPtrs..., id<Ts> *...);
            };

            template <>
            struct drop_impl_<list<>>
            {
                template <typename...Ts>
                static id<list<Ts...>> eval(id<Ts> *...);
            };

            template <typename List, typename N>
            struct drop_
            {
            };

            template <typename... Ts, typename N>
            struct drop_<list<Ts...>, N>
                : decltype(drop_impl_<repeat_n<N, void *>>::eval(detail::_nullptr_v<id<Ts>>()...))
            {
            };
        } // namespace detail

        template <typename List, typename N>
        using drop = _t<detail::drop_<List, N>>;

        template <typename List, std::size_t N>
        using drop_c = _t<detail::drop_<List, meta::size_t<N>>>;

        namespace lazy
        {
            template <typename List, typename N>
            using drop = defer<drop, List, N>;
        }

        // front
        namespace detail
        {
            template <typename List>
            struct front_
            {
            };

            template <typename Head, typename... List>
            struct front_<list<Head, List...>>
            {
                using type = Head;
            };
        } // namespace detail

        template <typename List>
        using front = _t<detail::front_<List>>;

        namespace lazy
        {
            template <typename List>
            using front = defer<front, List>;
        }

        // back
        namespace detail
        {
            template <typename List>
            struct back_
            {
            };

            template <typename Head, typename... List>
            struct back_<list<Head, List...>>
            {
                using type = at_c<list<Head, List...>, sizeof...(List)>;
            };
        } // namespace detail

        template <typename List>
        using back = _t<detail::back_<List>>;

        namespace lazy
        {
            template <typename List>
            using back = defer<back, List>;
        }

        // push_front
        namespace detail
        {
            template <typename List, typename T>
            struct push_front_
            {
            };

            template <typename... List, typename T>
            struct push_front_<list<List...>, T>
            {
                using type = list<T, List...>;
            };
        } // namespace detail

        template <typename List, typename T>
        using push_front = _t<detail::push_front_<List, T>>;

        namespace lazy
        {
            template <typename List, typename T>
            using push_front = defer<push_front, List, T>;
        }

        // pop_front
        namespace detail
        {
            template <typename List>
            struct pop_front_
            {
            };

            template <typename Head, typename... List>
            struct pop_front_<list<Head, List...>>
            {
                using type = list<List...>;
            };
        } // namespace detail

        template <typename List>
        using pop_front = _t<detail::pop_front_<List>>;

        namespace lazy
        {
            template <typename List>
            using pop_front = defer<pop_front, List>;
        }

        // push_back
        namespace detail
        {
            template <typename List, typename T>
            struct push_back_
            {
            };

            template <typename... List, typename T>
            struct push_back_<list<List...>, T>
            {
                using type = list<List..., T>;
            };
        } // namespace detail

        template <typename List, typename T>
        using push_back = _t<detail::push_back_<List, T>>;

        namespace lazy
        {
            template <typename List, typename T>
            using push_back = defer<push_back, List, T>;
        }
        namespace detail
        {
            template <typename T, typename U>
            using min_ = if_<less<U, T>, U, T>;

            template <typename T, typename U>
            using max_ = if_<less<U, T>, T, U>;
        }

        template <typename... Ts>
        using min = fold<pop_front<list<Ts...>>, front<list<Ts...>>, quote<detail::min_>>;

        template <typename... Ts>
        using max = fold<pop_front<list<Ts...>>, front<list<Ts...>>, quote<detail::max_>>;

        namespace lazy
        {
            template <typename... Ts>
            using min = defer<min, Ts...>;

            template <typename... Ts>
            using max = defer<max, Ts...>;
        }

        // empty
        template <typename List>
        using empty = bool_<0 == size<List>::type::value>;

        namespace lazy
        {
            template <typename List>
            using empty = defer<empty, List>;
        }

        // pair
        template <typename F, typename S>
        using pair = list<F, S>;

        template <typename Pair>
        using first = front<Pair>;

        template <typename Pair>
        using second = front<pop_front<Pair>>;

        namespace lazy
        {
            template <typename Pair>
            using first = defer<first, Pair>;

            template <typename Pair>
            using second = defer<second, Pair>;
        }

        // find_index
        namespace detail
        {
            // With thanks to Peter Dimov:
            constexpr std::size_t find_index_i_(bool const *const first, bool const *const last,
                                                std::size_t N = 0)
            {
                return first == last ? npos::value : *first ? N
                                                            : find_index_i_(first + 1, last, N + 1);
            }

            template <typename List, typename T>
            struct find_index_
            {
            };

            template <typename V>
            struct find_index_<list<>, V>
            {
                using type = npos;
            };

            template <typename... T, typename V>
            struct find_index_<list<T...>, V>
            {
                static constexpr bool s_v[] = {std::is_same<T, V>::value...};
                using type = size_t<find_index_i_(s_v, s_v + sizeof...(T))>;
            };
        } // namespace detail

        template <typename List, typename T>
        using find_index = _t<detail::find_index_<List, T>>;

        namespace lazy
        {
            template <typename List, typename T>
            using find_index = defer<find_index, List, T>;
        }

        // reverse_find_index
        namespace detail
        {
            // With thanks to Peter Dimov:
            constexpr std::size_t reverse_find_index_i_(bool const *const first,
                                                        bool const *const last, std::size_t N)
            {
                return first == last
                           ? npos::value
                           : *(last - 1) ? N - 1 : reverse_find_index_i_(first, last - 1, N - 1);
            }

            template <typename List, typename T>
            struct reverse_find_index_
            {
            };

            template <typename V>
            struct reverse_find_index_<list<>, V>
            {
                using type = npos;
            };

            template <typename... T, typename V>
            struct reverse_find_index_<list<T...>, V>
            {
                static constexpr bool s_v[] = {std::is_same<T, V>::value...};
                using type = size_t<reverse_find_index_i_(s_v, s_v + sizeof...(T), sizeof...(T))>;
            };
        } // namespace detail

        template <typename List, typename T>
        using reverse_find_index = _t<detail::reverse_find_index_<List, T>>;

        namespace lazy
        {
            template <typename List, typename T>
            using reverse_find_index = defer<reverse_find_index, List, T>;
        }

        // reverse_find
        namespace detail
        {
            template <typename List, typename T, typename State = list<>>
            struct reverse_find_
            {
            };

            template <typename T, typename State>
            struct reverse_find_<list<>, T, State>
            {
                using type = State;
            };

            template <typename Head, typename... List, typename T, typename State>
            struct reverse_find_<list<Head, List...>, T, State>
                : reverse_find_<list<List...>, T, State>
            {
            };

            template <typename... List, typename T, typename State>
            struct reverse_find_<list<T, List...>, T, State>
                : reverse_find_<list<List...>, T, list<T, List...>>
            {
            };
        }

        template <typename List, typename T>
        using find = drop<List, min<find_index<List, T>, size<List>>>;

        namespace lazy
        {
            template <typename List, typename T>
            using find = defer<find, List, T>;
        }

        template <typename List, typename T>
        using reverse_find = drop<List, min<reverse_find_index<List, T>, size<List>>>;

        namespace lazy
        {
            template <typename List, typename T>
            using reverse_find = defer<reverse_find, List, T>;
        }

        // find_if
        namespace detail
        {
            template <typename List, typename Fun>
            struct find_if_
            {
            };

            template <typename Fun>
            struct find_if_<list<>, Fun>
            {
                using type = list<>;
            };

            template <typename Head, typename... List, typename Fun>
            struct find_if_<list<Head, List...>, Fun>
                : if_<invoke<Fun, Head>, id<list<Head, List...>>, find_if_<list<List...>, Fun>>
            {
            };
        } // namespace detail

        template <typename List, typename Fun>
        using find_if = _t<detail::find_if_<List, Fun>>;

        namespace lazy
        {
            template <typename List, typename Fun>
            using find_if = defer<find_if, List, Fun>;
        }

        // reverse_find_if
        namespace detail
        {
            template <typename List, typename Fun, typename State = list<>>
            struct reverse_find_if_
            {
            };

            template <typename Fun, typename State>
            struct reverse_find_if_<list<>, Fun, State>
            {
                using type = State;
            };

            template <typename Head, typename... List, typename Fun, typename State>
            struct reverse_find_if_<list<Head, List...>, Fun, State>
                : reverse_find_if_<list<List...>, Fun,
                                   if_<invoke<Fun, Head>, list<Head, List...>, State>>
            {
            };
        }

        template <typename List, typename Fun>
        using reverse_find_if = _t<detail::reverse_find_if_<List, Fun>>;

        namespace lazy
        {
            template <typename List, typename Fun>
            using reverse_find_if = defer<reverse_find_if, List, Fun>;
        }

        // replace
        namespace detail
        {
            template <typename List, typename T, typename U>
            struct replace_
            {
            };

            template <typename... List, typename T, typename U>
            struct replace_<list<List...>, T, U>
            {
                using type = list<if_<std::is_same<T, List>, U, List>...>;
            };
        } // namespace detail

        template <typename List, typename T, typename U>
        using replace = _t<detail::replace_<List, T, U>>;

        namespace lazy
        {
            template <typename List, typename T, typename U>
            using replace = defer<replace, T, U>;
        }

        // replace_if
        namespace detail
        {
            template <typename List, typename C, typename U>
            struct replace_if_
            {
            };

            template <typename... List, typename C, typename U>
            struct replace_if_<list<List...>, C, U>
            {
                using type = list<if_<invoke<C, List>, U, List>...>;
            };
        } // namespace detail

        template <typename List, typename C, typename U>
        using replace_if = _t<detail::replace_if_<List, C, U>>;

        namespace lazy
        {
            template <typename List, typename C, typename U>
            using replace_if = defer<replace_if, C, U>;
        }

        // count
        namespace detail
        {
            template <typename State, typename Val, typename T>
            using count_fn = if_<std::is_same<Val, T>, inc<State>, State>;
        }

        template <typename List, typename T>
        using count = fold<List, meta::size_t<0>, bind_back<quote<detail::count_fn>, T>>;

        namespace lazy
        {
            template <typename List, typename T>
            using count = defer<count, List, T>;
        }

        // count_if
        namespace detail
        {
            template <typename State, typename Val, typename Fn>
            using count_if_fn = if_<invoke<Fn, Val>, inc<State>, State>;
        }

        template <typename List, typename Fn>
        using count_if = fold<List, meta::size_t<0>, bind_back<quote<detail::count_if_fn>, Fn>>;

        namespace lazy
        {
            template <typename List, typename Fn>
            using count_if = defer<count_if, List, Fn>;
        }

        // transform
        namespace detail
        {
            template <typename, typename = void>
            struct transform_
            {
            };

            template <typename... Ts, typename Fun>
            struct transform_<list<list<Ts...>, Fun>, void_<invoke<Fun, Ts>...>>
            {
                using type = list<invoke<Fun, Ts>...>;
            };

            template <typename... Ts0, typename... Ts1, typename Fun>
            struct transform_<list<list<Ts0...>, list<Ts1...>, Fun>,
                              void_<invoke<Fun, Ts0, Ts1>...>>
            {
                using type = list<invoke<Fun, Ts0, Ts1>...>;
            };
        } // namespace detail

        template <typename... Args>
        using transform = _t<detail::transform_<list<Args...>>>;

        namespace lazy
        {
            template <typename... Args>
            using transform = defer<transform, Args...>;
        }

        // filter
        namespace detail
        {
            template <typename Pred>
            struct filter_
            {
                template <typename State, typename A>
                using invoke = if_<invoke<Pred, A>, push_back<State, A>, State>;
            };
        } // namespace detail

        template <typename List, typename Pred>
        using filter = fold<List, list<>, detail::filter_<Pred>>;

        namespace lazy
        {
            template <typename List, typename Pred>
            using filter = defer<filter, List, Pred>;
        }

        // static_const
        namespace detail
        {
            template <typename T>
            struct static_const
            {
                static constexpr T value{};
            };

            // Avoid potential ODR violations with global objects:
            template <typename T>
            constexpr T static_const<T>::value;
        } // namespace detail


        // for_each
        namespace detail
        {
            struct for_each_fn
            {
                template <class UnaryFunction, class... Args>
                constexpr auto operator()(list<Args...>, UnaryFunction f) const -> UnaryFunction
                {
                    return (void)std::initializer_list<int>{((void)f(Args{}), 0)...}, f;
                }
            };
        } // namespace detail

        namespace
        {

            constexpr auto &&for_each = detail::static_const<detail::for_each_fn>::value;

        }

        // transpose
        template <typename ListOfLists>
        using transpose = fold<ListOfLists, repeat_n<size<front<ListOfLists>>, list<>>,
                               bind_back<quote<transform>, quote<push_back>>>;

        namespace lazy
        {
            template <typename ListOfLists>
            using transpose = defer<transpose, ListOfLists>;
        }

        // zip_with
        template <typename Fun, typename ListOfLists>
        using zip_with = transform<transpose<ListOfLists>, uncurry<Fun>>;

        namespace lazy
        {
            template <typename Fun, typename ListOfLists>
            using zip_with = defer<zip_with, Fun, ListOfLists>;
        }

        // zip
        template <typename ListOfLists>
        using zip = transpose<ListOfLists>;

        namespace lazy
        {
            template <typename ListOfLists>
            using zip = defer<zip, ListOfLists>;
        }

        // as_list
        namespace detail
        {
            template <typename T>
            using uncvref_t = _t<std::remove_cv<_t<std::remove_reference<T>>>>;

            // Indirection here needed to avoid Core issue 1430
            // http://open-std.org/jtc1/sc22/wg21/docs/cwg_active.html#1430
            template <typename Sequence>
            struct as_list_ : lazy::invoke<uncurry<curry<quote_trait<id>>>, uncvref_t<Sequence>>
            {
            };
        } // namespace detail

        template <typename Sequence>
        using as_list = _t<detail::as_list_<Sequence>>;

        namespace lazy
        {
            template <typename Sequence>
            using as_list = defer<as_list, Sequence>;
        }

        // reverse
        template <typename List>
        using reverse = reverse_fold<List, list<>, quote<push_back>>;

        namespace lazy
        {
            template <typename List>
            using reverse = defer<reverse, List>;
        }

        template <typename F>
        using not_fn = compose<quote<not_>, F>;

        namespace lazy
        {
            template <typename F>
            using not_fn = defer<not_fn, F>;
        }

        // all_of
        template <typename List, typename F>
        using all_of = empty<find_if<List, not_fn<F>>>;

        namespace lazy
        {
            template <typename List, typename Fn>
            using all_of = defer<all_of, List, Fn>;
        }

        // any_of
        template <typename List, typename F>
        using any_of = not_<empty<find_if<List, F>>>;

        namespace lazy
        {
            template <typename List, typename Fn>
            using any_of = defer<any_of, List, Fn>;
        }

        // none_of
        template <typename List, typename F>
        using none_of = empty<find_if<List, F>>;

        namespace lazy
        {
            template <typename List, typename Fn>
            using none_of = defer<none_of, List, Fn>;
        }

        // in
        template <typename List, typename T>
        using in = not_<empty<find<List, T>>>;

        namespace lazy
        {
            template <typename List, typename T>
            using in = defer<in, List, T>;
        }

        // inherit
        namespace detail
        {
            template<typename List>
            struct inherit_
            {
            };

            template<typename ...List>
            struct inherit_<list<List...>> : List...
            {
                using type = inherit_;
            };
        }

        template <typename List>
        using inherit = meta::_t<detail::inherit_<List>>;

        namespace lazy
        {
            template <typename List>
            using inherit = defer<inherit, List>;
        }

        // set
        // Used to improve the performance of \c meta::unique.
        namespace detail
        {
            template <typename Set, typename T>
            struct in_
            {
            };

            template <typename... Set, typename T>
            struct in_<list<Set...>, T> : std::is_base_of<id<T>, inherit<list<id<Set>...>>>
            {
            };

            template <typename Set, typename T>
            struct insert_back_
            {
            };

            template <typename... Set, typename T>
            struct insert_back_<list<Set...>, T>
            {
                using type = if_<in_<list<Set...>, T>, list<Set...>, list<Set..., T>>;
            };
        } // namespace detail

        // unique
        template <typename List>
        using unique = fold<List, list<>, quote_trait<detail::insert_back_>>;

        namespace lazy
        {
            template <typename List>
            using unique = defer<unique, List>;
        }

        // partition
        namespace detail
        {
            template <typename Pred>
            struct partition_
            {
                template <typename, typename, typename = void>
                struct impl
                {
                };
                template <typename... Yes, typename... No, typename A>
                struct impl<pair<list<Yes...>, list<No...>>, A,
                            void_<bool_<invoke<Pred, A>::type::value>>>
                {
                    using type = if_<invoke<Pred, A>, pair<list<Yes..., A>, list<No...>>,
                                     pair<list<Yes...>, list<No..., A>>>;
                };
                template <typename State, typename A>
                using invoke = _t<impl<State, A>>;
            };
        } // namespace detail

        template <typename List, typename Pred>
        using partition = fold<List, pair<list<>, list<>>, detail::partition_<Pred>>;

        namespace lazy
        {
            template <typename List, typename Pred>
            using partition = defer<partition, List, Pred>;
        }

        // sort
        namespace detail
        {
            template <typename, typename, typename = void>
            struct sort_
            {
            };

            template <typename Pred>
            struct sort_<list<>, Pred>
            {
                using type = list<>;
            };

            template <typename A, typename Pred>
            struct sort_<list<A>, Pred>
            {
                using type = list<A>;
            };

            template <typename A, typename B, typename... List, typename Pred>
            struct sort_<
                list<A, B, List...>, Pred,
                void_<_t<sort_<first<partition<list<B, List...>, bind_back<Pred, A>>>, Pred>>>>
            {
                using P = partition<list<B, List...>, bind_back<Pred, A>>;
                using type =
                    concat<_t<sort_<first<P>, Pred>>, list<A>, _t<sort_<second<P>, Pred>>>;
            };
        }

        // clang-format off
        // clang-format on
        template <typename List, typename Pred>
        using sort = _t<detail::sort_<List, Pred>>;

        namespace lazy
        {
            template <typename List, typename Pred>
            using sort = defer<sort, List, Pred>;
        }

        // lambda_
        namespace detail
        {
            template <typename T, int = 0>
            struct protect_;

            template <typename, int = 0>
            struct vararg_;

            template <typename T, int = 0>
            struct is_valid_;

            // Returns which branch to evaluate
            template <typename If, typename... Ts>
            using lazy_if_ = lazy::_t<defer<_if_, If, protect_<Ts>...>>;

            template <typename A, typename T, typename F, typename Ts>
            struct subst1_
            {
                using type = list<list<T>>;
            };
            template <typename T, typename F, typename Ts>
            struct subst1_<F, T, F, Ts>
            {
                using type = list<>;
            };
            template <typename A, typename T, typename F, typename Ts>
            struct subst1_<vararg_<A>, T, F, Ts>
            {
                using type = list<Ts>;
            };

            template <typename As, typename Ts>
            using substitutions_ = push_back<
                join<transform<
                    concat<As, repeat_n_c<size<Ts>{} + 2 - size<As>{}, back<As>>>,
                    concat<Ts, repeat_n_c<2, back<As>>>,
                    bind_back<quote_trait<subst1_>, back<As>, drop_c<Ts, size<As>{} - 2>>>>,
                list<back<As>>>;

            template <typename As, typename Ts>
            using substitutions =
                invoke<if_c<(size<Ts>{} + 2 >= size<As>{}), quote<substitutions_>>, As, Ts>;

            template <typename T>
            struct is_vararg_ : std::false_type
            {
            };
            template <typename T>
            struct is_vararg_<vararg_<T>> : std::true_type
            {
            };

            template <typename Tags>
            using is_variadic_ = is_vararg_<at<push_front<Tags, void>, dec<size<Tags>>>>;

            template <typename Tags, bool IsVariadic = is_variadic_<Tags>::value>
            struct lambda_;

            // Non-variadic lambda implementation
            template <typename... As>
            struct lambda_<list<As...>, false>
            {
            private:
                static constexpr std::size_t arity = sizeof...(As)-1;
                using Tags = list<As...>; // Includes the lambda body as the last arg!
                using F = back<Tags>;
                template <typename T, typename Args>
                struct impl;
                template <typename T, typename Args>
                using lazy_impl_ = lazy::_t<defer<impl, T, protect_<Args>>>;
                template <typename, typename, typename = void>
                struct subst_
                {
                };
                template <template <typename...> class C, typename... Ts, typename Args>
                struct subst_<defer<C, Ts...>, Args, void_<C<_t<impl<Ts, Args>>...>>>
                {
                    using type = C<_t<impl<Ts, Args>>...>;
                };
                template <typename T, template <T...> class C, T... Is, typename Args>
                struct subst_<defer_i<T, C, Is...>, Args, void_<C<Is...>>>
                {
                    using type = C<Is...>;
                };
                template <typename T, typename Args>
                struct impl : if_c<(reverse_find_index<Tags, T>() != npos()),
                                   lazy::at<Args, reverse_find_index<Tags, T>>, id<T>>
                {
                };
                template <typename T, typename Args>
                struct impl<protect_<T>, Args>
                {
                    using type = T;
                };
                template <typename T, typename Args>
                struct impl<is_valid_<T>, Args>
                {
                    using type = is_trait<impl<T, Args>>;
                };
                template <typename If, typename... Ts, typename Args>
                struct impl<defer<if_, If, Ts...>, Args> // Short-circuit if_
                    : impl<lazy_impl_<lazy_if_<If, Ts...>, Args>, Args>
                {
                };
                template <typename Bool, typename... Ts, typename Args>
                struct impl<defer<and_, Bool, Ts...>, Args> // Short-circuit and_
                    : impl<lazy_impl_<lazy_if_<Bool, lazy::and_<Ts...>, protect_<std::false_type>>,
                                      Args>,
                           Args>
                {
                };
                template <typename Bool, typename... Ts, typename Args>
                struct impl<defer<or_, Bool, Ts...>, Args> // Short-circuit or_
                    : impl<lazy_impl_<lazy_if_<Bool, protect_<std::true_type>, lazy::or_<Ts...>>,
                                      Args>,
                           Args>
                {
                };
                template <template <typename...> class C, typename... Ts, typename Args>
                struct impl<defer<C, Ts...>, Args> : subst_<defer<C, Ts...>, Args>
                {
                };
                template <typename T, template <T...> class C, T... Is, typename Args>
                struct impl<defer_i<T, C, Is...>, Args> : subst_<defer_i<T, C, Is...>, Args>
                {
                };
                template <template <typename...> class C, typename... Ts, typename Args>
                struct impl<C<Ts...>, Args> : subst_<defer<C, Ts...>, Args>
                {
                };
                template <typename... Ts, typename Args>
                struct impl<lambda_<list<Ts...>, false>, Args>
                {
                    using type = compose<uncurry<lambda_<list<As..., Ts...>, false>>,
                                         curry<bind_front<quote<concat>, Args>>>;
                };
                template <typename... Bs, typename Args>
                struct impl<lambda_<list<Bs...>, true>, Args>
                {
                    using type = compose<typename lambda_<list<As..., Bs...>, true>::thunk,
                                         bind_front<quote<concat>, transform<Args, quote<list>>>,
                                         curry<bind_front<quote<substitutions>, list<Bs...>>>>;
                };

            public:
                template <typename... Ts>
                using invoke = _t<if_c<sizeof...(Ts) == arity, impl<F, list<Ts..., F>>>>;
            };

            // Lambda with variadic placeholder (broken out due to less efficient compile-time
            // resource usage)
            template <typename... As>
            struct lambda_<list<As...>, true>
            {
            private:
                template <typename T, bool IsVar>
                friend struct lambda_;
                using Tags = list<As...>; // Includes the lambda body as the last arg!
                template <typename T, typename Args>
                struct impl;
                template <typename Args>
                using eval_impl_ = bind_back<quote_trait<impl>, Args>;
                template <typename T, typename Args>
                using lazy_impl_ = lazy::_t<defer<impl, T, protect_<Args>>>;
                template <template <typename...> class C, typename Args, typename Ts>
                using try_subst_ = apply<quote<C>, join<transform<Ts, eval_impl_<Args>>>>;
                template <typename, typename, typename = void>
                struct subst_
                {
                };
                template <template <typename...> class C, typename... Ts, typename Args>
                struct subst_<defer<C, Ts...>, Args, void_<try_subst_<C, Args, list<Ts...>>>>
                {
                    using type = list<try_subst_<C, Args, list<Ts...>>>;
                };
                template <typename T, template <T...> class C, T... Is, typename Args>
                struct subst_<defer_i<T, C, Is...>, Args, void_<C<Is...>>>
                {
                    using type = list<C<Is...>>;
                };
                template <typename T, typename Args>
                struct impl : if_c<(reverse_find_index<Tags, T>() != npos()),
                                   lazy::at<Args, reverse_find_index<Tags, T>>, id<list<T>>>
                {
                };
                template <typename T, typename Args>
                struct impl<protect_<T>, Args>
                {
                    using type = list<T>;
                };
                template <typename T, typename Args>
                struct impl<is_valid_<T>, Args>
                {
                    using type = list<is_trait<impl<T, Args>>>;
                };
                template <typename If, typename... Ts, typename Args>
                struct impl<defer<if_, If, Ts...>, Args> // Short-circuit if_
                    : impl<lazy_impl_<lazy_if_<If, Ts...>, Args>, Args>
                {
                };
                template <typename Bool, typename... Ts, typename Args>
                struct impl<defer<and_, Bool, Ts...>, Args> // Short-circuit and_
                    : impl<lazy_impl_<lazy_if_<Bool, lazy::and_<Ts...>, protect_<std::false_type>>,
                                      Args>,
                           Args>
                {
                };
                template <typename Bool, typename... Ts, typename Args>
                struct impl<defer<or_, Bool, Ts...>, Args> // Short-circuit or_
                    : impl<lazy_impl_<lazy_if_<Bool, protect_<std::true_type>, lazy::or_<Ts...>>,
                                      Args>,
                           Args>
                {
                };
                template <template <typename...> class C, typename... Ts, typename Args>
                struct impl<defer<C, Ts...>, Args> : subst_<defer<C, Ts...>, Args>
                {
                };
                template <typename T, template <T...> class C, T... Is, typename Args>
                struct impl<defer_i<T, C, Is...>, Args> : subst_<defer_i<T, C, Is...>, Args>
                {
                };
                template <template <typename...> class C, typename... Ts, typename Args>
                struct impl<C<Ts...>, Args> : subst_<defer<C, Ts...>, Args>
                {
                };
                template <typename... Bs, bool IsVar, typename Args>
                struct impl<lambda_<list<Bs...>, IsVar>, Args>
                {
                    using type =
                        list<compose<typename lambda_<list<As..., Bs...>, true>::thunk,
                                     bind_front<quote<concat>, Args>,
                                     curry<bind_front<quote<substitutions>, list<Bs...>>>>>;
                };
                struct thunk
                {
                    template <typename S, typename R = _t<impl<back<Tags>, S>>>
                    using invoke = if_c<size<R>{} == 1, front<R>>;
                };

            public:
                template <typename... Ts>
                using invoke = invoke<thunk, substitutions<Tags, list<Ts...>>>;
            };
        }

        // lambda
        template <typename... Ts>
        using lambda = if_c<(sizeof...(Ts) > 0), detail::lambda_<list<Ts...>>>;

        // is_valid
        template <typename T>
        using is_valid = detail::is_valid_<T>;

        // vararg
        template <typename T>
        using vararg = detail::vararg_<T>;

        // protect
        template <typename T>
        using protect = detail::protect_<T>;

        // var
        template <typename Tag, typename Value>
        struct var;

        namespace detail
        {
            template <typename... As>
            struct let_
            {
            };
            template <typename Fn>
            struct let_<Fn>
            {
                using type = lazy::invoke<lambda<Fn>>;
            };
            template <typename Tag, typename Value, typename... Rest>
            struct let_<var<Tag, Value>, Rest...>
            {
                using type = lazy::invoke<lambda<Tag, _t<let_<Rest...>>>, Value>;
            };
        }

        template <typename... As>
        using let = _t<_t<detail::let_<As...>>>;

        namespace lazy
        {
            template <typename... As>
            using let = defer<let, As...>;
        }

        // Some argument placeholders for use in \c lambda expressions.
        inline namespace placeholders
        {
            // regular placeholders:
            struct _a;
            struct _b;
            struct _c;
            struct _d;
            struct _e;
            struct _f;
            struct _g;
            struct _h;
            struct _i;

            // variadic placeholders:
            using _args = vararg<void>;
            using _args_a = vararg<_a>;
            using _args_b = vararg<_b>;
            using _args_c = vararg<_c>;
        } // namespace placeholders

        // cartesian_product
        namespace detail
        {
            template <typename M2, typename M>
            struct cartesian_product_fn
            {
                template <typename X>
                struct lambda0
                {
                    template <typename Xs>
                    using lambda1 = list<push_front<Xs, X>>;
                    using type = join<transform<M2, quote<lambda1>>>;
                };
                using type = join<transform<M, quote_trait<lambda0>>>;
            };
        } // namespace detail

        template <typename ListOfLists>
        using cartesian_product =
            reverse_fold<ListOfLists, list<list<>>, quote_trait<detail::cartesian_product_fn>>;

        namespace lazy
        {
            template <typename ListOfLists>
            using cartesian_product = defer<cartesian_product, ListOfLists>;
        }

        // add_const_if
        template <typename If>
        using add_const_if = if_<If, quote_trait<std::add_const>, quote_trait<id>>;

        template <bool If>
        using add_const_if_c = if_c<If, quote_trait<std::add_const>, quote_trait<id>>;

        // integer_sequence

#ifndef __cpp_lib_integer_sequence
        template <typename T, T... Is>
        struct integer_sequence
        {
            using value_type = T;
            static constexpr std::size_t size() noexcept { return sizeof...(Is); }
        };
#endif

        namespace detail
        {
            // Glue two sets of integer_sequence together
            template <typename I1, typename I2, typename I3>
            struct integer_sequence_cat;

            template <typename T, T... N1, T... N2, T... N3>
            struct integer_sequence_cat<integer_sequence<T, N1...>, integer_sequence<T, N2...>,
                                        integer_sequence<T, N3...>>
            {
                using type = integer_sequence<T, N1..., (sizeof...(N1) + N2)...,
                                              (sizeof...(N1) + sizeof...(N2) + N3)...>;
            };

            template <typename T, std::size_t N>
            struct make_integer_sequence_
                : integer_sequence_cat<_t<make_integer_sequence_<T, N / 2>>,
                                       _t<make_integer_sequence_<T, N / 2>>,
                                       _t<make_integer_sequence_<T, N % 2>>>
            {
            };

            template <typename T>
            struct make_integer_sequence_<T, 0>
            {
                using type = integer_sequence<T>;
            };

            template <typename T>
            struct make_integer_sequence_<T, 1>
            {
                using type = integer_sequence<T, 0>;
            };
        } // namespace detail

        template <typename T, T N>
        using make_integer_sequence = _t<detail::make_integer_sequence_<T, (std::size_t)N>>;

        template <std::size_t... Is>
        using index_sequence = integer_sequence<std::size_t, Is...>;

        template <std::size_t N>
        using make_index_sequence = make_integer_sequence<std::size_t, N>;

        namespace detail
        {
            template <typename State, typename Ch>
            using atoi_ = if_c<(Ch::value >= '0' && Ch::value <= '9'),
                               std::integral_constant<typename State::value_type,
                                                      State::value * 10 + (Ch::value - '0')>>;
        }

        inline namespace literals
        {
            template <char... Chs>
            constexpr fold<list<char_<Chs>...>, meta::size_t<0>, quote<detail::atoi_>> operator"" _z()
            {
                return {};
            }
        }

        // integer_range
        namespace detail
        {
            template <class T, T offset, class U>
            struct offset_integer_sequence_
            {
            };

            template <class T, T offset, T... Ts>
            struct offset_integer_sequence_<T, offset, meta::integer_sequence<T, Ts...>>
            {
                using type = meta::integer_sequence<T, (Ts + offset)...>;
            };
        } // namespace detail

        template <class T, T from, T to>
        using integer_range = meta::_t< 
            detail::offset_integer_sequence_<T, from, meta::make_integer_sequence<T, to - from>>>;
    } // namespace v1
} // namespace meta

#if defined(__clang__) && defined(_LIBCPP_VERSION) && _LIBCPP_VERSION <= 1101

_LIBCPP_BEGIN_NAMESPACE_STD
template <class>
class _LIBCPP_TYPE_VIS_ONLY allocator;
template <class, class>
struct _LIBCPP_TYPE_VIS_ONLY pair;
template <class>
struct _LIBCPP_TYPE_VIS_ONLY hash;
template <class>
struct _LIBCPP_TYPE_VIS_ONLY less;
template <class>
struct _LIBCPP_TYPE_VIS_ONLY equal_to;
template <class>
struct _LIBCPP_TYPE_VIS_ONLY char_traits;
template <class, class>
class _LIBCPP_TYPE_VIS_ONLY list;
template <class, class>
class _LIBCPP_TYPE_VIS_ONLY forward_list;
template <class, class>
class _LIBCPP_TYPE_VIS_ONLY vector;
template <class, class>
class _LIBCPP_TYPE_VIS_ONLY deque;
template <class, class, class>
class _LIBCPP_TYPE_VIS_ONLY basic_string;
template <class, class, class, class>
class _LIBCPP_TYPE_VIS_ONLY map;
template <class, class, class, class>
class _LIBCPP_TYPE_VIS_ONLY multimap;
template <class, class, class>
class _LIBCPP_TYPE_VIS_ONLY set;
template <class, class, class>
class _LIBCPP_TYPE_VIS_ONLY multiset;
template <class, class, class, class, class>
class _LIBCPP_TYPE_VIS_ONLY unordered_map;
template <class, class, class, class, class>
class _LIBCPP_TYPE_VIS_ONLY unordered_multimap;
template <class, class, class, class>
class _LIBCPP_TYPE_VIS_ONLY unordered_set;
template <class, class, class, class>
class _LIBCPP_TYPE_VIS_ONLY unordered_multiset;
template <class, class>
class _LIBCPP_TYPE_VIS_ONLY queue;
template <class, class, class>
class _LIBCPP_TYPE_VIS_ONLY priority_queue;
template <class, class>
class _LIBCPP_TYPE_VIS_ONLY stack;
_LIBCPP_END_NAMESPACE_STD

namespace meta
{
    inline namespace v1
    {
        namespace detail
        {
            template <typename T, typename A = std::allocator<T>>
            using std_list = std::list<T, A>;
            template <typename T, typename A = std::allocator<T>>
            using std_forward_list = std::forward_list<T, A>;
            template <typename T, typename A = std::allocator<T>>
            using std_vector = std::vector<T, A>;
            template <typename T, typename A = std::allocator<T>>
            using std_deque = std::deque<T, A>;
            template <typename T, typename C = std::char_traits<T>, typename A = std::allocator<T>>
            using std_basic_string = std::basic_string<T, C, A>;
            template <typename K, typename V, typename C = std::less<K>,
                      typename A = std::allocator<std::pair<K const, V>>>
            using std_map = std::map<K, V, C, A>;
            template <typename K, typename V, typename C = std::less<K>,
                      typename A = std::allocator<std::pair<K const, V>>>
            using std_multimap = std::multimap<K, V, C, A>;
            template <typename K, typename C = std::less<K>, typename A = std::allocator<K>>
            using std_set = std::set<K, C, A>;
            template <typename K, typename C = std::less<K>, typename A = std::allocator<K>>
            using std_multiset = std::multiset<K, C, A>;
            template <typename K, typename V, typename H = std::hash<K>,
                      typename C = std::equal_to<K>,
                      typename A = std::allocator<std::pair<K const, V>>>
            using std_unordered_map = std::unordered_map<K, V, H, C, A>;
            template <typename K, typename V, typename H = std::hash<K>,
                      typename C = std::equal_to<K>,
                      typename A = std::allocator<std::pair<K const, V>>>
            using std_unordered_multimap = std::unordered_multimap<K, V, H, C, A>;
            template <typename K, typename H = std::hash<K>, typename C = std::equal_to<K>,
                      typename A = std::allocator<K>>
            using std_unordered_set = std::unordered_set<K, H, C, A>;
            template <typename K, typename H = std::hash<K>, typename C = std::equal_to<K>,
                      typename A = std::allocator<K>>
            using std_unordered_multiset = std::unordered_multiset<K, H, C, A>;
            template <typename T, typename C = std_deque<T>>
            using std_queue = std::queue<T, C>;
            template <typename T, typename C = std_vector<T>,
                      class D = std::less<typename C::value_type>>
            using std_priority_queue = std::priority_queue<T, C, D>;
            template <typename T, typename C = std_deque<T>>
            using std_stack = std::stack<T, C>;
        }

        template <>
        struct quote<::std::list> : quote<detail::std_list>
        {
        };
        template <>
        struct quote<::std::deque> : quote<detail::std_deque>
        {
        };
        template <>
        struct quote<::std::forward_list> : quote<detail::std_forward_list>
        {
        };
        template <>
        struct quote<::std::vector> : quote<detail::std_vector>
        {
        };
        template <>
        struct quote<::std::basic_string> : quote<detail::std_basic_string>
        {
        };
        template <>
        struct quote<::std::map> : quote<detail::std_map>
        {
        };
        template <>
        struct quote<::std::multimap> : quote<detail::std_multimap>
        {
        };
        template <>
        struct quote<::std::set> : quote<detail::std_set>
        {
        };
        template <>
        struct quote<::std::multiset> : quote<detail::std_multiset>
        {
        };
        template <>
        struct quote<::std::unordered_map> : quote<detail::std_unordered_map>
        {
        };
        template <>
        struct quote<::std::unordered_multimap> : quote<detail::std_unordered_multimap>
        {
        };
        template <>
        struct quote<::std::unordered_set> : quote<detail::std_unordered_set>
        {
        };
        template <>
        struct quote<::std::unordered_multiset> : quote<detail::std_unordered_multiset>
        {
        };
        template <>
        struct quote<::std::queue> : quote<detail::std_queue>
        {
        };
        template <>
        struct quote<::std::priority_queue> : quote<detail::std_priority_queue>
        {
        };
        template <>
        struct quote<::std::stack> : quote<detail::std_stack>
        {
        };
    }
}

#endif

#if defined(__clang__)
#pragma GCC diagnostic pop
#endif
#endif