我应该如何制作功能咖喱？

Question

在 C++14 中，柯里化函数或函数对象的好方法是什么？

特别是，我有一个重载函数foo，其中包含一些随机数量的重载：一些重载可以通过 ADL 找到，其他的可能在无数地方定义。

我有一个辅助对象：

static struct {
  template<class...Args>
  auto operator()(Args&&...args)const
  -> decltype(foo(std::forward<Args>(args)...))
    { return (foo(std::forward<Args>(args)...));}
} call_foo;

这让我可以将重载集作为单个对象传递。

如果我想咖喱foo，我该怎么做？

由于curry 和部分函数应用程序经常互换使用，curry 我的意思是如果foo(a,b,c,d) 是一个有效的调用，那么curry(call_foo)(a)(b)(c)(d) 必须是一个有效的调用。

Answer 1

这是我目前最好的尝试。

#include <iostream>
#include <utility>
#include <memory>

SFINAE 实用程序助手类：

template<class T>struct voider{using type=void;};
template<class T>using void_t=typename voider<T>::type;

一个特征类，它告诉你 Sig 是否是一个有效的调用——即，如果std::result_of<Sig>::type 是定义的行为。在某些 C++ 实现中，只需检查 std::result_of 就足够了，但这不是标准要求的：

template<class Sig,class=void>
struct is_invokable:std::false_type {};
template<class F, class... Ts>
struct is_invokable<
  F(Ts...),
  void_t<decltype(std::declval<F>()(std::declval<Ts>()...))>
>:std::true_type {
  using type=decltype(std::declval<F>()(std::declval<Ts>()...));
};
template<class Sig>
using invoke_result=typename is_invokable<Sig>::type;
template<class T> using type=T;

Curry 助手是一种手动 lambda。它捕获一个函数和一个参数。它没有写成 lambda，因此我们可以在右值上下文中使用它时启用正确的右值转发，这在柯里化时很重要：

template<class F, class T>
struct curry_helper {
  F f;
  T t;
  template<class...Args>
  invoke_result< type<F const&>(T const&, Args...) >
  operator()(Args&&...args)const&
  {
    return f(t, std::forward<Args>(args)...);
  }
  template<class...Args>
  invoke_result< type<F&>(T const&, Args...) >
  operator()(Args&&...args)&
  {
    return f(t, std::forward<Args>(args)...);
  }
  template<class...Args>
  invoke_result< type<F>(T const&, Args...) >
  operator()(Args&&...args)&&
  {
    return std::move(f)(std::move(t), std::forward<Args>(args)...);
  }
};

肉和土豆：

template<class F>
struct curry_t {
  F f;
  template<class Arg>
  using next_curry=curry_t< curry_helper<F, std::decay_t<Arg> >;
  // the non-terminating cases.  When the signature passed does not evaluate
  // we simply store the value in a curry_helper, and curry the result:
  template<class Arg,class=std::enable_if_t<!is_invokable<type<F const&>(Arg)>::value>>
  auto operator()(Arg&& arg)const&
  {
    return next_curry<Arg>{{ f, std::forward<Arg>(arg) }};
  }
  template<class Arg,class=std::enable_if_t<!is_invokable<type<F&>(Arg)>::value>>
  auto operator()(Arg&& arg)&
  {
    return next_curry<Arg>{{ f, std::forward<Arg>(arg) }};
  }
  template<class Arg,class=std::enable_if_t<!is_invokable<F(Arg)>::value>>
  auto operator()(Arg&& arg)&&
  {
    return next_curry<Arg>{{ std::move(f), std::forward<Arg>(arg) }};
  }
  // These are helper functions that make curry(blah)(a,b,c) somewhat of a shortcut for curry(blah)(a)(b)(c)
  // *if* the latter is valid, *and* it isn't just directly invoked.  Not quite, because this can *jump over*
  // terminating cases...
  template<class Arg,class...Args,class=std::enable_if_t<!is_invokable<type<F const&>(Arg,Args...)>::value>>
  auto operator()(Arg&& arg,Args&&...args)const&
  {
    return next_curry<Arg>{{ f, std::forward<Arg>(arg) }}(std::forward<Args>(args)...);
  }
  template<class Arg,class...Args,class=std::enable_if_t<!is_invokable<type<F&>(Arg,Args...)>::value>>
  auto operator()(Arg&& arg,Args&&...args)&
  {
    return next_curry<Arg>{{ f, std::forward<Arg>(arg) }}(std::forward<Args>(args)...);
  }
  template<class Arg,class...Args,class=std::enable_if_t<!is_invokable<F(Arg,Args...)>::value>>
  auto operator()(Arg&& arg,Args&&...args)&&
  {
    return next_curry<Arg>{{ std::move(f), std::forward<Arg>(arg) }}(std::forward<Args>(args)...);
  }

  // The terminating cases.  If we run into a case where the arguments would evaluate, this calls the underlying curried function:
  template<class... Args,class=std::enable_if_t<is_invokable<type<F const&>(Args...)>::value>>
  auto operator()(Args&&... args,...)const&
  {
    return f(std::forward<Args>(args)...);
  }
  template<class... Args,class=std::enable_if_t<is_invokable<type<F&>(Args...)>::value>>
  auto operator()(Args&&... args,...)&
  {
    return f(std::forward<Args>(args)...);
  }
  template<class... Args,class=std::enable_if_t<is_invokable<F(Args...)>::value>>
  auto operator()(Args&&... args,...)&&
  {
    return std::move(f)(std::forward<Args>(args)...);
  }
};

template<class F>
curry_t<typename std::decay<F>::type> curry( F&& f ) { return {std::forward<F>(f)}; }

最后的功能很幽默。

请注意，没有进行类型擦除。另请注意，理论上手工制作的解决方案可以少得多moves，但我认为我不需要在任何地方复制。

这是一个测试函数对象：

static struct {
  double operator()(double x, int y, std::nullptr_t, std::nullptr_t)const{std::cout << "first\n"; return x*y;}
  char operator()(char c, int x)const{std::cout << "second\n"; return c+x;}
  void operator()(char const*s)const{std::cout << "hello " << s << "\n";}
} foo;

还有一些测试代码来看看它是如何工作的：

int main() {
  auto f = curry(foo);
  // testing the ability to "jump over" the second overload:
  std::cout << f(3.14,10,std::nullptr_t{})(std::nullptr_t{}) << "\n";
  // Call the 3rd overload:
  f("world");
  // call the 2nd overload:
  auto x =  f('a',2);
  std::cout << x << "\n";
  // again:
  x =  f('a')(2);
}

live example

生成的代码有点混乱。许多方法必须重复 3 次才能以最佳方式处理 &、const& 和 && 案例。 SFINAE 条款冗长而复杂。我最终使用了可变参数 和 可变参数，其中可变参数确保方法中不重要的签名差异（我认为优先级较低，并不重要，SFINAE 确保只有一个重载永远有效，this 限定符除外）。

curry(call_foo) 的结果是一个对象，一次可以调用一个参数，也可以一次调用多个参数。你可以用 3 个参数调用它，然后是 1，然后是 1，然后是 2，而且它大部分都是正确的。除了尝试向它提供参数并查看调用是否有效之外，没有任何证据可以告诉您它需要多少参数。这是处理重载情况所必需的。

多参数情况的一个怪癖是它不会将数据包部分传递给一个curry，而是将其余部分用作返回值的参数。我可以通过更改相对轻松地更改：

    return curry_t< curry_helper<F, std::decay_t<Arg> >>{{ f, std::forward<Arg>(arg) }}(std::forward<Args>(args)...);

到

    return (*this)(std::forward<Arg>(arg))(std::forward<Args>(args)...);

还有另外两个类似的。这将阻止“跳过”原本有效的重载的技术。想法？这意味着curry(foo)(a,b,c) 在逻辑上与curry(foo)(a)(b)(c) 相同，这看起来很优雅。

感谢@Casey，他的回答激发了很多灵感。

---

最新版本。它使(a,b,c) 的行为与(a)(b)(c) 非常相似，除非它是直接起作用的调用。

#include <type_traits>
#include <utility>

template<class...>
struct voider { using type = void; };
template<class...Ts>
using void_t = typename voider<Ts...>::type;

template<class T>
using decay_t = typename std::decay<T>::type;

template<class Sig,class=void>
struct is_invokable:std::false_type {};
template<class F, class... Ts>
struct is_invokable<
  F(Ts...),
  void_t<decltype(std::declval<F>()(std::declval<Ts>()...))>
>:std::true_type {};

#define RETURNS(...) decltype(__VA_ARGS__){return (__VA_ARGS__);}

template<class D>
class rvalue_invoke_support {
  D& self(){return *static_cast<D*>(this);}
  D const& self()const{return *static_cast<D const*>(this);}
public:
  template<class...Args>
  auto operator()(Args&&...args)&->
  RETURNS( invoke( this->self(), std::forward<Args>(args)... ) )

  template<class...Args>
  auto operator()(Args&&...args)const&->
  RETURNS( invoke( this->self(), std::forward<Args>(args)... ) )

  template<class...Args>
  auto operator()(Args&&...args)&&->
  RETURNS( invoke( std::move(this->self()), std::forward<Args>(args)... ) )

  template<class...Args>
  auto operator()(Args&&...args)const&&->
  RETURNS( invoke( std::move(this->self()), std::forward<Args>(args)... ) )
};

namespace curryDetails {
  // Curry helper is sort of a manual lambda.  It captures a function and one argument
  // It isn't written as a lambda so we can enable proper rvalue forwarding when it is
  // used in an rvalue context, which is important when currying:
  template<class F, class T>
  struct curry_helper: rvalue_invoke_support<curry_helper<F,T>> {
    F f;
    T t;

    template<class A, class B>
    curry_helper(A&& a, B&& b):f(std::forward<A>(a)), t(std::forward<B>(b)) {}

    template<class curry_helper, class...Args>
    friend auto invoke( curry_helper&& self, Args&&... args)->
    RETURNS( std::forward<curry_helper>(self).f( std::forward<curry_helper>(self).t, std::forward<Args>(args)... ) )
  };
}

namespace curryNS {
  // the rvalue-ref qualified function type of a curry_t:
  template<class curry>
  using function_type = decltype(std::declval<curry>().f);

  template <class> struct curry_t;

  // the next curry type if we chain given a new arg A0:
  template<class curry, class A0>
  using next_curry = curry_t<::curryDetails::curry_helper<decay_t<function_type<curry>>, decay_t<A0>>>;

  // 3 invoke_ overloads
  // The first is one argument when invoking f with A0 does not work:
  template<class curry, class A0>
  auto invoke_(std::false_type, curry&& self, A0&&a0 )->
  RETURNS(next_curry<curry, A0>{std::forward<curry>(self).f,std::forward<A0>(a0)})

  // This is the 2+ argument overload where invoking with the arguments does not work
  // invoke a chain of the top one:
  template<class curry, class A0, class A1, class... Args>
  auto invoke_(std::false_type, curry&& self, A0&&a0, A1&& a1, Args&&... args )->
  RETURNS(std::forward<curry>(self)(std::forward<A0>(a0))(std::forward<A1>(a1), std::forward<Args>(args)...))

  // This is the any number of argument overload when it is a valid call to f:
  template<class curry, class...Args>
  auto invoke_(std::true_type, curry&& self, Args&&...args )->
  RETURNS(std::forward<curry>(self).f(std::forward<Args>(args)...))

  template<class F>
  struct curry_t : rvalue_invoke_support<curry_t<F>> {
    F f;

    template<class... U>curry_t(U&&...u):f(std::forward<U>(u)...){}

    template<class curry, class...Args>
    friend auto invoke( curry&& self, Args&&...args )->
    RETURNS(invoke_(is_invokable<function_type<curry>(Args...)>{}, std::forward<curry>(self), std::forward<Args>(args)...))
  };
}

template<class F>
curryNS::curry_t<decay_t<F>> curry( F&& f ) { return {std::forward<F>(f)}; }

#include <iostream>

static struct foo_t {
  double operator()(double x, int y, std::nullptr_t, std::nullptr_t)const{std::cout << "first\n"; return x*y;}
  char operator()(char c, int x)const{std::cout << "second\n"; return c+x;}
  void operator()(char const*s)const{std::cout << "hello " << s << "\n";}
} foo;

int main() {

  auto f = curry(foo);
  using C = decltype((f));
  std::cout << is_invokable<curryNS::function_type<C>(const char(&)[5])>{} << "\n";
  invoke( f, "world" );
  // Call the 3rd overload:
  f("world");
  // testing the ability to "jump over" the second overload:
  std::cout << f(3.14,10,nullptr,nullptr) << "\n";
  // call the 2nd overload:
  auto x = f('a',2);
  std::cout << x << "\n";
  // again:
  x =  f('a')(2);
  std::cout << x << "\n";
  std::cout << is_invokable<decltype(foo)(double, int)>{} << "\n";
  std::cout << is_invokable<decltype(foo)(double)>{} << "\n";
  std::cout << is_invokable<decltype(f)(double, int)>{} << "\n";
  std::cout << is_invokable<decltype(f)(double)>{} << "\n";
  std::cout << is_invokable<decltype(f(3.14))(int)>{} << "\n";
  decltype(std::declval<decltype((foo))>()(std::declval<double>(), std::declval<int>())) y = {3};
  (void)y;
  // std::cout << << "\n";
}

live version

Answer 2

这是我使用热切语义的尝试，即，一旦积累了足够的参数以对原始函数进行有效调用 (Demo at Coliru)，就立即返回：

namespace detail {
template <unsigned I>
struct priority_tag : priority_tag<I-1> {};
template <> struct priority_tag<0> {};

// High priority overload.
// If f is callable with zero args, return f()
template <typename F>
auto curry(F&& f, priority_tag<1>) -> decltype(std::forward<F>(f)()) {
    return std::forward<F>(f)();
}

// Low priority overload.
// Return a partial application
template <typename F>
auto curry(F f, priority_tag<0>) {
    return [f](auto&& t) {
        return curry([f,t=std::forward<decltype(t)>(t)](auto&&...args) ->
          decltype(f(t, std::forward<decltype(args)>(args)...)) {
            return f(t, std::forward<decltype(args)>(args)...);
        }, priority_tag<1>{});
    };
}
} // namespace detail

// Dispatch to the implementation overload set in namespace detail.
template <typename F>
auto curry(F&& f) {
    return detail::curry(std::forward<F>(f), detail::priority_tag<1>{});
}

还有一个没有急切语义的替代实现，它需要额外的() 来调用部分应用程序，从而可以访问例如f(int) 和 f(int, int) 都来自同一个重载集：

template <typename F>
class partial_application {
    F f_;
public:
    template <typename T>
    explicit partial_application(T&& f) :
        f_(std::forward<T>(f)) {}

    auto operator()() { return f_(); }

    template <typename T>
    auto operator()(T&&);
};

template <typename F>
auto curry_explicit(F&& f) {
    return partial_application<F>{std::forward<F>(f)};
}

template <typename F>
template <typename T>
auto partial_application<F>::operator()(T&& t) {
    return curry_explicit([f=f_,t=std::forward<T>(t)](auto&&...args) ->
      decltype(f_(t, std::forward<decltype(args)>(args)...)) {
        return f(t, std::forward<decltype(args)>(args)...);
    });
}

Answer 3

这不是一个小问题。使所有权语义正确是棘手的。为了比较，让我们考虑几个 lambda 以及它们如何表达所有权：

[=]() {}         // capture by value, can't modify values of captures
[=]() mutable {} // capture by value, can modify values of captures

[&]() {}     // capture by reference, can modify values of captures

[a, &b, c = std::move(foo)]() {} // mixture of value and reference, move-only if foo is
                                 // can't modify value of a or c, but can b

默认情况下，我的实现按值捕获，在传递std::reference_wrapper<> 时按引用捕获（与std::make_tuple() 和std::ref() 的行为相同），并按原样转发调用参数（左值仍然是左值，右值仍然是右值）。我无法为mutable 确定一个令人满意的解决方案，所以所有的价值捕获都有效 const。

只移动类型的捕获使函子只移动。这反过来意味着如果c 是curry_t 并且d 是仅移动类型，并且c(std::move(d)) 不调用捕获的函子，那么将c(std::move(d)) 绑定到左值意味着后续调用要么必须包含足够的参数来调用捕获的函子，或者必须将左值转换为右值（可能通过std::move()）。这需要注意参考限定符。请记住，*this 始终是左值，因此必须将引用限定符应用于 operator()。

没有办法知道捕获的函子需要多少个参数，因为可能有任意数量的重载，所以要小心。没有static_asserts 那个sizeof...(Captures) < max(N_ARGS)。

总体而言，实现需要大约 70 行代码。正如 cmets 中所讨论的，我遵循了 curry(foo)(a, b, c, d) 和 foo(a, b, c, d) （大致）等效的约定，允许访问每个重载。

---

#include <cstddef>
#include <functional>
#include <type_traits>
#include <tuple>
#include <utility>

template<typename Functor>
auto curry(Functor&& f);

namespace curry_impl
{
    /* helper: typing using type = T; is tedious */
    template<typename T> struct identity { using type = T; };

    /* helper: SFINAE magic :) */
    template<typename...> struct void_t_impl : identity<void> {};
    template<typename... Ts> using void_t = typename void_t_impl<Ts...>::type;

    /* helper: true iff F(Args...) is invokable */
    template<typename Signature, typename = void> struct is_invokable                                                                    : std::false_type {};
    template<typename F, typename... Args> struct is_invokable<F(Args...), void_t<decltype(std::declval<F>()(std::declval<Args>()...))>> : std::true_type  {};

    /* helper: unwraps references wrapped by std::ref() */
    template<typename T> struct unwrap_reference                            : identity<T>  {};
    template<typename T> struct unwrap_reference<std::reference_wrapper<T>> : identity<T&> {};
    template<typename T> using unwrap_reference_t = typename unwrap_reference<T>::type;

    /* helper: same transformation as applied by std::make_tuple() *
    *         decays to value type unless wrapped with std::ref() *
    *    use: modeling value & reference captures                 *
    *         e.g. c(a) vs c(std::ref(a))                         */
    template<typename T> struct decay_reference : unwrap_reference<std::decay_t<T>> {};
    template<typename T> using decay_reference_t = typename decay_reference<T>::type;

    /* helper: true iff all template arguments are true */
    template<bool...> struct all : std::true_type {};
    template<bool... Booleans> struct all<false, Booleans...> : std::false_type {};
    template<bool... Booleans> struct all<true, Booleans...> : all<Booleans...> {};

    /* helper: std::move(u) iff T is not an lvalue                       *
    *    use: save on copies when curry_t is an rvalue                  *
    *         e.g. c(a)(b)(c) should only copy functor, a, b, etc. once */
    template<bool = false> struct move_if_value_impl       { template<typename U> auto&& operator()(U&& u) { return std::move(u); } };
    template<>             struct move_if_value_impl<true> { template<typename U> auto&  operator()(U&  u) { return u; } };
    template<typename T, typename U> auto&& move_if_value(U&& u) { return move_if_value_impl<std::is_lvalue_reference<T>{}>{}(std::forward<U>(u)); }

    /* the curry wrapper/functor */
    template<typename Functor, typename... Captures>
    struct curry_t {
        /* unfortunately, ref qualifiers don't change *this (always lvalue),   *
        * so qualifiers have to be on operator(),                             *
        * even though only invoke_impl(std::false_type, ...) needs qualifiers */
    #define OPERATOR_PARENTHESES(X, Y) \
        template<typename... Args> \
        auto operator()(Args&&... args) X { \
            return invoke_impl_##Y(is_invokable<Functor(Captures..., Args...)>{}, std::index_sequence_for<Captures...>{}, std::forward<Args>(args)...); \
        }

        OPERATOR_PARENTHESES(&,  lv)
        OPERATOR_PARENTHESES(&&, rv)
    #undef OPERATOR_PARENTHESES

        Functor functor;
        std::tuple<Captures...> captures;

    private:
        /* tag dispatch for when Functor(Captures..., Args...) is an invokable expression *
        * see above comment about duplicate code                             */
    #define INVOKE_IMPL_TRUE(X) \
        template<typename... Args, std::size_t... Is> \
        auto invoke_impl_##X(std::true_type, std::index_sequence<Is...>, Args&&... args) { \
            return functor(std::get<Is>(captures)..., std::forward<Args>(args)...); \
        }

        INVOKE_IMPL_TRUE(lv)
        INVOKE_IMPL_TRUE(rv)
    #undef INVOKE_IMPL_TRUE

        /* tag dispatch for when Functor(Capture..., Args...) is NOT an invokable expression *
        * lvalue ref qualifier version copies all captured values/references     */
        template<typename... Args, std::size_t... Is>
        auto invoke_impl_lv(std::false_type, std::index_sequence<Is...>, Args&&... args) {
            static_assert(all<std::is_copy_constructible<Functor>{}, std::is_copy_constructible<Captures>{}...>{}, "all captures must be copyable or curry_t must an rvalue");
            return curry_t<Functor, Captures..., decay_reference_t<Args>...>{
                functor,
                std::tuple<Captures..., decay_reference_t<Args>...>{
                    std::get<Is>(captures)...,
                    std::forward<Args>(args)...
                }
            };
        }

        /* tag dispatch for when F(As..., Args...) is NOT an invokable expression        *
        * rvalue ref qualifier version moves all captured values, copies all references */
        template<typename... Args, std::size_t... Is>
        auto invoke_impl_rv(std::false_type, std::index_sequence<Is...>, Args&&... args) {
            return curry_t<Functor, Captures..., decay_reference_t<Args>...>{
                move_if_value<Functor>(functor),
                std::tuple<Captures..., decay_reference_t<Args>...>{
                    move_if_value<Captures>(std::get<Is>(captures))...,
                    std::forward<Args>(args)...
                }
            };
        }
    };
}

/* helper function for creating curried functors */
template<typename Functor>
auto curry(Functor&& f) {
    return curry_impl::curry_t<curry_impl::decay_reference_t<Functor>>{std::forward<Functor>(f), {}};
}

Live demo on Coliru 演示引用限定符语义。

Answer 4

这是我在学习可变参数模板时一直在使用的代码。
这是用于函数指针的 ATD 和 std::function 上的 ATD 的玩具示例。
我已经在 lambdas 上做了例子，但还没有找到提取参数的方法，所以 lamnda 还没有 ATD

#include <iostream>
#include <tuple>
#include <type_traits>
#include <functional>
#include <algorithm>


//this is helper class for calling (variadic) func from std::tuple
template <typename F,typename ...Args>
struct TupleCallHelper
{
    template<int ...> struct seq {};
    template<int N, int ...S> struct gens : gens<N-1, N-1, S...> {};
    template<int ...S> struct gens<0, S...>{ typedef seq<S...> type; };
    template<int ...S>
    static inline auto callFunc(seq<S...>,std::tuple<Args...>& params, F f) -> 
           decltype(f(std::get<S>(params) ...))
    {
        return f(std::get<S>(params) ... );
    }

    static inline auto delayed_dispatch(F& f, std::tuple<Args... >&  args) ->  
          decltype(callFunc(typename gens<sizeof...(Args)>::type(),args , f))
    {
        return callFunc(typename gens<sizeof...(Args)>::type(),args , f);
    }
};




template <int Depth,typename F,typename ... Args>
struct CurriedImpl;

//curried base class, when all args are consumed
template <typename F,typename ... Args>
struct CurriedImpl<0,F,Args...>
{
    std::tuple<Args...> m_tuple;
    F m_func;

    CurriedImpl(const F& a_func):m_func(a_func)
    {
    }
    auto operator()() -> 
        decltype(TupleCallHelper<F,Args...>::delayed_dispatch(m_func,m_tuple))
    {
        return TupleCallHelper<F,Args...>::delayed_dispatch(m_func,m_tuple);
    }
};

template <typename F,typename ... Args>
struct CurriedImpl<-1,F,Args ... > ; //this is against weird gcc bug

//curried before all args are consumed (stores arg in tuple)
template <int Depth,typename F,typename ... Args>
struct CurriedImpl : public CurriedImpl<Depth-1,F,Args...>
{
    using parent_t = CurriedImpl<Depth-1,F,Args...>;

    CurriedImpl(const F& a_func): parent_t(a_func)
    {
    }
    template <typename First>
    auto operator()(const First& a_first) -> CurriedImpl<Depth-1,F,Args...>
    {
        std::get<sizeof...(Args)-Depth>(parent_t::m_tuple) = a_first;
        return *this;
    }

    template <typename First, typename... Rem>
    auto operator()(const First& a_first,Rem ... a_rem) -> 
         CurriedImpl<Depth-1-sizeof...(Rem),F,Args...>
    {
        CurriedImpl<Depth-1,F,Args...> r = this->operator()(a_first);
        return r(a_rem...);
    }
};


template <typename F, typename ... Args>
struct Curried: public CurriedImpl<sizeof...(Args),F,Args...>
{   
    Curried(F a_f):
        CurriedImpl<sizeof...(Args),F,Args...>(a_f)
    {
    }
};


template<typename A>
int varcout( A a_a)
{
    std::cout << a_a << "\n" ;
    return 0;
}

template<typename A,typename ... Var>
int varcout( A a_a, Var ... a_var)
{
    std::cout << a_a << "\n" ;
    return varcout(a_var ...);
}

template <typename F, typename ... Args>
auto curried(F(*a_f)(Args...)) -> Curried<F(*)(Args...),Args...>
{
   return Curried<F(*)(Args...),Args...>(a_f);
}

template <typename R, typename ... Args>
auto curried(std::function<R(Args ... )> a_f) -> Curried<std::function<R(Args ... )>,Args...>
{
   return Curried<std::function<R(Args ... )>,Args...>(a_f);
}

int main()
{

    //function pointers
    auto f = varcout<int,float>;
    auto curried_funcp = curried(f);
    curried_funcp(1)(10)(); 

    //atd for std::function
    std::function<int(int,float)> fun(f);
    auto curried_func = curried(fun);
    curried_func(2)(5)();
    curried_func(2,5)();//works too

    //example with std::lambda using  Curried  
    auto  lamb = [](int a , int b , std::string& s){
        std::cout << a + b << s ; 
    };

    Curried<decltype(lamb),int,int,std::string> co(lamb);

    auto var1 = co(2);
    auto var2 = var1(1," is sum\n");
    var2(); //prints -> "3 is sum"
}