How can I curry variadic template template parameters?

Question

Variadic template template parameters accept any template:

template
struct Test1 {
    using type = int;
};

template

        

Answer 1

After some problems of my own, I came up with this solution which will work for any template class (also the ones you provide in your post).
The core of this solution is is_valid_specialization which is used as the condition on whether or not the currying process may be considered complete:

#include <iostream>
#include <type_traits>

template<template<typename...> class C, typename... T>
struct is_valid_specialization {
    typedef struct { char _; } yes;
    typedef struct { yes _[2]; } no;

    template<template<typename...> class D>
    static yes test(D<T...>*);
    template<template<typename...> class D>
    static no test(...);

    constexpr static bool value = (sizeof(test<C>(0)) == sizeof(yes));
};

namespace detail {

    template<template<typename...> class BeCurry, bool = false, typename... S>
    struct Currying {

        template<typename... T>
        using apply = Currying<BeCurry, is_valid_specialization<BeCurry, S..., T...>::value, S..., T...>;
    };

    template<template<typename...> class BeCurry, typename... S>
    struct Currying<BeCurry, true, S...> {

        template<typename... T>
        using apply = Currying<BeCurry, is_valid_specialization<BeCurry, S..., T...>::value, S..., T...>;

        using type = typename BeCurry<S...>::type;
    };
}

template<template<typename...> class BeCurry>
using Currying = detail::Currying<BeCurry, is_valid_specialization<BeCurry>::value>;

template<typename T>
struct Test1 { using type = int; };

template<typename T1, typename T2>
struct Test2 { using type = char*; };

template<typename...>
struct Test3 { using type = double; };

using curry  = Currying<Test1>;
using curry2 = Currying<Test2>;
using curry3 = Currying<Test3>;

template<typename T>
void pretty_print(T) {
    std::cout << __PRETTY_FUNCTION__ << std::endl;
}

int main() {
    pretty_print(typename curry::apply<char>::type{});
    pretty_print(typename curry2::apply<int>::apply<char>::type{});
    pretty_print(typename curry3::type{});
}

Output on ideone

Answer 2

Simple solution is:

template
    <
        template <typename...> class BeCurry,
        typename... Params
    >
struct Currying
{
    template <typename... OtherParams>
    using curried = BeCurry<Params..., OtherParams...>;

    template <typename... OtherParams>
    using type = typename curried<OtherParams...>::type;

    template <typename... NewParams>
    using apply = Currying<curried, NewParams...>;
};

But it does not work with templates like Test1 and Test2 due to compilation errors (under gcc, at least). A workaround for this problem looks like this:

template
    <
        template <typename...> class BeCurry,
        typename... Params
    >
struct Curry
{
    using type = BeCurry<Params...>;
};

template
    <
        template <typename...> class BeCurry
    >
struct Curry<BeCurry>
{
    using type = BeCurry<>;
};

And now lines

template <typename... OtherParams>
using curried = BeCurry<Params..., OtherParams...>;

should be replaced with lines

template <typename... OtherParams>
using curried = typename Curry<BeCurry, Params..., OtherParams...>::type;

Example of using:

#include <iostream>
#include <typeinfo>

template <typename T>
void print_type(T t)
{
    std::cout << typeid(t).name() << std::endl;
}

// ...

print_type(Currying<Test1>::type<int>{});
print_type(Currying<Test1>::apply<int>::type<>{});
print_type(Currying<Test2>::type<int, char>{});
print_type(Currying<Test2>::apply<int>::type<char>{});
print_type(Currying<Test2>::apply<int>::apply<char>::type<>{});
print_type(Currying<Test2>::apply<int, char>::type<>{});

Full example at ideone.