How do I solve "template argument deduction/substitution failure" when implementing multi-type arithmetic operators

Question

I can't seem to find the correct way to implement it, this seems to be the closest to the right way but I am getting a template argument deduction error. Can anyone point out where I went wrong?

I am trying to add arithmetic capabilities to std::variant without needing to std::get first:

#include <iostream>
#include <variant>

template<typename... Types>
class variant : public std::variant<Types...> {
    private:
      template <class Op, typename T, int index = 0>
      decltype(auto) calc(const T& other) const {
        if(sizeof...(Types) == 0 || index >= sizeof...(Types)){
          return;
        }

        using ST = std::variant_alternative_t<index, std::variant<Types...>>;

        if(std::holds_alternative<ST>(
          std::variant<Types...>(*this)
        )){
          if(std::is_same<T, variant<Types...>>::value){
            return Op()(std::get<ST>(*this), std::get<ST>(other));
          }
          else{
            return Op()(std::get<ST>(*this), other);
          }
        }

        return this->calc<Op, index+1>(other);
      }

    public:
      using std::variant<Types...>::variant;

      template <typename T>
      decltype(auto) operator-(const T& other) const {
        return this->calc<std::minus>(other);
      }

      // other operations will be added; std::plus, etc.
};

int main()
{
    variant<int, double> vt1 = 2.3;
    variant<int, double> vt2 = 5;

    std::cout << "first: " << (vt1 - 2) << std::endl; 

    std::cout << "second: " << (vt2 - vt1) << std::endl; 

    return 0;
}

Answer 1

You have several issues:

1. std::minus is not a type, but a template. It cannot bind to class Op. You might want to use std::minus<> instead.
2. When you call calc<Op, index + 1>() from calc<Op, index>() you get infinite recursion. The if condition at the beginning does not help, because a compiler still has to generate that call: this condition is checked at the run-time, not at the compile-time. You need if constexpr.
3. Inconsistent types for decltype(auto) return type. All non-discarded branches should return the same type.
4. Op()(std::get<ST>(*this), std::get<ST>(other)) will throw if *this and other hold different types (and in your example they do hold different types).

Instead of fixing all these and reinventing std::visit, you can simply define free functions and use std::visit in the implementation:

namespace impl {
    template<class T>
    auto get_value(const T& t) {
        return t;
    }

    template<class... Ts>
    auto get_value(const std::variant<Ts...>& var) {
        using T = std::common_type_t<Ts...>;
        return std::visit([](T value) { return value; }, var);
    }

    template<class Op, class T, class U>
    auto var_op(Op op, const T& t, const U& u) {
        return op(get_value(t), get_value(u));
    }
}

template<class... Ts, class U>
auto operator-(const std::variant<Ts...>& var, const U& u) {
    return impl::var_op(std::minus<>{}, var, u);
}

template<class U, class... Ts>
auto operator-(const U& u, const std::variant<Ts...>& var) {
    return impl::var_op(std::minus<>{}, u, var);
}

template<class... Ts, class... Us>
auto operator-(const std::variant<Ts...>& var1, 
               const std::variant<Us...>& var2) {
    return impl::var_op(std::minus<>{}, var1, var2);
}

If you want to limit these functions to your own class my_variant derived from std::variant, you need to fix get_value() by adding static_cast, because std::visit uses some helper classes (like std::variant_size) that are not specialized for my_variant:

template<class... Ts>
class my_variant : public std::variant<Ts...> {
public:
    using std::variant<Ts...>::variant;
};

...

namespace impl {
    template<class... Ts>
    auto get_value(const my_variant<Ts...>& var) {
        using T = std::common_type_t<Ts...>;
        return std::visit([](T value) { return value; }, 
            static_cast<const std::variant<Ts...>&>(var));
    }
}