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Simple Template Currying

Currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions, each with a single argument. I've discussed Currying on this blog previously in Fun With Lambdas C++14 Style and Dependently-Typed Curried printf. Both blogposts discuss currying of functions proper. I.e., they discuss how C++ can treat functions as values at runtime.

However, currying is not limited to just functions. Types can also be curried---if they take type arguments. In C++, we call them templates. Templates are "functions" at type level. For example, passing two type arguments std::string and int to std::map gives std::map<std::string, int>. So std::map is a type-level function that takes two (type) arguments and gives another type as a result. They are also known as type constructors.

So, the question today is: Can C++ templates be curried? As it turns out, they can be. Rather easily. So, here we go...
#include <type_traits>
#include <functional>
#include <map>
#include <iostream>

template <template <class...> class C, class... T, class D = C<T...>>
constexpr std::true_type valid(std::nullptr_t);

template <template <class...> class C, class... T>
constexpr std::false_type valid(...);

template <class TrueFalse, template <class...> class C, class... ArgsSoFar>
struct curry_impl;

template <template <class...> class C, class... ArgsSoFar>
struct curry_impl<std::true_type, C, ArgsSoFar...> {
  using type = C<ArgsSoFar...>;
};

template <template <class...> class C, class... ArgsSoFar>
struct curry_impl<std::false_type, C, ArgsSoFar...> {
  template <class... MoreArgs>
  using apply = curry_impl<decltype(valid<C, ArgsSoFar..., MoreArgs...>(nullptr)), C, ArgsSoFar..., MoreArgs...>;
};

template <template <class...> class C>
struct curry {
  template <class... U>
  using apply = curry_impl<decltype(valid<C, U...>(nullptr)), C, U...>;
};

int main(void) {
  using CurriedIsSame = curry<std::is_same>;
  static_assert(curry<std::is_same>::apply<int>::apply<int>::type::value);

  curry<std::less>::apply<int>::type less;
  std::cout << std::boolalpha << less(5, 4); // prints false

  using CurriedMap = curry<std::map>;
  using MapType = CurriedMap::apply<int>::apply<long, std::less<int>, std::allocator<std::pair<const int, long>>>::type;
  static_assert(std::is_same<MapType, std::map<int, long>>::value);
}
Wandbox

The technique is very simple. There's a function called valid that has two overloads. The first one returns std::true_type only if C<T..> is a valid instantiation of template C with argument list T.... Otherwise, it returns std::false_type. C is type constructor that we would like to curry. This function uses the SFINAE idiom.

curry_impl is the core implementation of template currying. It has two specializations. The std::true_type specialization is selected when valid returns std::true_type. I.e., curried version of the type constructor has received the minimum number of type arguments to form a complete type. In other words, ArgsSoFar are enough. curry_impl<C, ArgsSoFar...>::type is same as instantiation of the type constructor with the valid type arguments (C<ArgsSoFar...>).

Note that C++ allows templates to have default type arguments. Therefore, a template could be instantiated by providing "minimum" number of arguments. For example, std::map could be instantiated in three ways giving the same type:
  • std::map<int, long>
  • std::map<int, long, std::less<int>>
  • std::map<int, long, std::less<int>, std::pair<const int, long>>

When ArgsSoFar are not enough, curry_impl<std::false_type> carries the partial list of type arguments (ArgsSoFar) at class template level. It allows passing one or more type arguments (MoreArgs) to the type constructor through the apply typedef. When ArgsSoFar and MoreArgs are enough to form a valid instantiation, curry_impl<std::true_type> is chosen which yields the fully instantiated type.

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