Skip to main content

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>;

  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);

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.


Popular Content

Unit Testing C++ Templates and Mock Injection Using Traits

Unit testing your template code comes up from time to time. (You test your templates, right?) Some templates are easy to test. No others. Sometimes it's not clear how to about injecting mock code into the template code that's under test. I've seen several reasons why code injection becomes challenging. Here I've outlined some examples below with roughly increasing code injection difficulty. Template accepts a type argument and an object of the same type by reference in constructor Template accepts a type argument. Makes a copy of the constructor argument or simply does not take one Template accepts a type argument and instantiates multiple interrelated templates without virtual functions Lets start with the easy ones. Template accepts a type argument and an object of the same type by reference in constructor This one appears straight-forward because the unit test simply instantiates the template under test with a mock type. Some assertion might be tested in

Covariance and Contravariance in C++ Standard Library

Covariance and Contravariance are concepts that come up often as you go deeper into generic programming. While designing a language that supports parametric polymorphism (e.g., templates in C++, generics in Java, C#), the language designer has a choice between Invariance, Covariance, and Contravariance when dealing with generic types. C++'s choice is "invariance". Let's look at an example. struct Vehicle {}; struct Car : Vehicle {}; std::vector<Vehicle *> vehicles; std::vector<Car *> cars; vehicles = cars; // Does not compile The above program does not compile because C++ templates are invariant. Of course, each time a C++ template is instantiated, the compiler creates a brand new type that uniquely represents that instantiation. Any other type to the same template creates another unique type that has nothing to do with the earlier one. Any two unrelated user-defined types in C++ can't be assigned to each-other by default. You have to provide a

Multi-dimensional arrays in C++11

What new can be said about multi-dimensional arrays in C++? As it turns out, quite a bit! With the advent of C++11, we get new standard library class std::array. We also get new language features, such as template aliases and variadic templates. So I'll talk about interesting ways in which they come together. It all started with a simple question of how to define a multi-dimensional std::array. It is a great example of deceptively simple things. Are the following the two arrays identical except that one is native and the other one is std::array? int native[3][4]; std::array<std::array<int, 3>, 4> arr; No! They are not. In fact, arr is more like an int[4][3]. Note the difference in the array subscripts. The native array is an array of 3 elements where every element is itself an array of 4 integers. 3 rows and 4 columns. If you want a std::array with the same layout, what you really need is: std::array<std::array<int, 4>, 3> arr; That's quite annoying for