C++20: Define the Concepts Equal and Ordering

In my last post, I defined the concept Equal. Now, I go one step further and use the concept Equal to define the concept Ordering.

Here is a short reminder of where I ended with my last post. I defined the concept of Equal and a function areEqual to use it.

template<typename T>
concept Equal =
    requires(T a, T b) {
        { a == b } -> bool;
        { a != b } -> bool;
};


bool areEqual(Equal auto fir, Equal auto sec) {                       
  return fir == sec;
}

My Wrong Usage of the Concept Equal

I used the concept of Equal in my last post in the wrong way. The concept Equal requires that a and b have the same type but the function areEqual allows fir and sec to be different types that both support the concept Equal. Using a constrained template parameter instead of placeholder syntax solves the issue:

template <Equal T>
bool areEqual(T fir, T sec) {
    fir == sec;
}

Now, fir and sec must have the same type. 

Thanks a lot to Corentin Jabot for pointing out this inconsistency. 

Additionally, the concept Equal should not check if the equal and unequal operator returns a bool but something implicitly or explicitly convertible to a bool. Here we are. 

template<typename T>
concept Equal =
    requires(T a, T b) {
        { a == b } -> std::convertible_to<bool>;
        { a != b } -> std::convertible_to<bool>;
};

I have to add. std::convertible_to is a concept and requires the header <concepts>.  

template <class From, class To>
concept convertible_to =
  std::is_convertible_v<From, To> &&
  requires(From (&f)()) {
    static_cast<To>(f());
  };

The C++ 20 standard has already defined two concepts for equality comparing:

• std::equality_comparable: corresponds to my concept Equal
• std::equality_comparable_with: allows the comparison of values of different type; e.g.: 1.0 == 1.0f

The Challenge

I ended my last post by presenting a part of the type class hierarchy of Haskell.

The class hierarchy shows that the type class Ord is a refinement of the type class Eq. This can elegantly be expressed in Haskell.

class Eq a where
    (==) :: a -> a -> Bool
    (/=) :: a -> a -> Bool

class Eq a => Ord a where
    compare :: a -> a -> Ordering
    (<) :: a -> a -> Bool
    (<=) :: a -> a -> Bool
    (>) :: a -> a -> Bool
    (>=) :: a -> a -> Bool
    max :: a -> a -> a

Here is my challenge. Can I express such as relationship quite elegantly with concepts in C++20? For simplicity reasons, I ignore the functions compare and max of Haskell's type class. Of course, I can.

The Concept Ordering

Thanks to requires-expression, the definition of the concept Ordering looks quite similar to the definition of the type class Equal.  

template <typename T>
concept Ordering =
    Equal<T> &&
    requires(T a, T b) {
        { a <= b } -> std::convertible_to<bool>;
        { a < b } -> std::convertible_to<bool>;
        { a > b } -> std::convertible_to<bool>;
        { a >= b } -> std::convertible_to<bool>;
    };

Okay, let me try it out.

// conceptsDefinitionOrdering.cpp

#include <concepts>
#include <iostream>
#include <unordered_set>

template<typename T>
concept Equal =
    requires(T a, T b) {
        { a == b } -> std::convertible_to<bool>;
        { a != b } -> std::convertible_to<bool>;
    };


template <typename T>
concept Ordering =
    Equal<T> &&
    requires(T a, T b) {
        { a <= b } -> std::convertible_to<bool>;
        { a < b } -> std::convertible_to<bool>;
        { a > b } -> std::convertible_to<bool>;
        { a >= b } -> std::convertible_to<bool>;
    };

template <Equal T>
bool areEqual(T a, T b) {
    return a == b;
}

template <Ordering T>
T getSmaller(T a, T b) {
    return (a < b) ? a : b;
}
    
int main() {
  
    std::cout << std::boolalpha << std::endl;
  
    std::cout << "areEqual(1, 5): " << areEqual(1, 5) << std::endl;
  
    std::cout << "getSmaller(1, 5): " << getSmaller(1, 5) << std::endl;
  
    std::unordered_set<int> firSet{1, 2, 3, 4, 5};
    std::unordered_set<int> secSet{5, 4, 3, 2, 1};
  
    std::cout << "areEqual(firSet, secSet): " << areEqual(firSet, secSet) << std::endl;
  
    // auto smallerSet = getSmaller(firSet, secSet);
  
    std::cout << std::endl;
  
}

The function getSmaller requires that both arguments a and b support the concept Ordering, and both have the same type. This requirement holds for numbers 1 and 5. 

Of course, a std::unordered_set does not support order. The actual MSVC compiler is very specific when I try to compile the line auto smaller = getSmaller(firSet, secSet) with the flag /std:c++latest.

By the way. The error message is obvious: the associated constraints are not satisfied.

Of course, the concept Ordering is already part of the C++20 standard.

• std::three_way_comparable: corresponds to my concept Ordering
  
• std::three_way_comparable_with: allows the comparison of values of different type; e.g.: 1.0 < 1.0f

Maybe, you are irritated by the term three-way. With C++20, we get the three-way comparison operator, the spaceship operator. <=>. Here is the first overview: C++20: The Core Language. I will write about the three-way comparison operator in a future post. 

Compiler Support

I learn new stuff by trying it out. Maybe, you don't have an actual MSVC available. In this case, use the current GCC (trunk) on the Compiler Explorer. GCC supports the C++20 syntax for concepts. Here is the conceptsDefinitionOrdering.cpp for further experiments: https://godbolt.org/z/uyVFX8.  

What's next?

When you want to define a concrete type that works well in the C++ ecosystem, you should define a type that "behaves link an int".  Such a concrete type could be copied and the result of the copy operation is independent of the original one and has the same value.  Formally, your concrete type should be regular. In the next post, I will define the concepts Regular and SemiRegular.