I wrote a few posts about using concepts. Concepts are a named set of requirements. Let's define a few concepts in this post.
A concept can be defined by a function template or by a variable template. A variable template is new with C++14 and declares a family of variables. If you use a function template for your concept, it's called a function concept; in the second case a variable concept.
template<typename T>
concept bool Integral = std::is_integral<T>::value;
}
template<typename T>
concept bool Equal(){
return requires(T a, T b) {
{ a == b } > bool;
{ a != b } > bool;
};
}
Integral is a variable concept and Equal is a functional concept. Both return a boolean.
 The type parameter T fulfils the variable concept Integral if std::is_integral<T>::value returns true.
 The type parameter T fulfils the function concept Equal if there are overloaded operators == and != for T that returns a boolean.
To be honest, the function concept Equal look very familiar to me. Why? You will see it in a few sentences. But, let me first apply the concept.
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// conceptsDefintionEqual.cpp
#include <iostream>
template<typename T>
concept bool Equal(){
return requires(T a, T b) {
{ a == b } > bool;
{ a != b } > bool;
};
}
bool areEqual(Equal a, Equal b){
return a == b;
}
/*
struct WithoutEqual{
bool operator==(const WithoutEqual& other) = delete;
};
struct WithoutUnequal{
bool operator!=(const WithoutUnequal& other) = delete;
};
*/
int main(){
std::cout << std::boolalpha << std::endl;
std::cout << "areEqual(1, 5): " << areEqual(1, 5) << std::endl;
/*
bool res = areEqual(WithoutEqual(), WithoutEqual());
bool res2 = areEqual(WithoutUnequal(), WithoutUnequal());
*/
std::cout << std::endl;
}

I used the concept Equal in the (generic) function areEqual (line 13 to 15). That's not so exciting. Here is the output of the function areEqual:
What is more interesting, is if I use the class WithoutEqual and WithoutUnequal.I set for both the == or respectively the != operator to delete. The compiler complains immediately that both types do not fulfil the concept.
Equal look familiar to me. Now, you see, why.
The concept Equal and Ord
This is part of the type hierarchy of Haskell's type classes. You have a kind of inheritance between the type classes, denoted by arrows. If you look in the left corner at the top, you will see the typeclass Eq.Now I'm curious how the definition of Eq will look like.
class Eq a where
(==) :: a > a > Bool
(/=) :: a > a > Bool
template<typename T>
concept bool Equal(){
return requires(T a, T b) {
{ a == b } > bool;
{ a != b } > bool;
};
}
Let's have a closer look at Haskell's typeclass Eq. Eq requires from its instances, that
 they have equal == and inequal /= operation that returns a Bool.
 both take two arguments (a > a) of the same type.
Of course, the instances are the concrete types such as Int.
Now, I have two questions in mind, if I look at Haskell's type hierarchy. How is the definition of the typeclass Ord in Haskell and can we model the inheritance relation in C++?
How is the definition of the typeclass Ord in Haskell?
Ord
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
The most interesting point about the typeclass Ord is the first line of it definition. An instance of the typeclass Ord has to be already an instance of the typeclass Eq. Ordering is an enumeration having the values EQ, LT, and GT.
How can we model the concept Ord in C++?
Eq > Ord
Of course, we can just define the concept Ord by using all requirement of Eq and of Ord. But we can do better in C++:
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// conceptsDefintionOrd.cpp
#include <iostream>
#include <unordered_set>
template<typename T>
concept bool Equal(){
return requires(T a, T b){
{ a == b } > bool;
{ a != b } > bool;
};
}
template <typename T>
concept bool Ord(){
return requires(T a, T b){
requires Equal<T>();
{ a <= b } > bool;
{ a < b } > bool;
{ a > b } > bool;
{ a >= b } > bool;
};
}
bool areEqual(Equal a, Equal b){
return a == b;
}
Ord getSmaller(Ord a, Ord 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;
}

To make my job a little bit easier, I ignored the requirements compare and max in the concept Ord. The key point about the concept is the line requires Equal<T>(). Here I require that the type parameter T has to fulfil the requirement Equal. If I use more requirements such as in the definition of the concept Equal, each requirement from top to bottom will be checked. That will be done in a shortcircuiting evaluation. So the first requirement returning false will end the process.
Equality and inequality are defined for the data types int and std::unordered_set. Therefore, the output should not surprise you.
That will change dramatically if I use line 44 because the smaller/bigger operators are not defined for std::unordered_set.
What's next?
I wrote a few articles for the German LinuxMagazin and iX about C++17. One of my blog readers asked me if they are available in English? I simply answered no. But I promised him to write about C++17 in my next post.
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Thanks in particular to Jon Hess, Lakshman, Christian Wittenhorst, Sherhy Pyton, Dendi Suhubdy, Sudhakar Belagurusamy, and Richard Sargeant.
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