Concepts Overview

Introduction

Concepts is a new language feature fully supported in C++20 that aims to simply generic programming and equip users with type safety. The following is a quick overview of concepts, mostly adopted and inspired by the concepts and constraints documentation page.

Concepts

Pre-defined Concepts

Many useful pre-defined concepts have already been defined in <concepts> header, which are only available starting from gcc-10. One can view documentation pages for these concepts in this page. You may copy and paste the possible implementations for these concepts into your code to build on top of them.

equality_comparable (simplified)

Looking at their implementation is one of the best ways to learn how to use concepts! Here is a simplified implementation of equality_comparable, which we also saw in class, of the one in this page:

template<class T, class U = T>
concept equality_comparable = 
    requires(T t, U u) {
        { t == u } -> bool;
        { t != u } -> bool;
        { u == t } -> bool;
        { u != t } -> bool;
    };

What does this mean? equality_comparable is given two types in general, where the second type is by default the same as the first type if unspecified, and checks that the expressions using operator== and operator!= on these types are valid as well as return a value of type bool.

The requires-expression can be used to specify variable names with certain types, and these variables can be used in expressions like { t == u }. Note that none of these variables ever get allocated and are purely there to see if the expressions are syntactically valid! Lastly, the return-type-constraint (stuff followed by ->) must be a concept starting from C++20. In TS version (experimental), they allow this constraint to be types, i.e. the following was allowed:

{ t == u } -> bool;

but was removed from the standard in C++20 (so this doesn't actually compile with C++20, but does with previous standards with -fconcepts).

equality_comparable (not so simplified)

Ok, the previous section was a bit simplified (which is OK for homework!), but how do they do it in the standard library implementation?

Digging through the documentation, the following implementation is a lot closer to the actual one:

template<class T, class U = T>
concept equality_comparable = 
    requires(const std::remove_reference_t<T>& t,
             const std::remove_reference_t<U>& u) {
        { t == u } -> std::boolean;
        { t != u } -> std::boolean;
        { u == t } -> std::boolean;
        { u != t } -> std::boolean;
    };

One preliminary thing has to be introduced and that's <type_traits> header. Take a look at type_traits for a lot of cool metaprogramming tools that you can (but not required to) use for this assignment and to understand existing implementations of concepts. A lot of low-level concepts actually end up wrapping some of these tools. Moreover, most of the concepts are defined using these tools.

Here's an example of a tool in <type_traits> that comes up frequently, as we see above:

template< class T >
using remove_reference_t = typename remove_reference<T>::type;  // since C++14

Note that remove_reference is actually a class template. Think of remove_reference as a mapping from a template parameter T to some other type, which gets stored as a member alias type. It is specially written such that it will give you whatever type you passed in minus the &'s essentially:

std::remove_reference_t<int> x; 
std::remove_reference_t<int&> y; 
std::remove_reference_t<int&&> z;
// x, y, and z are all of type int

remove_reference_t is just being used in equality_comparable to ensure that whatever gets passed in as T will be stripped of any references (&'s). This way, std::remove_reference_t<T>& is truly an lvalue reference type.

Note also that std::boolean is a pre-defined concept in <concepts>. It checks whether a type can be used in Boolean context. It takes in a single template parameter, but note that we never specified the parameter, i.e. didn't do something like

{ t == u } -> std::boolean</* something */>;

When specifying return-type-constraint, the compiler substitutes the first parameter with the return type of the expression.

User-defined Concepts

Let's try implementing a couple of concepts. One example I just concocted is Incrementable. A type T satisfies Incrementable if the following hold: let x be an object of type T and

• x++ compiles and returns something that is convertible to T
• ++x compiles and returns something that is T&

Here is a possible implementation of the new concept Incrementable:

template <class T>
concept Incrementable = 
    requires(T x) {
        { x++ } -> std::convertible_to<T>;
        { ++x } -> std::same_as< std::add_lvalue_reference_t<
                                 std::remove_reference_t<T> > >;
    };

Turns out, <concepts> implements the concept convertible_to and same_as, and <type_traits> contains add_lvalue_reference_t and remove_reference_t. You can read more about them in the documentation page.

We can also define Decrementable in a similar way:

template <class T>
concept Decrementable = 
    requires(T x) {
        { x-- } -> std::convertible_to<T>;
        { --x } -> std::same_as< std::add_lvalue_reference_t<
                                 std::remove_reference_t<T> > >;
    };

Now you can combine these building blocks to create a more complex concept. Let's define a type to satisfy the concept Crementable if it satisfies Incrementable and Decrementable. The following is a possible implementation:

template <class T>
concept Crementable = Incrementable<T> && Decrementable<T>;

How do we use these concepts?

Let's write a couple of stupid, but instructive functions. We will first write a double-incrementing function using both prefix and postfix operator++. As shown in lecture, we'll use the lifting method to motivate the need for the above concepts.

Consider the following function that compiles even with pre-C++11 compiler.

int& double_increment(int& x) 
{int y = x++; return ++x;}

It first postfix-increments x and stores the result into y, which is of type int. And then prefix-increment x, hence double-incrementing, and return as an lvalue reference.

Of course, this function actually applies more generally to other types such as char, double, Complex, etc. We can generalize this by using templates as follows:

template <class T>
T& double_increment(T& x)
{T y = x++; return ++x;}

The problem now is that T is way too general - what if x++ or ++x doesn't even compile for some types? What if x++ returns something so crazy that it cannot even be converted to type T? The last step is to constrain the type T such that both expressions are valid, x++ returns something that can be converted to T, and ++x returns something of type T&. This is precisely our Incrementable concept! Using concepts, we can fully generalize the function as such:

template <Incrementable T>
T& double_increment(T& x)
{T y = x++; return ++x;}

The following is a test code that uses Incrementable concept:

struct incrementable
{
    incrementable& operator++() {return *this;}; 
    incrementable operator++(int) {return *this;} 
    int x = 0;
};

struct not_incrementable
{
    int& operator++() {return ++x;};    // prefix operator++; note: int& not same as not_incrementable&
    not_incrementable operator++(int) 
    {return *this;} 
    int x = 0;
};

template <Incrementable T>
T& double_increment(T& x)
{T y = x++; return ++x;}

int main()
{
    // Sanity-check
    int x = 2;
    assert(double_increment(x) == 4);
    assert(x == 4);

    // Test struct incrementable 
    incrementable inc;
    double_increment(inc);

    // compiler error if the following uncommented
    //not_incrementable ninc;
    //double_increment(ninc);
    
    std::cerr << "PASSED\n";

    return 0;
}

Note that the struct incrementable satisfies the concept Incrementable. The struct not_incrementable satisfies all of the constraints of Incrementable except that the return type of prefix operator++ is int&, which is not the same as not_incrementable&. Hence, you will get a compiler error once you pass it to double_increment!

The test code is located in src directory - feel free to play around with it! Try coming up with example functions like double_increment for the other concepts (Decrementable, Crementable), and write test code to verify your implementation.

How do I go about defining concepts for this assignment?

The previous sections covered how one can write a concept. This assignment specifically requires you to use iterator-related concepts. This section is for those who are either forced to write concepts on their own (no gcc-10), or interested in getting practice with writing concepts.

From the lifting method described above, we have to first understand how the generic types should be constrained so we must look at the documentation page for std::find, std::find_if, std::sort. You will see under Parameters, a tiny section called Type Requirements, which explains the properties assumed for each of the template parameters.

For example, std::find requires that the template parameter InputIt must meet the requirements of LegacyInputIterator. If you check out the page for LegacyInputIterator, you will see a list of requirements that look eerily similar in format as the one for Incrementable described in this section. Note that a lot of these concepts build on top of other lower-level concepts - you just have to recursively go down. Feel free to approximate these concepts, but make sure you are at least constraining the types enough such that all of the things assumed by the functions std::find, std::find_if, std::sort are valid. For example, std::find will do something like *first == val. So, you must at least constrain your input iterator concept (whatever you end up naming it) such that this expression is valid.

Here is a complete list of links that may be helpful including those referenced in this README :

• Iterator Library
  • iterator_traits
• concepts header
• concepts documentation
• type_traits header

---

Hopefully, this was helpful in getting you started with the assignment and understanding what concepts is all about! :)