Something like `declval` for concepts

Question

When you are working with templates and with decltype you often need an instance of a certain type even though you do not have any the moment. In this case,

Answer 1

Is there a something similar for concepts? i.e. a function which would create and imaginary type for a concept.

The term for this is an archetype. Coming up with archetypes would be a very valuable feature, and is critical for doing things like definition checking. From T.C.'s answer:

Thus, even if you could magically synthesize some unique type, you still have no guarantee that F operates on all Incrementable types.

The way to do that would be to synthesize an archetype that as minimally as possible meets the criteria of the concept. As he says, there is no archetype generation in C++20, and is seems impossible given the current incarnation of concepts.

---

Coming up with the correct archetype is incredibly difficult. For example, for

template 
concept Incrementable = requires(T t){
   { ++t } -> T;                       
};

It is tempting to write:

struct Incrementable_archetype {
    Incrementable_archetype operator++();
};

But that is not "as minimal as possible" - this type is default constructible and copyable (not requirements that Incrementable imposes), and its operator++ returns exactly T, which is also not the requirement. So a really hardcore archetype would look like:

struct X {
    X() = delete;
    X(X const&) = delete;
    X& operator=(X const&) = delete;

    template  operator,(T&&) = delete;

    struct Y {
        operator X() &&;
    };
    Y operator++();
};

If your function works for X, then it probably works for all Incrementable types. If your function doesn't work for X, then you probably need to either change the implementation so it does or change the constraints to to allow more functionality.

For more, check out the Boost Concept Check Library which is quite old, but is very interesting to at least read the documentation.