Constraints not satisfied for template template concept requiring static template method

Question

I'm trying to implement Functor and various other category-theoretic concepts using C++ concepts, but am getting compile errors:

http://coliru.stacked-crooked.com/a/e8b6eb387229bddf

Here's my full code (I know that requiring fmap<int, int> does not verify fmap for any two types, and I plan to change it to fmap<int, std::string> or something to achieve a slightly stronger test -- or instead, possibly alter the Functor concept so that it takes in addition to F, two types T and U and verifies the existence of fmap<T, U>, but that's all after I figure out how to fix the error that I'm getting):

#include <functional>
#include <iostream>
#include <vector>

// empty Functor_Impl struct - specialize for each functor
template<template<class> class F> struct Functor_Impl {};

// std::vector Functor implementation
template<>
struct Functor_Impl<std::vector> {
    template<class T, class U>
    static std::vector<U> fmap(std::vector<T> x, std::function<U(T)> f) {
        std::vector<U> out;
        out.reserve(x.size());
        for (int i = 0; i < x.size(); i++) {
            out.push_back(f(x[i]));
        }
        return out;
    }
};

// Functor concept requires Functor_Impl<F> to have fmap
template<template<class> class F>
concept bool Functor = requires(F<int> x) {
    {Functor_Impl<F>::template fmap<int, int>(x)} -> F<int>;
};

// Test function using constraint.
template<template<class> class F, class T>
requires Functor<F>
F<T> mult_by_2(F<T> a) {
    return Functor_Impl<F>::template fmap<T, T>(a, [](T x) {
        return x * 2;
    });
}

int main() {
    std::vector<int> x = {1, 2, 3};
    std::vector<int> x2 = mult_by_2(x);
    for (int i = 0; i < x2.size(); i++) {
        std::cout << x2[i] << std::endl;
    }
}

And the compile error:

lol@foldingmachinebox:~/p/website-editor$ g++ foo.cpp -std=c++17 -fconcepts -o foo
foo.cpp: In function ‘int main()’:
foo.cpp:39:38: error: cannot call function ‘F<T> mult_by_2(F<T>) [with F = std::vector; T = int]’
     std::vector<int> x2 = mult_by_2(x);
                                      ^
foo.cpp:31:6: note:   constraints not satisfied
 F<T> mult_by_2(F<T> a) {
      ^~~~~~~~~
foo.cpp:24:14: note: within ‘template<template<class> class F> concept const bool Functor<F> [with F = std::vector]’
 concept bool Functor = requires(F<int> x) {
              ^~~~~~~
foo.cpp:24:14: note:     with ‘std::vector<int> x’
foo.cpp:24:14: note: the required expression ‘Functor_Impl<F>::fmap<int, int>(x)’ would be ill-formed

I'm guessing that my syntax for the concept itself is wrong - that it's treating a variable as a function, or vice versa, since I'm not very familiar with the concept syntax, and in addition some of the example code on cppreference.com does not compile under GCC's implementation (e.g. concept EqualityComparable does not compile, it must be changed to concept bool EqualityComparable).

If I remove requires Functor<F> from the mult_by_2 function declaration, then the code compiles and runs.

Answer 1

The problem is exactly what the error message says: Functor_Impl<F>::template fmap<int, int>(x) is not a valid expression. Functor_Impl<std::vector>::fmap has two parameters, not one.