Function pointers are the most basic way of passing functions around, which can also be used in C. (See the C documentation for more details).

For the purpose of callable objects, a function pointer can be defined as:

typedef returnType(*name)(arguments);                       // All
using name = returnType(*)(arguments);                      // <= C++11
using name = std::add_pointer<returnType(arguments)>::type; // <= C++11
using name = std::add_pointer_t<returnType(arguments)>;     // <= C++14

If we would be using a function pointer for writing our own vector sort, it would look like:

using LessThanFunctionPtr = std::add_pointer_t<bool(int, int)>;
void sortVectorInt(std::vector<int>&v, LessThanFunctionPtr lessThan) {
    if (v.size() < 2)
        return;
    if (v.size() == 2) {
        if (!lessThan(v.front(), v.back())) // Invoke the function pointer
            std::swap(v.front(), v.back());
        return;
    }
    std::sort(v, lessThan);
}

bool lessThanInt(int lhs, int rhs) { return lhs < rhs; }
sortVectorInt(vectorOfInt, lessThanInt); // Passes the pointer to a free function

struct GreaterThanInt {
   static bool cmp(int lhs, int rhs) { return lhs > rhs; }
};
sortVectorInt(vectorOfInt, &GreaterThanInt::cmp); // Passes the pointer to a static member function

Alternatively, we could have invoked the function pointer one of following ways:

• (*lessThan)(v.front(), v.back()) // All
• std::invoke(lessThan, v.front(), v.back()) // <= C++17

Every class which overloads the operator() can be used as a function object. These classes can be written by hand (often referred to as functors) or automatically generated by the compiler by writing Lambdas from C++11 on.

struct Person {
    std::string name;
    unsigned int age;
};

// Functor which find a person by name
struct FindPersonByName {
    FindPersonByName(const std::string &name) : _name(name) {}

    // Overloaded method which will get called
    bool operator()(const Person &person) const {
         return person.name == _name;
    }
private:
    std::string _name;
};

std::vector<Person> v; // Assume this contains data
std::vector<Person>::iterator iFind =
    std::find_if(v.begin(), v.end(), FindPersonByName("Foobar"));
// ...

As functors have their own identity, they cannot be put in a typedef and these have to be accepted via template argument. The definition of std::find_if can look like:

template<typename Iterator, typename Predicate>
Iterator find_if(Iterator begin, Iterator end, Predicate &predicate) {
     for (Iterator i = begin, i != end, ++i)
         if (predicate(*i))
             return i;
     return end;
}

From C++17 on, the calling of the predicate can be done with invoke: std::invoke(predicate, *i).