Question

I see function objects used often together with STL algorithms. Did function objects came about because of these algorithms? When do you use a function object in C++? What is its benefits?

Answer 1

As said jdv, functors are used instead of function pointers, that are harder to optimize and inline for the compiler; moreover, a fundamental advantage of functors is that they can easily preserve a state between calls to them¹, so they can work differently depending on the other times they have been called, keep track somehow of the parameters they have used, …

For example, if you want to sum all the elements in two containers of ints you may do something like this:

struct
{
    int sum;
    void operator()(int element) { sum+=element; }
} functor;
functor.sum=0;
functor = std::for_each(your_first_container.begin(), your_first_container.end(), functor);
functor = std::for_each(your_second_container.begin(), your_second_container.end(), functor);
std::cout<<"The sum of all the elements is: "<<functor.sum<<std::endl;

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1. Actually, as R Samuel Klatchko pointed out below, they can support multiple independent states, one for each functor instance:
   

   A slightly more precise statement is that functors can support multiple independent states (functions can support a single state via statics/globals which is neither thread-safe nor reentrant).

   Functors enables you to use even more complicated states, for example a shared state (static fields) and a private state (instance fields). However this further flexibility is rarely used.