Why does std::function accept a this reference in the signature?

Question

Member functions have an implicit this pointer parameter. Why does std::function accept this signature, then, where S is a simple class? (complete sample)

std::function<void(S &)> func = &S::foo;

Calling it works, too, and distinguishes objects:

S s1 = {5};
S s2 = {6};

func(s1); //prints 5
func(s2); //prints 6

What I'd normally expect is that it needs a pointer, which works as well: (complete sample)

std::function<void(S * const)> func = &S::foo;

S s1 = {5};
S s2 = {6};

func(&s1); //prints 5
func(&s2); //prints 6

Why does the first one work when I pass a reference into the member function when the implicit this parameter is a pointer?

Answer 1

Because std::function is correctly designed. The fact that this is a pointer is an accident of history and a detail internal to the member function. The fact should have no impact on the design decisions of users of the function.

The designers of std::function decided, rightly, to accept member functions when the first parameter type in the signature is a reference.