template-based test function for unary operators?

Somewhat a C++ beginner, I'm trying to make a general test function
that could test unary operators (or methods) of an object of any class.

Arguments are a member-pointer to the function, a single input
argument of some type for that function, and the expected result of
some type. Then it tests if the result is as expected, and does some
logging of the results (pass, fail) etc.

Well, the template "mess" does not quite work out.

Below is the code. After that, the error messages.

--------------------------------------------------------

class A {
   int f (int c) { return c; }
   int f (const char c) { return c; }
   A& operator+= (A const& a) { return *this; }
};

template <class rettype, class argtype, class btype>
bool unary_op_test(rettype (*func)(argtype),
btype self, argtype arg, rettype expect)
{
    rettype rv = self.func(arg);
    bool result = (rv == expect);
    return result;
}

int main ()
{
   A aa;
   int (A::*p1)(int) = &A::f;
   A& (A::*p2)(A const&) = &A::operator+=;
   unary_op_test<int,int,A&>(p1, aa, 12, 12);
   unary_op_test<A&,A&,A&>(p2, aa, aa, aa);
   unary_op_test<A&,const A&,A&>(p2, aa, aa, aa);
}

--------------------------------------------------------

$ g++ -Wall -pedantic test.cc
test.cc: In function 'int main()':
test.cc:21: error: no matching function for call to
'unary_op_test(int (A::*&)(int), A&, int, int)'
test.cc:22: error: no matching function for call to
'unary_op_test(A& (A::*&)(const A&), A&, A&, A&)'
test.cc:23: error: no matching function for call to
'unary_op_test(A& (A::*&)(const A&), A&, A&, A&)'

--------------------------------------------------------

How come "A& (A::*&)(const A&)" does not map to "rettype
(*func)(argtype)"<templated> i.e. to "A&(*func)(const A&)"?

Sure some beginner mistake somewhere... :)

Any ideas?

  - Jan