Rationale:

This is simply a contradiction: the argument_type typedef, and the argument type itself, are not the same.

Proposed resolution:

Replace the top portion of the definition of the class template const_mem_fun_t in 20.5.8, p8

template <class S, class T> class const_mem_fun_t
          : public unary_function<T*, S> {

with

template <class S, class T> class const_mem_fun_t
          : public unary_function<const T*, S> {

Also replace the top portion of the definition of the class template const_mem_fun1_t in 20.5.8, p9

template <class S, class T, class A> class const_mem_fun1_t
          : public binary_function<T*, A, S> {

with

template <class S, class T, class A> class const_mem_fun1_t
          : public binary_function<const T*, A, S> {

The class templates const_mem_fun_t in 20.5.8, p8 and const_mem_fun1_t in 20.5.8, p9 derive from unary_function<T*, S>, and binary_function<T*, A, S>, respectively. Consequently, their argument_type, and first_argument_type members, respectively, are both defined to be T* (non-const). However, their function call member operator takes a const T* argument. It is my opinion that argument_type should be const T* instead, so that one can easily refer to it in generic code. The example below derived from existing code fails to compile due to the discrepancy:

template <class T>
void foo (typename T::argument_type arg)   // #1
{
    typename T::result_type (T::*pf) (typename T::argument_type) const =   // #2
        &T::operator();
}

struct X { /* ... */ };

int main ()
{
    const X x;
    foo<std::const_mem_fun_t<void, X> >(&x);   // #3
}

#1 foo() takes a plain unqualified X* as an argument
#2 the type of the pointer is incompatible with the type of the member function
#3 the address of a constant being passed to a function taking a non-const X*