In Mr Kenny Kerr's this column, he defined a struct and a typedef like this:
struct boolean_struct { int member; };
typedef int boolean_struct::* boolean_type;
Then what is the meaning of this typedef?
Another question is concerning the following code:
operator boolean_type() const throw()
{
    return Traits::invalid() != m_value ? &boolean_struct::member : nullptr;
}
What is the meaning of "&boolean_struct::member" ?
In Mr Kenny Kerr's this column, he defined a struct and a typedef like this:
struct boolean_struct { int member; }; typedef int boolean_struct::* boolean_type;Then what is the meaning of this typedef?
The typedef creates a type called boolean_type which is equivalent to a pointer to an int member inside a boolean_struct object.
It's not the same thing to a pointer to an int. The difference is that an object of boolean_type requires a boolean_struct object in order to dereference it. A normal pointer to an int does not. The best way to see how this is different is via some code examples.
Consider only normal pointers to ints:
struct boolean_struct { int member; }; 
int main()
{
    // Two boolean_struct objects called bs1 and bs2 respectively:
    boolean_struct bs1;
    boolean_struct bs2;
    // Initialize each to have a unique value for member:
    bs1.member = 7;
    bs2.member = 14;
    // Obtaining a pointer to an int, which happens to be inside a boolean_struct:
    int* pi1 = &(bs1.member);
    // I can dereference it simply like this:
    int value1 = *pi1;
    // value1 now has value 7.
    // Obtaining another pointer to an int, which happens to be inside
    // another boolean_struct:
    int* pi2 = &(bs2.member);
    // Again, I can dereference it simply like this:
    int value2 = *pi2; 
    // value2 now has value 14.
    return 0;
}
Now consider if we used pointers to int members inside a boolean_struct:
struct boolean_struct { int member; }; 
typedef int boolean_struct::* boolean_type;   
int main()
{
    // Two boolean_struct objects called bs1 and bs2 respectively: 
    boolean_struct bs1; 
    boolean_struct bs2; 
    // Initialize each to have a unique value for member: 
    bs1.member = 7; 
    bs2.member = 14; 
    // Obtaining a pointer to an int member inside a boolean_struct
    boolean_type pibs = &boolean_struct::member;
    // Note that in order to dereference it I need a boolean_struct object (bs1):
    int value3 = bs1.*pibs;
    // value3 now has value 7.
    // I can use the same pibs variable to get the value of member from a
    // different boolean_struct (bs2):
    int value4 = bs2.*pibs;
    // value4 now has value 14.
    return 0;
} 
As you can see, the syntax and their behavior are different.
Another question is concerning the following code:
operator boolean_type() const throw() { return Traits::invalid() != m_value ? &boolean_struct::member : nullptr; }What is the meaning of "&boolean_struct::member" ?
This returns the address of the member variable inside a boolean_struct. See above code example.
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