Can you explain for me what the typedef is doing here?
typedef bool (C::*implementation_defined_bool_type)(bool) const;
typedefs a pointer to a const member function of a type C, which takes a bool as input parameter and also returns a bool.
While,
operator implementation_defined_bool_type() const
Takes in an object of type C and returns a type implementation_defined_bool_type.
It is known as an Conversion Operator.
what is the purpose of it?
It implements the "Safe Bool Idiom", which aims to validate an object in a boolean context.
Note that the Safe Bool Idiom is obsolete with the C++11 Standard.
Good Read:
The Safe Bool Idiom