c# - Overriding Equals and type casting -

in following example third evaluation returns false, good, fourth example returns true..
don't quite understand how works however, default object.equals compares 2 references object equality, , seeing a , b both point unique instance of string, should return false, in third example not in fourth.
understand why returns true in 2nd example seeing .equals() method overridden in string class, in fourth example we're casting string object.
wouldn't call object.equals in case?

static void main() {     // create 2 equal distinct strings     string = new string(new char[] {'h', 'e', 'l', 'l', 'o'});     string b = new string(new char[] {'h', 'e', 'l', 'l', 'o'});      console.writeline (a == b); // returns true     console.writeline (a.equals(b)); // returns true      // let's see happens same tests     // variables of type object     object c = a;     object d = b;      console.writeline (c == d); // returns false     console.writeline (c.equals(d)); // returns true } 

the clue words "by default". string overrides object.equals custom implementation. since object.equals polymorphic method (virtual / override / etc), most-derived implementation gets used if variable (/expression) type object.

==, however, not polymorphic; implementation used depends entirely on variable (/expression) type. in case, since known type object, comparison available reference equality.

perhaps more succinctly:

class foo {     public override string tostring() { return "hi"; } } //... object obj = new foo(); string s = obj.tostring(); // "hi" 

this same principle: derived overload of virtual method used, regardless of type compiler knows (object in case).