Demo: http://dpaste.dzfl.pl/72015697

Test case:
import std.stdio;

void main()
{
	C c = new C("foo");	
	writeln(c == "foo");
}

class C
{
	string v;
	
	// This does not work
	alias v this;
	
	this(string val) { v = val; }
}

Result:
testcase.d(8): Error: function object.Object.opEquals (Object lhs, Object rhs) is not callable using argument types (string)
testcase.d(8): Error: expected 2 function arguments, not 1