I like Nick Coghlan's suggestion in msg140493, but I think he was giving up too soon in the "or" cases, and I think the confusion could be slightly reduced by some re-spellings around return values and comments about short-circuiting. def not_op(op, other): # "not a < b" handles "a >= b" # "not a <= b" handles "a > b" # "not a >= b" handles "a < b" # "not a > b" handles "a <= b" op_result = op(other) if op_result is NotImplemented: return NotImplemented return not op_result def op_or_eq(op, self, other): # "a < b or a == b" handles "a <= b" # "a > b or a == b" handles "a >= b" op_result = op(other) if op_result is NotImplemented return self.__eq__(other) or NotImplemented if op_result: return True return self.__eq__(other) def not_op_and_not_eq(op, self, other): # "not (a < b or a == b)" handles "a > b" # "not a < b and a != b" is equivalent # "not (a > b or a == b)" handles "a < b" # "not a > b and a != b" is equivalent op_result = op(other) if op_result is NotImplemented: return NotImplemented if op_result: return False return self.__ne__(other) def not_op_or_eq(op, self, other): # "not a <= b or a == b" handles "a >= b" # "not a >= b or a == b" handles "a <= b" op_result = op(other) if op_result is NotImplemented: return self.__eq__(other) or NotImplemented if op_result: return self.__eq__(other) return True def op_and_not_eq(op, self, other): # "a <= b and not a == b" handles "a < b" # "a >= b and not a == b" handles "a > b" op_result = op(other) if op_result is NotImplemented: return NotImplemented if op_result: return self.__ne__(other) return False