He forgot to turn off lights when he left the classroom

题目

He forgot to turn off lights when he left the classroom
是 to turn还是turning?标准答案上和老师讲的都是to turn,但是我记得一个概念是：
forget to do 忘记要去做某事.(未做)
forget doing 忘记做过某事.(已做)
按照句意来说,他已经做过了这件事,为什么还要用to turn?

答案