Having been shown around the library,we were taken to see the lab.

题目

Having been shown around the library,we were taken to see the lab.
为什么是“Having been shown”而不是“To show”,做目的状语不可以吗

答案

不可以啊,翻译就不对啊.
如果是目的状语的话就会是
我们被带去看实验室,目的是展示图书馆.
不通