Socrates' conversation as reported by Plato were full of a shrewd humor reported.

【答】在as reported by Plato 句中有主语。as 就是主语，它是关系代词，指代Socrates’ conversation，as 在定语从句中作主语，省略了 was，补充完整为：

Socrates' conversation as was reported by Plato were full of a shrewd humor reported.

主句：Socrates' conversation were full of a shrewd humor reported.

定语从句：as was reported by Plato 

英语在朝着表达简洁的方向发展，as 的这种用法其实是一种省略现象。as 之后其实省略了be。又如：

The project will go forward as (is) planned.  工程将按计划进行。

Everything happened as (was) expected.  一切都像预料的那样发生了。

以上两句，as 指代前文整个主句的内容，应看作关系代词，但表达的是比较意义，as 本身在从句中作主语。

用于此句式的这类动词，多是“计划，想象，预料，叙述，描述，提及，说及，显示，指出”之类的词，多用于议论文体。除了as planned 以外，常见的有：

as expected 正如预料的那样

as imagined 正如想象的那样

as arranged 正如计划的那样

as seen from above 正如从上述看的那样

as told before 正如前述

as shown above 正如上面显示的那样

as said 正如说过的（那样）

as mentioned 正如提到的（那样）

as described 正如描述的（那样）

as discussed 正如讨论过的（那样）

as noted 正如叙述到的（那样）

as stated 正如说指出的（那样）

as announced 正如宣布的（那样）

as pointed out 正如已经指出的（那样）

as indicated 如前所示（那样）

as hinted 正如已经暗示的（那样）

as told 正如已经告知的（那样）

as already shown 如已显示（那样）

as emphasized 正如已经强调的（那样）

as observed 正如已观察到的（那样）

as explained 正如已经解释过的（那样）

as suggested 正如已经提出的（那样）

以下例句是没有省略be 的情况：

1. Schizophrenia is not a "split mind" as is popularly believed. 

精神分裂症并非人们普遍认为的那样是“分裂的精神”。

来自柯林斯例句

2. As is stated above, this principle applies to all cases. 

如前文所讲, 这一原则适合所有案例。

来自《简明英汉词典》

3. Electron micrographs give some indication here as is shown in Fig 3.12. 

电子显微照片给出的一些说明示于图3.12中。

The game was exciting , as was instanced by the score. 

依分数所示,这场比赛是很紧张的。

来自《现代英汉综合大词典》

4. Homologous parts, as has been remarked by some authors, tend to cohere. 

某些作者曾经说过,同源部分有互相合生的倾向。

来自辞典例句

5. As has been shown before, historicism is not opposed to'activism '. 

正如前面表明的, 历史决定论并不是与能动主义相对立的。

来自辞典例句

6. As has been shown, some are parodies of technical gestures or derivations from autistis gestures. 

如上所述, 一些动作是对技术动作的拙劣模仿或起源于表现自我。

来自英汉非文学 - 民俗

7. As has been argued, traditionally organized libraries have reached an impasse in terms of usability. 

如前所述, 按传统方式组织的图书馆的可用性已陷入绝境。

来自辞典例句