Native speakers do engage in a kind of grammatical computation.

Hi, I'm a university student. I came across this HP. I found your HP’ s discussion interesting and stimulating, so I’d like to join the discussion.

Whereas some linguists proclaim that humans have innate abilities to acquire language which other animals don’t have, and that language acquisition is the process of switching one’s brain into the target language, others say that language learning is done only through imitations. Which claim do you agree with?

Note the former insist that the differences, as shown in the following, are difficult to distinguish and acquire only through imitations and memorizations and by general reasoning abilities.
(1) Who do you want to visit? (2) Who do you want to visit you?
Likewise, it is quite difficult for non-native speakers to distinguish one incorrect sentence from among the four following sentences, whereas English native speakers can intuitively decide which sentence is ungrammatical.
(1) Who do you think is the best math teacher is?
(2) Who do you think the best math teacher is?
(3) How deep do you think is the lake?
(4) How deep do you think the lake is?
The incorrect sentence is (4). Note that
(5) You think that the best math teacher is John.
(6) You think that John is the beat math teacher.
(7) You think that the lake is three meters deep.
are correct, whereas
(8)* You think that the three meters deep is the lake.
is incorrect.
For example, in the process of the transformation from (5) to (1), John is replaced with who, and it is moved to the head of the sentence. That native speakers can intuitively know the (4) is incorrect partly could show that they engage in a kind of grammatical computations unconsciously and instantaneously.

I am looking forward to hearing from you.