I read in a book that for comparison, as ... as is used for affirmative statements, and so ... as is used to for negative statements. For example:
He is as tall as his brother.
He is not so tall as his father.
I did not find any other sources where such a "rule" is either confirmed or denied. Personally, the construct not so ... as sounds rather odd, and there doesn't seem to be anything wrong with not as ... as.
What is the correct "rule" in such cases, if there is one?
Two generations ago, when I was a high school student, the formal rule was as you have stated it: as ... as with affirmative comparatives, not so ... as with negative comparatives. But the distinction was never much observed in speech, and the tendency today is to use as ... as in both affirmative and negative contexts.
In any case, as Damkerng T. observes, so ... as is not accepted in affirmative comparatives. This has nothing to do with the construction so as to VERB, which is an adverbial of purpose.
Affirmative comparatives can only be made with as...as (as already noted); negative comparatives can be made with as...as or so...as.
Inequality
It's not as big as yours.
It's not so big as yours.
We didn't do as well as last time.
We didn't do so well as last time.
There aren't as many as there used to be.
There aren't so many as there used to be.
I can't believe any of the above would ever have been unacceptable.
Equality
It's as good as the old one.
It's so good as the old one. (No one would say this.)
He's as tall as his dad now.
He's so tall as his dad now. (Nor this.)
Idiomatic expressions
You can take it as long as you bring it back.
You can take it so long as you bring it back. (Sounds fine.)
As far as I know, it's about 10 miles.
So far as I know, it's about 10 miles. (??)
