Table traversing with multiple operations in ALTER TABLE - mysql

Question

Some databases, like MySQL [1] and PostgreSQL [2], support bundling of certain compatible ALTER TABLE statements (as non-standard SQL).
For example we can have:
ALTER TABLE `my_table`
DROP COLUMN `column_1`,
DROP COLUMN `column_2`,
...
or
ALTER TABLE
MODIFY `column_1` ... ,
MODIFY `column_2` ... ,
instead of having individual statements:
ALTER TABLE `my_table` DROP COLUMN `column_1`;
ALTER TABLE `my_table` DROP COLUMN `column_2`;
or
ALTER TABLE `my_table` MODIFY `column_1` ... ;
ALTER TABLE `my_table` MODIFY `column_2` ... ;
etc
For comparison of the same feature, PostgreSQL [2], which also implements this, will perform all operations in a single scan:
The main reason for providing the option to specify multiple changes in a single ALTER TABLE is that multiple table scans or rewrites can thereby be combined into a single pass over the table.
Although for DROP COLUMN specifically it will often not even need do that:
The DROP COLUMN form does not physically remove the column, but simply makes it invisible to SQL operations...
Questions:
Would the multi-column statement result in traversing all the rows just once and performing all changes needed?
How does MySQL actually perform DROP COLUMN? Does it also "hide" the columns first, or does it delete the data straight away?
Assumptions:
Using InnoDB
No indexes/complex defaults are involved in any of the columns we want to change/drop (so basically changes that would not require a temporary table when run as individual alter statements)
References:
[1] MySQL ALTER TABLE docs
[2] PostgreSQL ALTER TABLE docs

Answer 1

MySQL's InnoDB:
(This does not really answer the Questions, but provides a little more insight in the the bigger question of ALTER.)
If any of the alters needs to copy the table over, you are probably better off putting all alters into the same statement. Changing the PRIMARY KEY, for example, requires rebuilding the data that is clustered with the PK.
Some alters can be achieved by simply altering the schema; these are virtually instantaneous, and could be done via separate alter statements. Adding an option to ENUM was implemented long ago.
Some alters need some form of scan, but can do it "in the background". DROP INDEX can be done by quickly "hiding" it, then freeing up the BTree in the background.
I have left out a grey area in which you batch 'simple' alters. One would hope that ALTER is smart enough to simply go through them quickly, rather than deciding to copy the table over.

Answer 2

I got some useful feedback but decided to respond to my own question to provide a more concrete set of answers.
Would the multi-column statement result in traversing all the rows just once and performing all changes needed?
Yes, if the alter statement results in rebuilding the table then it only needs to do it once.*
* This answer comes from my own testing and other mostly anecdotal evidence (including #Uueerdo 's in this post). It would be useful to have some official docs for this...
How does MySQL actually perform DROP COLUMN? Does it also "hide" the columns first, or does it delete the data straight away?
MySQL will rebuild the table in place (rather than create a copy or just change metadata) for most column operations. Each specific case can be found in the Online DDL docs for InnoDB.
A few operations like renaming a column or setting a default value will just alter metadata, so they don't require a table rebuild.
However, dropping a column DOES require a full table rebuild.