only trigger b2_ab will fire, even though it will update column beta.
Column beta eventually changed but you never issued an UPDATE command with beta in the SET clause. The trigger only care about the later.
And in fact triggers on a table should never re-issue an actual command against the same table or you end up with infinite triggers.
I now understand that column specific triggers only consider the set clause, but that is not documented on "Overview of Trigger Behavior" and is only documented in the notes of the "CREATE TRIGGER" page. It seems like useful information that the WHEN clause of a TRIGGER evaluates the return value of the previously executed trigger function but the column specifier only considers the SET clause.
If i change the declaration of b3_bc by removing the column list or including column alpha,
things work as I expected and b2_ab cascades to b3_bc.
But that isn't how this works. There is no cascading. As soon as the UPDATE query is planned the set of triggers it is going to trigger is basically known and nothing those triggers do individually will change that (aside from raising an error). All you did by changing b3_bc is get it included in the ordered list of triggers that will be executed each time, and only when, an UPDATE command is executed against the named table.
Cascades was a bad choice of words on my part. Unlike the WHEN clause which is checked right before the function executes and which evaluates against the return value of the previous trigger function, the column specific trigger is only checked against the original NEW row. I think that the behavior of column-specific triggers, especially their difference in when/what they check against from triggers with a WHEN CLAUSE would be useful to document on this page.
If you still believe a meaningful change can be had here a concrete suggestion would be helpful. Otherwise maybe someone takes an interest at some point - but this particular confusion seems extremely rare.
I'm proposing that the "Overview of Trigger Behavior" page include information about column specific triggers as well, because they have different behavior from how the return value from one BEFORE trigger is the input to the next BEFORE trigger and from how the WHEN clause gets checked right before statement execution. Both those "see" the effects of previously executed BEFORE triggers but column specific triggers don't.
