PostgreSQL trigger prevents another from running

Let's pretend that:

create table T
(
    id bigserial primary key
  , a  int
  , b  int
  , c  int
);

      

        
        
        
      

    

I want to c

always equal a+b

and I want to prevent manual changes c

. Therefore, I create two triggers:

-- Prevents manual changes of c:

create or replace function no_changes() returns trigger as $$
begin
    if old.c is distinct from new.c then
        raise exception 'Can''t change c manually.';
    end if;
    return new;
end;
$$ language plpgsql;

create trigger no_changes
before update of c  -- 'before' so prevents changes in 'c'
on T
for each row
execute procedure no_changes();

-- Do c = a + b:

create or replace function change() returns trigger as $$
begin
    update T
    set c = a + b
    where id = new.id;
    return new;
end;
$$ language plpgsql;

create trigger change
after insert or update of a, b  -- 'after' so I'm sure the row is inserted/updated
on T
for each row
execute procedure change();

      

        
        
        
      

    

If I do this:

update T set c = 247;

      

        
        
        
      

    

I see the error "Cannot manually change c" and the column does not change. Fine.

However, if I do:

insert into T (a, b) values (4, 3);

      

        
        
        
      

    

Or:

update T set a = 3 where id = 2 -- suppose id = 2 exists

      

        
        
        
      

    

Then I get the same error message as before. Obviously, the command update

from change

invokes the trigger no_changes

, preventing the column from being updated c

.

Any ideas? Thank!