create table parent(
   id SERIAL PRIMARY KEY,
   numchildren integer not null default 0
);

create table child(
  id serial primary key
  parent_id integer NOT NULL REFERENCES parent(id)
);

CREATE OR REPLACE FUNCTION run_after_change() RETURNS TRIGGER AS $$
BEGIN
  IF TG_OP = 'DELETE' THEN
    UPDATE parent SET numchildren = (SELECT COUNT(*) FROM child WHERE OLD.parent_id = parent.id) WHERE OLD.parent_id = parent.id;
    RETURN OLD;
  ELSIF TG_OP = 'UPDATE' OR TG_OP = 'INSERT' THEN
    UPDATE parent SET numchildren = (SELECT COUNT(*) FROM child WHERE NEW.parent_id = parent.id) WHERE NEW.parent_id = parent.id;
    RETURN NEW;
  END IF;
END; $$ language 'plpgsql';

CREATE TRIGGER after_change
  AFTER DELETE OR INSERT OR UPDATE ON child
  FOR EACH ROW EXECUTE PROCEDURE run_after_change();