You should to define custom aggregate for this purpose:
CREATE OR REPLACE FUNCTION public.overlap_array_aggregate(anyarray, anyarray)
RETURNS anyarray
LANGUAGE plpgsql STRICT
AS $function$
BEGIN
RETURN ARRAY(SELECT unnest($1) INTERSECT SELECT unnest($2));
END;
$function$
CREATE AGGREGATE array_overlap_agg (
basetype = anyarray,
sfunc = overlap_array_aggregate,
stype = anyarray );
Then it is working as you expect:
postgres=# SELECT * FROM foo;
┌─────────────┐
│ a │
╞═════════════╡
│ {1,2,3,4} │
│ {1,2,6,7} │
│ {1,2,3,8,9} │
└─────────────┘
(3 rows)
postgres=# SELECT array_overlap_agg(a) FROM foo;
┌───────────────────┐
│ array_overlap_agg │
╞═══════════════════╡
│ {1,2} │
└───────────────────┘
(1 row)