MIN/MAX optimization for partitioned table

Consider the following schema:

    create table foo_archive (a int, b timestamp);
    create index foo_archive_idx on foo_archive(b);
    CREATE TABLE foo_archive_2007_01_01 (CONSTRAINT foo_archive_2007_01_01_b_check CHECK (((b >= '2007-01-01'::date) AND (b < '2007-01-02'::date)))) INHERITS (foo_archive);
    CREATE INDEX foo_archive_2007_01_01_idx ON foo_archive_2007_01_01 USING btree (b);
    CREATE TABLE foo_archive_2007_01_02 (CONSTRAINT foo_archive_2007_01_02_b_check CHECK (((b >= '2007-01-02'::date) AND (b < '2007-01-03'::date)))) INHERITS (foo_archive);
    CREATE INDEX foo_archive_2007_01_02_idx ON foo_archive_2007_01_02 USING btree (b);
    ...

Currently the optimizer yields the following plan:

    postgres=# explain select max(b) from foo_archive;
                                             QUERY PLAN                                             
    -----------------------------------------------------------------------------------------------------
     Aggregate  (cost=18602.00..18602.01 rows=1 width=8)
       ->  Append  (cost=0.00..16005.00 rows=1038800 width=8)
         ->  Seq Scan on foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_01 foo_archive  (cost=0.00..1331.99 rows=86399 width=8)
         ->  Seq Scan on foo_archive_2007_01_02 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_03 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_04 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_05 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_06 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_07 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_08 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_09 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_10 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_11 foo_archive  (cost=0.00..1332.00 rows=86400 width=8)
         ->  Seq Scan on foo_archive_2007_01_12 foo_archive  (cost=0.00..765.01 rows=49601 width=8)
         ->  Seq Scan on foo_archive_2007_01_13 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_14 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_15 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_16 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_17 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_18 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_19 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_20 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_21 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_22 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_23 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_24 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_25 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_26 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_27 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_28 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_29 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_30 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
         ->  Seq Scan on foo_archive_2007_01_31 foo_archive  (cost=0.00..29.40 rows=1940 width=8)
    (34 rows)

As we can see, the optimizer does not take advantage of the indexes on column b in the children relations.

Attached is a patch that will take advantage of the indexes (when they're available and if the index path is cheaper) and yield the following plan.

    postgres=# explain select max(b) from foo_archive;
                                                                    QUERY PLAN                                                                    
    ---------------------------------------------------------------------------------------------------------------------------------------------------
     Aggregate  (cost=1.54..1.55 rows=1 width=0)
       InitPlan 1 (returns $0)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_idx on foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 2 (returns $1)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_01_idx on foo_archive_2007_01_01 foo_archive  (cost=0.00..2719.24 rows=86399 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 3 (returns $2)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_02_idx on foo_archive_2007_01_02 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 4 (returns $3)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_03_idx on foo_archive_2007_01_03 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 5 (returns $4)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_04_idx on foo_archive_2007_01_04 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 6 (returns $5)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_05_idx on foo_archive_2007_01_05 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 7 (returns $6)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_06_idx on foo_archive_2007_01_06 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 8 (returns $7)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_07_idx on foo_archive_2007_01_07 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 9 (returns $8)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_08_idx on foo_archive_2007_01_08 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 10 (returns $9)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_09_idx on foo_archive_2007_01_09 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 11 (returns $10)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_10_idx on foo_archive_2007_01_10 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 12 (returns $11)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_11_idx on foo_archive_2007_01_11 foo_archive  (cost=0.00..2719.26 rows=86400 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 13 (returns $12)
         ->  Limit  (cost=0.00..0.03 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_12_idx on foo_archive_2007_01_12 foo_archive  (cost=0.00..1568.27 rows=49601 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 14 (returns $13)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_13_idx on foo_archive_2007_01_13 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 15 (returns $14)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_14_idx on foo_archive_2007_01_14 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 16 (returns $15)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_15_idx on foo_archive_2007_01_15 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 17 (returns $16)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_16_idx on foo_archive_2007_01_16 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 18 (returns $17)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_17_idx on foo_archive_2007_01_17 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 19 (returns $18)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_18_idx on foo_archive_2007_01_18 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 20 (returns $19)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_19_idx on foo_archive_2007_01_19 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 21 (returns $20)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_20_idx on foo_archive_2007_01_20 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 22 (returns $21)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_21_idx on foo_archive_2007_01_21 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 23 (returns $22)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_22_idx on foo_archive_2007_01_22 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 24 (returns $23)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_23_idx on foo_archive_2007_01_23 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 25 (returns $24)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_24_idx on foo_archive_2007_01_24 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 26 (returns $25)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_25_idx on foo_archive_2007_01_25 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 27 (returns $26)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_26_idx on foo_archive_2007_01_26 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 28 (returns $27)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_27_idx on foo_archive_2007_01_27 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 29 (returns $28)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_28_idx on foo_archive_2007_01_28 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 30 (returns $29)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_29_idx on foo_archive_2007_01_29 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 31 (returns $30)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_30_idx on foo_archive_2007_01_30 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       InitPlan 32 (returns $31)
         ->  Limit  (cost=0.00..0.04 rows=1 width=8)
           ->  Index Scan Backward using foo_archive_2007_01_31_idx on foo_archive_2007_01_31 foo_archive  (cost=0.00..73.35 rows=1940 width=8)
                 Filter: (b IS NOT NULL)
       ->  Append  (cost=0.00..0.32 rows=32 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
         ->  Result  (cost=0.00..0.01 rows=1 width=0)
    (162 rows)

Does this patch make sense for 8.5 to optimize for this particular class of queries?  Specifically queries of the form:

    SELECT MAX(col) FROM tab WHERE ...;
    SELECT MIN(col) FROM tab WHERE ...;

Thanks, Alan