Partial index on enum type is not being used, type issue?

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I have run into the following issue: A table contains an enum column, and a partial unique index is available on the table. This index contains exactly the row I am querying for. Unfortunately the index is not always used, and I don't really understand why.

The attachments enumTest.sql shows the script reproducing the behaviour, and the enumTest.log shows the result when running on PostgreSQL 13.4.
There doesn't seem to be any difference from PG11 through 14-RC1.

First off I tried to do a simple test to see if the index was being used:

EXPLAIN (analyze, costs, buffers, verbose) SELECT val FROM table_test_enum WHERE val = 'Ole' and dat IS NULL;
						  QUERY PLAN
------------------------------------------------------------------------
Index Only Scan using table_test_enum_val_idx on public.table_test_enum (cost=0.12..4.14 rows=1 width=4) (actual time=0.014..0.016 rows=1 loops=1)
   Output: val
   Heap Fetches: 0
 Planning Time: 0.436 ms
 Execution Time: 0.048 ms
(5 rows)

All is fine, but in my application the query is executed as a prepared statement, using a varchar parameter:

PREPARE qry1(varchar) AS SELECT val FROM table_test_enum WHERE val = $1::type_table_test_enum AND dat IS NULL;
EXPLAIN (analyze, costs, buffers, verbose) EXECUTE qry1('Ole');
                                                   QUERY PLAN
----------------------------------------------------------------------
Seq Scan on public.table_test_enum (cost=0.00..66.52 rows=1 width=4) (actual time=1.131..1.133 rows=1 loops=1)
   Output: val
Filter: ((table_test_enum.dat IS NULL) AND (table_test_enum.val = ('Ole'::cstring)::type_table_test_enum))
   Rows Removed by Filter: 3000
 Planning Time: 0.261 ms
 Execution Time: 1.162 ms
(6 rows)

To my surprise the planner decides not to use the index. This is the part I do not understand. Why is the result different here? There is obviously a cast that happens before the equality, does the cstring cast have anything to do with this? Hints are welcome!

So I tried to prepare a statement with a parameter of type type_table_test_enum instead, unsurprisingly, this works fine. No mentioning of cstring in the plan. I also tried to use a parameter of unknown type, which I would think would be analogous to the first statement with the literal 'Ole', and that looks fine.
So why is the varchar version not using the index?
Any thoughs on this?

	Regards,
		Kim Johan Andersson
SELECT version();

CREATE TYPE type_table_test_enum AS ENUM ( 'Ole', 'Bole', 'Skole' );
CREATE TABLE table_test_enum ( val type_table_test_enum NOT NULL, dat date );
CREATE UNIQUE INDEX ON table_test_enum ( val ) WHERE val = 'Ole' AND dat IS NULL;

INSERT INTO table_test_enum SELECT 'Ole', current_date FROM generate_series( 1, 1000 );
INSERT INTO table_test_enum SELECT 'Bole', current_date FROM generate_series( 1, 1000 );
INSERT INTO table_test_enum SELECT 'Skole', current_date FROM generate_series( 1, 1000 );
INSERT INTO table_test_enum VALUES ( 'Ole', NULL );
VACUUM (analyze) table_test_enum;

EXPLAIN (analyze, costs, buffers, verbose) SELECT val FROM table_test_enum WHERE val = 'Ole' and dat IS NULL;

PREPARE qry1(varchar) AS SELECT val FROM table_test_enum WHERE val = $1::type_table_test_enum AND dat IS NULL;
PREPARE qry2(type_table_test_enum) AS select val FROM table_test_enum WHERE val = $1 AND dat IS NULL;
PREPARE qry3(unknown) AS SELECT val FROM table_test_enum WHERE val = $1 AND dat IS NULL;

EXPLAIN (analyze, costs, buffers, verbose) EXECUTE qry1('Ole');
EXPLAIN (analyze, costs, buffers, verbose) EXECUTE qry2('Ole');
EXPLAIN (analyze, costs, buffers, verbose) EXECUTE qry3('Ole');

DEALLOCATE qry1;
DEALLOCATE qry2;
DEALLOCATE qry3;

DROP TABLE table_test_enum;
DROP TYPE type_table_test_enum;
                                                     version
------------------------------------------------------------------------------------------------------------------
 PostgreSQL 13.4 (Debian 13.4-1.pgdg100+1) on x86_64-pc-linux-gnu, compiled by gcc (Debian 8.3.0-6) 8.3.0, 64-bit
(1 row)

CREATE TYPE
CREATE TABLE
CREATE INDEX
INSERT 0 1000
INSERT 0 1000
INSERT 0 1000
INSERT 0 1
VACUUM
                                                                     QUERY PLAN
-----------------------------------------------------------------------------------------------------------------------------------------------------
 Index Only Scan using table_test_enum_val_idx on public.table_test_enum  (cost=0.12..4.14 rows=1 width=4) (actual time=0.014..0.016 rows=1 loops=1)
   Output: val
   Heap Fetches: 0
 Planning Time: 0.436 ms
 Execution Time: 0.048 ms
(5 rows)

PREPARE
PREPARE
PREPARE
                                                   QUERY PLAN
-----------------------------------------------------------------------------------------------------------------
 Seq Scan on public.table_test_enum  (cost=0.00..66.52 rows=1 width=4) (actual time=1.131..1.133 rows=1 loops=1)
   Output: val
   Filter: ((table_test_enum.dat IS NULL) AND (table_test_enum.val = ('Ole'::cstring)::type_table_test_enum))
   Rows Removed by Filter: 3000
 Planning Time: 0.261 ms
 Execution Time: 1.162 ms
(6 rows)

                                                                     QUERY PLAN
-----------------------------------------------------------------------------------------------------------------------------------------------------
 Index Only Scan using table_test_enum_val_idx on public.table_test_enum  (cost=0.12..4.14 rows=1 width=4) (actual time=0.023..0.026 rows=1 loops=1)
   Output: val
   Heap Fetches: 0
 Planning Time: 0.256 ms
 Execution Time: 0.054 ms
(5 rows)

                                                                     QUERY PLAN
-----------------------------------------------------------------------------------------------------------------------------------------------------
 Index Only Scan using table_test_enum_val_idx on public.table_test_enum  (cost=0.12..4.14 rows=1 width=4) (actual time=0.019..0.023 rows=1 loops=1)
   Output: val
   Heap Fetches: 0
 Planning Time: 0.259 ms
 Execution Time: 0.051 ms
(5 rows)

DEALLOCATE
DEALLOCATE
DEALLOCATE
DROP TABLE
DROP TYPE

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