-- bool check
CREATE TABLE booltmp (a bool);
INSERT INTO booltmp VALUES (false), (true);
SET enable_seqscan=on;
SELECT count(*) FROM booltmp WHERE a <  true;
 count 
-------
     1
(1 row)

SELECT count(*) FROM booltmp WHERE a <= true;
 count 
-------
     2
(1 row)

SELECT count(*) FROM booltmp WHERE a  = true;
 count 
-------
     1
(1 row)

SELECT count(*) FROM booltmp WHERE a >= true;
 count 
-------
     1
(1 row)

SELECT count(*) FROM booltmp WHERE a >  true;
 count 
-------
     0
(1 row)

CREATE INDEX boolidx ON booltmp USING gist ( a );
SET enable_seqscan=off;
SELECT count(*) FROM booltmp WHERE a <  true;
 count 
-------
     1
(1 row)

SELECT count(*) FROM booltmp WHERE a <= true;
 count 
-------
     2
(1 row)

SELECT count(*) FROM booltmp WHERE a  = true;
 count 
-------
     1
(1 row)

SELECT count(*) FROM booltmp WHERE a >= true;
 count 
-------
     1
(1 row)

SELECT count(*) FROM booltmp WHERE a >  true;
 count 
-------
     0
(1 row)

-- Test index-only scans
SET enable_bitmapscan=off;
EXPLAIN (COSTS OFF)
SELECT * FROM booltmp WHERE a;
                QUERY PLAN                
------------------------------------------
 Index Only Scan using boolidx on booltmp
   Index Cond: (a = true)
(2 rows)

SELECT * FROM booltmp WHERE a;
 a 
---
 t
(1 row)

EXPLAIN (COSTS OFF)
SELECT * FROM booltmp WHERE NOT a;
                QUERY PLAN                
------------------------------------------
 Index Only Scan using boolidx on booltmp
   Index Cond: (a = false)
(2 rows)

SELECT * FROM booltmp WHERE NOT a;
 a 
---
 f
(1 row)