should be it

external/duckdb/test/optimizer/statistics/statistics_is_null.test

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+# name: test/optimizer/statistics/statistics_is_null.test
+# description: Test filter propagation in IS NULL/IS NOT NULL operands
+# group: [statistics]
+
+statement ok
+SET default_null_order='nulls_first';
+
+statement ok
+CREATE TABLE integers AS SELECT * FROM (VALUES (1), (2), (3)) tbl(i);
+
+statement ok
+CREATE TABLE integers2 AS SELECT * FROM (VALUES (4), (5), (NULL)) tbl(i);
+
+statement ok
+PRAGMA explain_output = OPTIMIZED_ONLY;
+
+# we can statically determine IS NULL/IS NOT NULL are false, if there are no null values for this column
+query II
+EXPLAIN SELECT i IS NULL FROM integers;
+----
+logical_opt	<!REGEX>:.*IS NULL.*
+
+query II
+EXPLAIN SELECT i IS NOT NULL FROM integers;
+----
+logical_opt	<!REGEX>:.*IS NOT NULL.*
+
+# if there are null values, however, we have to execute the operator
+query II
+EXPLAIN SELECT i IS NULL FROM integers2;
+----
+logical_opt	<REGEX>:.*IS NULL.*
+
+query II
+EXPLAIN SELECT i IS NOT NULL FROM integers2;
+----
+logical_opt	<REGEX>:.*IS NOT NULL.*
+
+# filters remove null values, so even if the base column contains null values, we don't need to check IS NULL here
+query II
+EXPLAIN SELECT i IS NULL FROM integers2 WHERE i>0;
+----
+logical_opt	<!REGEX>:.*IS NULL.*
+
+# left/right outer joins with false condition can convert to cross product with constant NULL value, 
+# so we don't need to check IS NULL here, since it's always NULL
+query II
+EXPLAIN SELECT i2.i IS NULL FROM integers i1 LEFT JOIN integers i2 ON (false);
+----
+logical_opt	<!REGEX>:.*IS NULL.*
+
+# full outer joins can introduce nulls, even if the base tables do not contain them
+query II
+EXPLAIN SELECT i1.i IS NULL FROM integers i1 FULL OUTER JOIN integers i2 ON (false);
+----
+logical_opt	<REGEX>:.*IS NULL.*
+
+# verify that all these queries produce the correct results
+query I
+SELECT i IS NULL FROM integers;
+----
+0
+0
+0
+
+query I
+SELECT i IS NOT NULL FROM integers;
+----
+1
+1
+1
+
+query I
+SELECT i IS NULL FROM integers2;
+----
+0
+0
+1
+
+query I
+SELECT i IS NOT NULL FROM integers2;
+----
+1
+1
+0
+
+query I
+SELECT i IS NULL FROM integers2 WHERE i>0;
+----
+0
+0
+
+query I
+SELECT i2.i IS NULL FROM integers i1 LEFT JOIN integers i2 ON (false);
+----
+1
+1
+1
+
+query I
+SELECT i1.i IS NULL FROM integers i1 FULL OUTER JOIN integers i2 ON (false) ORDER BY i1.i;
+----
+1
+1
+1
+0
+0
+0
+
+# FIXME: we don't yet correctly track when columns don't contain valid values
+mode skip
+
+statement ok
+CREATE TABLE integers3 AS SELECT * FROM (VALUES (NULL), (NULL), (NULL)) tbl(i);
+
+# we can statically determine IS NULL/IS NOT NULL are true, if there are no valid values for this column
+query II
+EXPLAIN SELECT i IS NULL FROM integers3;
+----
+logical_opt	<!REGEX>:.*IS NULL.*
+
+query II
+EXPLAIN SELECT i IS NOT NULL FROM integers3;
+----
+logical_opt	<!REGEX>:.*IS NOT NULL.*
+
+query I
+SELECT i IS NULL FROM integers3;
+----
+true
+true
+true
+
+query I
+SELECT i IS NOT NULL FROM integers3;
+----
+false
+false
+false