Hello, David!

> I've made a pass over v10. I think it's in pretty good shape, but I
> did end up changing a few small things.

Thank you! I merged your changes to new patch version.

> The only thing that I'm a bit unsure of is the tests. I've read the
> thread and I see the discussion above about it. I'd personally have
> thought INFO was fine since ATTACH PARTITION does that, but I see
> objections.

It is unclear for me if we have consensus about INFO ereport in ATTACH 
PARTITION.

> It appears that all the tests just assume that the CHECK
> constraint was used to validate the SET NOT NULL. I'm not all that
> sure if there's any good reason not to set client_min_messages =
> 'debug1' just before your test then RESET client_min_messages;
> afterwards. No other tests seem to do it, but my only thoughts on the
> reason not to would be that it might fail if someone added another
> debug somewhere, but so what? they should update the expected results
> too.

Not sure we have consensus about debug messages in tests, so I did such test 
changes in additional patch.

> separate that part out and
> put back the function named PartConstraintImpliedByRelConstraint and
> have it do the IS NOT NULL building before calling
> ConstraintImpliedByRelConstraint(). No duplicate code that way and you
> also don't need to touch partbound.c

In this case we need extra argument for ConstraintImpliedByRelConstraint for 
some caller-provided existConstraint, right? Along with Relation itself? Then I 
need make copy of existConstraint, append relation constraints and call 
predicate_implied_by. If I understood correctly pseudocode would be:

PartConstraintImpliedByRelConstraint(rel, testConstraint)
  generate notNullConstraint from NOT NULL table attributes
  call ConstraintImpliedByRelConstraint(rel, testConstraint, notNullConstraint)

ConstraintImpliedByRelConstraint(rel, testConstraint, existsConstraint)
  copy existsConstraint to localExistsConstraint variable
  append relation constraints to localExistsConstraint list
  call predicate_implied_by
  
I thing redundant IS NOT NULL check is not issue here and we not need extra 
arguments for ConstraintImpliedByRelConstraint. Was not changed in attached 
version, but I will change if you think this would be better design.

regards, Sergei
diff --git a/doc/src/sgml/ref/alter_table.sgml b/doc/src/sgml/ref/alter_table.sgml
index 890b23afd6..926b3361ea 100644
--- a/doc/src/sgml/ref/alter_table.sgml
+++ b/doc/src/sgml/ref/alter_table.sgml
@@ -214,8 +214,17 @@ WITH ( MODULUS <replaceable class="parameter">numeric_literal</replaceable>, REM
     <listitem>
      <para>
       These forms change whether a column is marked to allow null
-      values or to reject null values.  You can only use <literal>SET
-      NOT NULL</literal> when the column contains no null values.
+      values or to reject null values.
+     </para>
+
+     <para>
+      <literal>SET NOT NULL</literal> may only be applied to a column
+      providing none of the records in the table contain a
+      <literal>NULL</literal> value for the column.  Ordinarily this is
+      checked during the <literal>ALTER TABLE</literal> by scanning the
+      entire table, however if a valid <literal>CHECK</literal> constraint is
+      found which proves no <literal>NULL</literal> can exist, then the
+      table scan is skipped.
      </para>
 
      <para>
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index a93b13c2fe..b03e1bc875 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -158,7 +158,7 @@ typedef struct AlteredTableInfo
 	/* Information saved by Phases 1/2 for Phase 3: */
 	List	   *constraints;	/* List of NewConstraint */
 	List	   *newvals;		/* List of NewColumnValue */
-	bool		new_notnull;	/* T if we added new NOT NULL constraints */
+	bool		verify_new_notnull; /* T if we should recheck NOT NULL */
 	int			rewrite;		/* Reason for forced rewrite, if any */
 	Oid			newTableSpace;	/* new tablespace; 0 means no change */
 	bool		chgPersistence; /* T if SET LOGGED/UNLOGGED is used */
@@ -370,6 +370,7 @@ static ObjectAddress ATExecDropNotNull(Relation rel, const char *colName, LOCKMO
 static void ATPrepSetNotNull(Relation rel, bool recurse, bool recursing);
 static ObjectAddress ATExecSetNotNull(AlteredTableInfo *tab, Relation rel,
 				 const char *colName, LOCKMODE lockmode);
+static bool NotNullImpliedByRelConstraints(Relation rel, Form_pg_attribute attr);
 static ObjectAddress ATExecColumnDefault(Relation rel, const char *colName,
 					Node *newDefault, LOCKMODE lockmode);
 static ObjectAddress ATExecAddIdentity(Relation rel, const char *colName,
@@ -4506,10 +4507,11 @@ ATRewriteTables(AlterTableStmt *parsetree, List **wqueue, LOCKMODE lockmode)
 		else
 		{
 			/*
-			 * Test the current data within the table against new constraints
-			 * generated by ALTER TABLE commands, but don't rebuild data.
+			 * If required, test the current data within the table against new
+			 * constraints generated by ALTER TABLE commands, but don't rebuild
+			 * data.
 			 */
-			if (tab->constraints != NIL || tab->new_notnull ||
+			if (tab->constraints != NIL || tab->verify_new_notnull ||
 				tab->partition_constraint != NULL)
 				ATRewriteTable(tab, InvalidOid, lockmode);
 
@@ -4670,13 +4672,13 @@ ATRewriteTable(AlteredTableInfo *tab, Oid OIDNewHeap, LOCKMODE lockmode)
 	}
 
 	notnull_attrs = NIL;
-	if (newrel || tab->new_notnull)
+	if (newrel || tab->verify_new_notnull)
 	{
 		/*
-		 * If we are rebuilding the tuples OR if we added any new NOT NULL
-		 * constraints, check all not-null constraints.  This is a bit of
-		 * overkill but it minimizes risk of bugs, and heap_attisnull is a
-		 * pretty cheap test anyway.
+		 * If we are rebuilding the tuples OR if we added any new but not
+		 * verified NOT NULL constraints, check all not-null constraints.
+		 * This is a bit of overkill but it minimizes risk of bugs, and
+		 * heap_attisnull is a pretty cheap test anyway.
 		 */
 		for (i = 0; i < newTupDesc->natts; i++)
 		{
@@ -5682,11 +5684,9 @@ ATExecAddColumn(List **wqueue, AlteredTableInfo *tab, Relation rel,
 		{
 			/*
 			 * If the new column is NOT NULL, and there is no missing value,
-			 * tell Phase 3 it needs to test that. (Note we don't do this for
-			 * an OID column.  OID will be marked not null, but since it's
-			 * filled specially, there's no need to test anything.)
+			 * tell Phase 3 it needs to check for NULLs.
 			 */
-			tab->new_notnull |= colDef->is_not_null;
+			tab->verify_new_notnull |= colDef->is_not_null;
 		}
 	}
 
@@ -6054,8 +6054,19 @@ ATExecSetNotNull(AlteredTableInfo *tab, Relation rel,
 
 		CatalogTupleUpdate(attr_rel, &tuple->t_self, tuple);
 
-		/* Tell Phase 3 it needs to test the constraint */
-		tab->new_notnull = true;
+		/*
+		 * Ordinarily phase 3 must ensure that no NULLs exist in columns that
+		 * are set NOT NULL, however, if we can find a constraint which proves
+		 * this then we can skip that.  However, we needn't bother looking if
+		 * we've already found that we must verify some other NOT NULL
+		 * constraint.
+		 */
+		if (!tab->verify_new_notnull &&
+			!NotNullImpliedByRelConstraints(rel, (Form_pg_attribute) GETSTRUCT(tuple)))
+		{
+			/* Tell Phase 3 it needs to test the constraint */
+			tab->verify_new_notnull = true;
+		}
 
 		ObjectAddressSubSet(address, RelationRelationId,
 							RelationGetRelid(rel), attnum);
@@ -6071,6 +6082,43 @@ ATExecSetNotNull(AlteredTableInfo *tab, Relation rel,
 	return address;
 }
 
+/*
+ * NotNullImpliedByRelConstraints
+ *		Does rel's existing constraints imply NOT NULL for the given attribute
+ */
+static bool
+NotNullImpliedByRelConstraints(Relation rel, Form_pg_attribute attr)
+{
+	NullTest   *nnulltest = makeNode(NullTest);
+
+	nnulltest->arg = (Expr *) makeVar(1,
+									  attr->attnum,
+									  attr->atttypid,
+									  attr->atttypmod,
+									  attr->attcollation,
+									  0);
+	nnulltest->nulltesttype = IS_NOT_NULL;
+
+	/*
+	 * argisrow=false is correct even for a composite column, because
+	 * attnotnull does not represent a SQL-spec IS NOT NULL test in such a
+	 * case, just IS DISTINCT FROM NULL.
+	 */
+	nnulltest->argisrow = false;
+	nnulltest->location = -1;
+
+	if (ConstraintImpliedByRelConstraint(rel, list_make1(nnulltest)))
+	{
+		ereport(DEBUG1,
+				(errmsg("verifying table \"%s\" NOT NULL constraint "
+						"on %s attribute by existed constraints",
+						RelationGetRelationName(rel), NameStr(attr->attname))));
+		return true;
+	}
+
+	return false;
+}
+
 /*
  * ALTER TABLE ALTER COLUMN SET/DROP DEFAULT
  *
@@ -14317,16 +14365,16 @@ ComputePartitionAttrs(ParseState *pstate, Relation rel, List *partParams, AttrNu
 }
 
 /*
- * PartConstraintImpliedByRelConstraint
- *		Do scanrel's existing constraints imply the partition constraint?
+ * ConstraintImpliedByRelConstraint
+ *		Do scanrel's existing constraints imply the given constraint?
  *
  * "Existing constraints" include its check constraints and column-level
- * NOT NULL constraints.  partConstraint describes the partition constraint,
- * in implicit-AND form.
+ * NOT NULL constraints.  testConstraint describes the constraint to validate.
+ * This must be in implicitly-AND form, must only contain immutable clauses
+ * and all Vars must be varno=1.
  */
 bool
-PartConstraintImpliedByRelConstraint(Relation scanrel,
-									 List *partConstraint)
+ConstraintImpliedByRelConstraint(Relation scanrel, List *testConstraint)
 {
 	List	   *existConstraint = NIL;
 	TupleConstr *constr = RelationGetDescr(scanrel)->constr;
@@ -14395,13 +14443,9 @@ PartConstraintImpliedByRelConstraint(Relation scanrel,
 	/*
 	 * Try to make the proof.  Since we are comparing CHECK constraints, we
 	 * need to use weak implication, i.e., we assume existConstraint is
-	 * not-false and try to prove the same for partConstraint.
-	 *
-	 * Note that predicate_implied_by assumes its first argument is known
-	 * immutable.  That should always be true for partition constraints, so we
-	 * don't test it here.
+	 * not-false and try to prove the same for testConstraint.
 	 */
-	return predicate_implied_by(partConstraint, existConstraint, true);
+	return predicate_implied_by(testConstraint, existConstraint, true);
 }
 
 /*
@@ -14423,7 +14467,7 @@ QueuePartitionConstraintValidation(List **wqueue, Relation scanrel,
 	 * Based on the table's existing constraints, determine whether or not we
 	 * may skip scanning the table.
 	 */
-	if (PartConstraintImpliedByRelConstraint(scanrel, partConstraint))
+	if (ConstraintImpliedByRelConstraint(scanrel, partConstraint))
 	{
 		if (!validate_default)
 			ereport(INFO,
diff --git a/src/backend/partitioning/partbounds.c b/src/backend/partitioning/partbounds.c
index e71eb3793b..a6bf41ac11 100644
--- a/src/backend/partitioning/partbounds.c
+++ b/src/backend/partitioning/partbounds.c
@@ -1177,7 +1177,7 @@ check_default_partition_contents(Relation parent, Relation default_rel,
 	 * not contain any row that would belong to the new partition, we can
 	 * avoid scanning the default partition.
 	 */
-	if (PartConstraintImpliedByRelConstraint(default_rel, def_part_constraints))
+	if (ConstraintImpliedByRelConstraint(default_rel, def_part_constraints))
 	{
 		ereport(INFO,
 				(errmsg("updated partition constraint for default partition \"%s\" is implied by existing constraints",
@@ -1221,7 +1221,7 @@ check_default_partition_contents(Relation parent, Relation default_rel,
 			 * that it will not contain any row that would belong to the new
 			 * partition, we can avoid scanning the child table.
 			 */
-			if (PartConstraintImpliedByRelConstraint(part_rel,
+			if (ConstraintImpliedByRelConstraint(part_rel,
 													 def_part_constraints))
 			{
 				ereport(INFO,
diff --git a/src/include/commands/tablecmds.h b/src/include/commands/tablecmds.h
index ec3bb90b01..759abba3f2 100644
--- a/src/include/commands/tablecmds.h
+++ b/src/include/commands/tablecmds.h
@@ -94,7 +94,7 @@ extern void RangeVarCallbackOwnsTable(const RangeVar *relation,
 
 extern void RangeVarCallbackOwnsRelation(const RangeVar *relation,
 							 Oid relId, Oid oldRelId, void *noCatalogs);
-extern bool PartConstraintImpliedByRelConstraint(Relation scanrel,
-									 List *partConstraint);
+extern bool ConstraintImpliedByRelConstraint(Relation scanrel,
+								 List *testConstraint);
 
 #endif							/* TABLECMDS_H */
diff --git a/src/test/regress/expected/alter_table.out b/src/test/regress/expected/alter_table.out
index 4db792cf2f..c8de23cb19 100644
--- a/src/test/regress/expected/alter_table.out
+++ b/src/test/regress/expected/alter_table.out
@@ -1065,6 +1065,41 @@ alter table myview alter column test set not null;
 ERROR:  "myview" is not a table or foreign table
 drop view myview;
 drop table atacc1;
+-- set not null verified by constraints
+create table atacc1 (test_a int, test_b int);
+insert into atacc1 values (null, 1);
+-- constraint not cover all values, should fail
+alter table atacc1 add constraint atacc1_constr_or check(test_a is not null or test_b < 10);
+alter table atacc1 alter test_a set not null;
+ERROR:  column "test_a" contains null values
+alter table atacc1 drop constraint atacc1_constr_or;
+-- not valid constraint, should fail
+alter table atacc1 add constraint atacc1_constr_invalid check(test_a is not null) not valid;
+alter table atacc1 alter test_a set not null;
+ERROR:  column "test_a" contains null values
+alter table atacc1 drop constraint atacc1_constr_invalid;
+-- with valid constraint
+update atacc1 set test_a = 1;
+alter table atacc1 add constraint atacc1_constr_a_valid check(test_a is not null);
+alter table atacc1 alter test_a set not null;
+delete from atacc1;
+insert into atacc1 values (2, null);
+alter table atacc1 alter test_a drop not null;
+-- test multiple set not null at same time
+-- test_a checked by atacc1_constr_a_valid, test_b should fail by table scan
+alter table atacc1 alter test_a set not null, alter test_b set not null;
+ERROR:  column "test_b" contains null values
+-- commands order has no importance
+alter table atacc1 alter test_b set not null, alter test_a set not null;
+ERROR:  column "test_b" contains null values
+-- valid one by table scan, one by check constraints
+update atacc1 set test_b = 1;
+alter table atacc1 alter test_b set not null, alter test_a set not null;
+alter table atacc1 alter test_a drop not null, alter test_b drop not null;
+-- both column has check constraints
+alter table atacc1 add constraint atacc1_constr_b_valid check(test_b is not null);
+alter table atacc1 alter test_b set not null, alter test_a set not null;
+drop table atacc1;
 -- test inheritance
 create table parent (a int);
 create table child (b varchar(255)) inherits (parent);
diff --git a/src/test/regress/sql/alter_table.sql b/src/test/regress/sql/alter_table.sql
index d80643037d..94c6a43a10 100644
--- a/src/test/regress/sql/alter_table.sql
+++ b/src/test/regress/sql/alter_table.sql
@@ -809,6 +809,41 @@ drop view myview;
 
 drop table atacc1;
 
+-- set not null verified by constraints
+create table atacc1 (test_a int, test_b int);
+insert into atacc1 values (null, 1);
+-- constraint not cover all values, should fail
+alter table atacc1 add constraint atacc1_constr_or check(test_a is not null or test_b < 10);
+alter table atacc1 alter test_a set not null;
+alter table atacc1 drop constraint atacc1_constr_or;
+-- not valid constraint, should fail
+alter table atacc1 add constraint atacc1_constr_invalid check(test_a is not null) not valid;
+alter table atacc1 alter test_a set not null;
+alter table atacc1 drop constraint atacc1_constr_invalid;
+-- with valid constraint
+update atacc1 set test_a = 1;
+alter table atacc1 add constraint atacc1_constr_a_valid check(test_a is not null);
+alter table atacc1 alter test_a set not null;
+delete from atacc1;
+
+insert into atacc1 values (2, null);
+alter table atacc1 alter test_a drop not null;
+-- test multiple set not null at same time
+-- test_a checked by atacc1_constr_a_valid, test_b should fail by table scan
+alter table atacc1 alter test_a set not null, alter test_b set not null;
+-- commands order has no importance
+alter table atacc1 alter test_b set not null, alter test_a set not null;
+
+-- valid one by table scan, one by check constraints
+update atacc1 set test_b = 1;
+alter table atacc1 alter test_b set not null, alter test_a set not null;
+
+alter table atacc1 alter test_a drop not null, alter test_b drop not null;
+-- both column has check constraints
+alter table atacc1 add constraint atacc1_constr_b_valid check(test_b is not null);
+alter table atacc1 alter test_b set not null, alter test_a set not null;
+drop table atacc1;
+
 -- test inheritance
 create table parent (a int);
 create table child (b varchar(255)) inherits (parent);
diff --git a/src/test/regress/expected/alter_table.out b/src/test/regress/expected/alter_table.out
index c8de23cb19..efa8126962 100644
--- a/src/test/regress/expected/alter_table.out
+++ b/src/test/regress/expected/alter_table.out
@@ -1028,6 +1028,8 @@ insert into atacc1 (test2, test) values (1, NULL);
 ERROR:  null value in column "test" violates not-null constraint
 DETAIL:  Failing row contains (null, 1).
 drop table atacc1;
+-- we want check if not null was implied by constraint
+set client_min_messages to 'debug1';
 -- alter table / alter column [set/drop] not null tests
 -- try altering system catalogs, should fail
 alter table pg_class alter column relname drop not null;
@@ -1043,15 +1045,19 @@ ERROR:  relation "non_existent" does not exist
 -- test checking for null values and primary key
 create table atacc1 (test int not null);
 alter table atacc1 add constraint "atacc1_pkey" primary key (test);
+DEBUG:  ALTER TABLE / ADD PRIMARY KEY will create implicit index "atacc1_pkey" for table "atacc1"
+DEBUG:  building index "atacc1_pkey" on table "atacc1" serially
 alter table atacc1 alter column test drop not null;
 ERROR:  column "test" is in a primary key
 alter table atacc1 drop constraint "atacc1_pkey";
 alter table atacc1 alter column test drop not null;
 insert into atacc1 values (null);
 alter table atacc1 alter test set not null;
+DEBUG:  verifying table "atacc1"
 ERROR:  column "test" contains null values
 delete from atacc1;
 alter table atacc1 alter test set not null;
+DEBUG:  verifying table "atacc1"
 -- try altering a non-existent column, should fail
 alter table atacc1 alter bar set not null;
 ERROR:  column "bar" of relation "atacc1" does not exist
@@ -1070,36 +1076,49 @@ create table atacc1 (test_a int, test_b int);
 insert into atacc1 values (null, 1);
 -- constraint not cover all values, should fail
 alter table atacc1 add constraint atacc1_constr_or check(test_a is not null or test_b < 10);
+DEBUG:  verifying table "atacc1"
 alter table atacc1 alter test_a set not null;
+DEBUG:  verifying table "atacc1"
 ERROR:  column "test_a" contains null values
 alter table atacc1 drop constraint atacc1_constr_or;
 -- not valid constraint, should fail
 alter table atacc1 add constraint atacc1_constr_invalid check(test_a is not null) not valid;
 alter table atacc1 alter test_a set not null;
+DEBUG:  verifying table "atacc1"
 ERROR:  column "test_a" contains null values
 alter table atacc1 drop constraint atacc1_constr_invalid;
 -- with valid constraint
 update atacc1 set test_a = 1;
 alter table atacc1 add constraint atacc1_constr_a_valid check(test_a is not null);
+DEBUG:  verifying table "atacc1"
 alter table atacc1 alter test_a set not null;
+DEBUG:  verifying table "atacc1" NOT NULL constraint on test_a attribute by existed constraints
 delete from atacc1;
 insert into atacc1 values (2, null);
 alter table atacc1 alter test_a drop not null;
 -- test multiple set not null at same time
 -- test_a checked by atacc1_constr_a_valid, test_b should fail by table scan
 alter table atacc1 alter test_a set not null, alter test_b set not null;
+DEBUG:  verifying table "atacc1" NOT NULL constraint on test_a attribute by existed constraints
+DEBUG:  verifying table "atacc1"
 ERROR:  column "test_b" contains null values
 -- commands order has no importance
 alter table atacc1 alter test_b set not null, alter test_a set not null;
+DEBUG:  verifying table "atacc1"
 ERROR:  column "test_b" contains null values
 -- valid one by table scan, one by check constraints
 update atacc1 set test_b = 1;
 alter table atacc1 alter test_b set not null, alter test_a set not null;
+DEBUG:  verifying table "atacc1"
 alter table atacc1 alter test_a drop not null, alter test_b drop not null;
 -- both column has check constraints
 alter table atacc1 add constraint atacc1_constr_b_valid check(test_b is not null);
+DEBUG:  verifying table "atacc1"
 alter table atacc1 alter test_b set not null, alter test_a set not null;
+DEBUG:  verifying table "atacc1" NOT NULL constraint on test_b attribute by existed constraints
+DEBUG:  verifying table "atacc1" NOT NULL constraint on test_a attribute by existed constraints
 drop table atacc1;
+reset client_min_messages;
 -- test inheritance
 create table parent (a int);
 create table child (b varchar(255)) inherits (parent);
diff --git a/src/test/regress/sql/alter_table.sql b/src/test/regress/sql/alter_table.sql
index 94c6a43a10..aa678ff6b8 100644
--- a/src/test/regress/sql/alter_table.sql
+++ b/src/test/regress/sql/alter_table.sql
@@ -776,6 +776,9 @@ insert into atacc1 (test2, test) values (2, 3);
 insert into atacc1 (test2, test) values (1, NULL);
 drop table atacc1;
 
+-- we want check if not null was implied by constraint
+set client_min_messages to 'debug1';
+
 -- alter table / alter column [set/drop] not null tests
 -- try altering system catalogs, should fail
 alter table pg_class alter column relname drop not null;
@@ -844,6 +847,8 @@ alter table atacc1 add constraint atacc1_constr_b_valid check(test_b is not null
 alter table atacc1 alter test_b set not null, alter test_a set not null;
 drop table atacc1;
 
+reset client_min_messages;
+
 -- test inheritance
 create table parent (a int);
 create table child (b varchar(255)) inherits (parent);

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