support create index on virtual generated column.

From 28852a6df9ebcfc68f8b97248eb811ec22307065 Mon Sep 17 00:00:00 2001
From: jian he <jian.universality@gmail.com>
Date: Mon, 14 Apr 2025 19:07:48 +0800
Subject: [PATCH v2 1/1] index on virtual generated column

* internally such index transformed into expression index.
  For example, an index on (b int GENERATED ALWAYS AS (a * 2) VIRTUAL)
  internal representation: an expression index on ((a * 2)).
* in pageinspect module, add some test to check the index content of virtual generated column.
* primary key, unique index over virtual generated column are not supported.
* expression index and predicate index over virtual generated columns are
  currently not supported.
* virtual generated column can not be in "include column"
* all types of indexes are supported, hash index, gist index regress test added.
* To support ALTER TABLE SET EXPRESSION, in pg_index, we need to track the original
  virtual generated column attribute number, so ALTER TABLE SET EXPRESSION can
  identify which index needs to be rebuilt.
* ALTER COLUMN SET DATA TYPE will also cause table rewrite, so we really
  need to track the virtual generated column attribute number that index was built on.

* if the partitioned table and partition both have an index, then the index over the virtual
  generated column should be the same expression. For example, the following last
  command should error out.

    CREATE TABLE parted (b integer,c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
    CREATE TABLE part (b integer,c integer,a integer GENERATED ALWAYS AS (c));
    create index on part(a);
    create index on parted(a);
    alter table parted ATTACH partition part for values from (1) to (10);

discussion: https://postgr.es/m/CACJufxGao-cypdNhifHAdt8jHfK6-HX=tRBovBkgRuxw063GaA@mail.gmail.com
commitfest entry: https://commitfest.postgresql.org/patch/5667/
---
 contrib/pageinspect/expected/btree.out        |  33 ++
 contrib/pageinspect/sql/btree.sql             |  21 ++
 doc/src/sgml/catalogs.sgml                    |  15 +
 src/backend/catalog/index.c                   |  69 ++++
 src/backend/commands/indexcmds.c              | 301 +++++++++++++++---
 src/backend/commands/tablecmds.c              |  61 ++++
 src/backend/parser/parse_utilcmd.c            |  25 +-
 src/backend/utils/adt/ruleutils.c             |  28 +-
 src/include/catalog/index.h                   |   6 +
 src/include/catalog/pg_index.h                |   1 +
 src/include/nodes/execnodes.h                 |   1 +
 src/test/regress/expected/fast_default.out    |   8 +
 .../regress/expected/generated_virtual.out    | 199 ++++++++++--
 src/test/regress/sql/fast_default.sql         |   6 +
 src/test/regress/sql/generated_virtual.sql    | 111 +++++--
 15 files changed, 803 insertions(+), 82 deletions(-)

diff --git a/contrib/pageinspect/expected/btree.out b/contrib/pageinspect/expected/btree.out
index 0aa5d73322f..56d57848cf7 100644
--- a/contrib/pageinspect/expected/btree.out
+++ b/contrib/pageinspect/expected/btree.out
@@ -183,6 +183,39 @@ tids       |
 
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 ERROR:  block number 2 is out of range for relation "test1_a_idx"
+---test index over virtual generated column
+CREATE TABLE test3 (a int8, b int4range, c int8 generated always as (a+1) virtual);
+INSERT INTO test3 VALUES (72057594037927936, '[0,1)');
+CREATE INDEX test3_a_idx ON test3 USING btree (c);
+SELECT * FROM bt_page_items('test3_a_idx', 1);
+-[ RECORD 1 ]-----------------------
+itemoffset | 1
+ctid       | (0,1)
+itemlen    | 16
+nulls      | f
+vars       | f
+data       | 01 00 00 00 00 00 00 01
+dead       | f
+htid       | (0,1)
+tids       | 
+
+--expect zero row.
+SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1))
+EXCEPT ALL
+SELECT * FROM bt_page_items(get_raw_page('test3_a_idx', 1));
+(0 rows)
+
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b ON test4 USING btree (b);
+CREATE INDEX test4_c ON test4 USING btree (c);
+ALTER TABLE test4 alter column b set data type text;
+---should return zero row.
+SELECT * FROM bt_page_items('test4_b', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_c', 1);
+(0 rows)
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/contrib/pageinspect/sql/btree.sql b/contrib/pageinspect/sql/btree.sql
index 102ebdefe3c..d3392c11d5f 100644
--- a/contrib/pageinspect/sql/btree.sql
+++ b/contrib/pageinspect/sql/btree.sql
@@ -32,6 +32,27 @@ SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 0));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 
+---test index over virtual generated column
+CREATE TABLE test3 (a int8, b int4range, c int8 generated always as (a+1) virtual);
+INSERT INTO test3 VALUES (72057594037927936, '[0,1)');
+CREATE INDEX test3_a_idx ON test3 USING btree (c);
+SELECT * FROM bt_page_items('test3_a_idx', 1);
+
+--expect zero row.
+SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1))
+EXCEPT ALL
+SELECT * FROM bt_page_items(get_raw_page('test3_a_idx', 1));
+
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b ON test4 USING btree (b);
+CREATE INDEX test4_c ON test4 USING btree (c);
+ALTER TABLE test4 alter column b set data type text;
+---should return zero row.
+SELECT * FROM bt_page_items('test4_b', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_c', 1);
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/doc/src/sgml/catalogs.sgml b/doc/src/sgml/catalogs.sgml
index cbd4e40a320..d7ee73373f5 100644
--- a/doc/src/sgml/catalogs.sgml
+++ b/doc/src/sgml/catalogs.sgml
@@ -4595,6 +4595,21 @@ SCRAM-SHA-256$<replaceable>&lt;iteration count&gt;</replaceable>:<replaceable>&l
       </para></entry>
      </row>
 
+     <row>
+      <entry role="catalog_table_entry"><para role="column_definition">
+       <structfield>indattrgenerated</structfield> <type>int2vector</type>
+       (references <link linkend="catalog-pg-attribute"><structname>pg_attribute</structname></link>.<structfield>attnum</structfield>)
+      </para>
+      <para>
+       This is an array of <structfield>indnatts</structfield> values that
+       indicate which table virtual generated columns this index indexes.
+       For example, a value of <literal>1 3</literal> would mean that the first
+       and the third table columns of this index entries are virtual generated
+       column. A zero in this array indicates that the corresponding index
+       attribute is not virtual generated column reference.
+      </para></entry>
+     </row>
+
      <row>
       <entry role="catalog_table_entry"><para role="column_definition">
        <structfield>indexprs</structfield> <type>pg_node_tree</type>
diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index 739a92bdcc1..dd379c2b79c 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -584,6 +584,12 @@ UpdateIndexRelation(Oid indexoid,
 	Relation	pg_index;
 	HeapTuple	tuple;
 	int			i;
+	int2vector *indgenkey;
+	int16	   *colgenerated;
+
+	colgenerated = palloc_array(int16, indexInfo->ii_NumIndexAttrs);
+	for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+		colgenerated[i] = indexInfo->ii_IndexAttrGeneratedNumbers[i];
 
 	/*
 	 * Copy the index key, opclass, and indoption info into arrays (should we
@@ -596,6 +602,7 @@ UpdateIndexRelation(Oid indexoid,
 	indclass = buildoidvector(opclassOids, indexInfo->ii_NumIndexKeyAttrs);
 	indoption = buildint2vector(coloptions, indexInfo->ii_NumIndexKeyAttrs);
 
+	indgenkey = buildint2vector(colgenerated, indexInfo->ii_NumIndexAttrs);
 	/*
 	 * Convert the index expressions (if any) to a text datum
 	 */
@@ -653,6 +660,7 @@ UpdateIndexRelation(Oid indexoid,
 	values[Anum_pg_index_indcollation - 1] = PointerGetDatum(indcollation);
 	values[Anum_pg_index_indclass - 1] = PointerGetDatum(indclass);
 	values[Anum_pg_index_indoption - 1] = PointerGetDatum(indoption);
+	values[Anum_pg_index_indattrgenerated - 1] = PointerGetDatum(indgenkey);
 	values[Anum_pg_index_indexprs - 1] = exprsDatum;
 	if (exprsDatum == (Datum) 0)
 		nulls[Anum_pg_index_indexprs - 1] = true;
@@ -1134,6 +1142,28 @@ index_create(Relation heapRelation,
 				}
 			}
 
+			/*
+			 * Internally, we convert index of virtual generation column into an
+			 * expression index. For example, if column 'b' is defined as (b INT
+			 * GENERATED ALWAYS AS (a * 2) VIRTUAL) then index over 'b' would
+			 * transformed into an expression index as ((a * 2)). As a result,
+			 * the pg_depend refobjsubid does not retain the original attribute
+			 * number of the virtual generated column. But we need rebuild any
+			 * index that was build on virtual generated column. so we need auto
+			 * dependencies on referenced virtual generated columns.
+			*/
+			for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+			{
+				if (indexInfo->ii_IndexAttrGeneratedNumbers[i] != 0)
+				{
+					ObjectAddressSubSet(referenced, RelationRelationId,
+										heapRelationId,
+										indexInfo->ii_IndexAttrGeneratedNumbers[i]);
+					add_exact_object_address(&referenced, addrs);
+					have_simple_col = false;
+				}
+			}
+
 			/*
 			 * If there are no simply-referenced columns, give the index an
 			 * auto dependency on the whole table.  In most cases, this will
@@ -2428,9 +2458,12 @@ IndexInfo *
 BuildIndexInfo(Relation index)
 {
 	IndexInfo  *ii;
+	HeapTuple	ht_idx;
 	Form_pg_index indexStruct = index->rd_index;
 	int			i;
 	int			numAtts;
+	Datum		indgenkeyDatum;
+	int2vector *indgenkey;
 
 	/* check the number of keys, and copy attr numbers into the IndexInfo */
 	numAtts = indexStruct->indnatts;
@@ -2454,9 +2487,19 @@ BuildIndexInfo(Relation index)
 					   index->rd_indam->amsummarizing,
 					   indexStruct->indisexclusion && indexStruct->indisunique);
 
+	ht_idx = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(indexStruct->indexrelid));
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* fill in attribute numbers */
 	for (i = 0; i < numAtts; i++)
+	{
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
+		ii->ii_IndexAttrGeneratedNumbers[i] = indgenkey->values[i];
+	}
+
+	ReleaseSysCache(ht_idx);
 
 	/* fetch exclusion constraint info if any */
 	if (indexStruct->indisexclusion)
@@ -2523,6 +2566,23 @@ BuildDummyIndexInfo(Relation index)
 	return ii;
 }
 
+/*
+ * IndexOverVirtualGenerated
+ *		Return whether this index is built on virtual generated column.
+ */
+bool
+IsIndexOverVirtualGenerated(const IndexInfo *info)
+{
+	int			i;
+
+	for (i = 0; i < info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(info->ii_IndexAttrGeneratedNumbers[i]))
+			return true;
+	}
+	return false;
+}
+
 /*
  * CompareIndexInfo
  *		Return whether the properties of two indexes (in different tables)
@@ -2585,6 +2645,15 @@ CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 				return false;
 		}
 
+		if (AttributeNumberIsValid(info1->ii_IndexAttrGeneratedNumbers[i]) ||
+			AttributeNumberIsValid(info2->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			/* fail if index over virtual generated column attribute does not match */
+			if (attmap->attnums[info2->ii_IndexAttrGeneratedNumbers[i] - 1] !=
+				info1->ii_IndexAttrGeneratedNumbers[i])
+				return false;
+		}
+
 		/* collation and opfamily are not valid for included columns */
 		if (i >= info1->ii_NumIndexKeyAttrs)
 			continue;
diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 33c2106c17c..f36edaf5e38 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -54,6 +54,7 @@
 #include "parser/parse_utilcmd.h"
 #include "partitioning/partdesc.h"
 #include "pgstat.h"
+#include "rewrite/rewriteHandler.h"
 #include "rewrite/rewriteManip.h"
 #include "storage/lmgr.h"
 #include "storage/proc.h"
@@ -90,9 +91,15 @@ static void ComputeIndexAttrs(IndexInfo *indexInfo,
 							  bool amcanorder,
 							  bool isconstraint,
 							  bool iswithoutoverlaps,
+							  bool is_primary,
 							  Oid ddl_userid,
 							  int ddl_sec_context,
 							  int *ddl_save_nestlevel);
+static void compute_generated_indexattrs(IndexInfo *indexInfo,
+										 Relation rel,
+										 bool is_primary,
+										 int attn,
+										 int attnum);
 static char *ChooseIndexName(const char *tabname, Oid namespaceId,
 							 const List *colnames, const List *exclusionOpNames,
 							 bool primary, bool isconstraint);
@@ -182,6 +189,7 @@ CheckIndexCompatible(Oid oldId,
 					 bool isWithoutOverlaps)
 {
 	bool		isconstraint;
+	bool		is_primary;
 	Oid		   *typeIds;
 	Oid		   *collationIds;
 	Oid		   *opclassIds;
@@ -214,6 +222,12 @@ CheckIndexCompatible(Oid oldId,
 	 */
 	isconstraint = false;
 
+	/*
+	 * We can pretend is_primary = false unconditionally.  It only serves to
+	 * decide the text of an error message that should never happen for us.
+	 */
+	is_primary = false;
+
 	numberOfAttributes = list_length(attributeList);
 	Assert(numberOfAttributes > 0);
 	Assert(numberOfAttributes <= INDEX_MAX_KEYS);
@@ -254,7 +268,7 @@ CheckIndexCompatible(Oid oldId,
 					  coloptions, attributeList,
 					  exclusionOpNames, relationId,
 					  accessMethodName, accessMethodId,
-					  amcanorder, isconstraint, isWithoutOverlaps, InvalidOid,
+					  amcanorder, isconstraint, isWithoutOverlaps, is_primary, InvalidOid,
 					  0, NULL);
 
 	/* Get the soon-obsolete pg_index tuple. */
@@ -905,6 +919,31 @@ DefineIndex(Oid tableId,
 	if (stmt->whereClause)
 		CheckPredicate((Expr *) stmt->whereClause);
 
+	/* virtual generated column over predicate indexes are not supported */
+	if (RelationGetDescr(rel)->constr &&
+		RelationGetDescr(rel)->constr->has_generated_virtual &&
+		stmt->whereClause)
+	{
+		Bitmapset  *indexattrs_pred = NULL;
+		int			j;
+
+		pull_varattnos(stmt->whereClause, 1, &indexattrs_pred);
+
+		j = -1;
+		while ((j = bms_next_member(indexattrs_pred, j)) >= 0)
+		{
+			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+
+			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+			{
+				ereport(ERROR,
+						errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+						errmsg("partial index on virtual generated columns are not supported"));
+				break;
+			}
+		}
+	}
+
 	/*
 	 * Parse AM-specific options, convert to text array form, validate.
 	 */
@@ -941,6 +980,7 @@ DefineIndex(Oid tableId,
 					  stmt->excludeOpNames, tableId,
 					  accessMethodName, accessMethodId,
 					  amcanorder, stmt->isconstraint, stmt->iswithoutoverlaps,
+					  stmt->primary,
 					  root_save_userid, root_save_sec_context,
 					  &root_save_nestlevel);
 
@@ -1102,9 +1142,6 @@ DefineIndex(Oid tableId,
 	/*
 	 * We disallow indexes on system columns.  They would not necessarily get
 	 * updated correctly, and they don't seem useful anyway.
-	 *
-	 * Also disallow virtual generated columns in indexes (use expression
-	 * index instead).
 	 */
 	for (int i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
 	{
@@ -1114,26 +1151,14 @@ DefineIndex(Oid tableId,
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("index creation on system columns is not supported")));
-
-
-		if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-			ereport(ERROR,
-					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-					stmt->primary ?
-					errmsg("primary keys on virtual generated columns are not supported") :
-					stmt->isconstraint ?
-					errmsg("unique constraints on virtual generated columns are not supported") :
-					errmsg("indexes on virtual generated columns are not supported"));
 	}
 
 	/*
-	 * Also check for system and generated columns used in expressions or
-	 * predicates.
+	 * Also check for system columns used in expressions or predicates.
 	 */
 	if (indexInfo->ii_Expressions || indexInfo->ii_Predicate)
 	{
 		Bitmapset  *indexattrs = NULL;
-		int			j;
 
 		pull_varattnos((Node *) indexInfo->ii_Expressions, 1, &indexattrs);
 		pull_varattnos((Node *) indexInfo->ii_Predicate, 1, &indexattrs);
@@ -1146,24 +1171,6 @@ DefineIndex(Oid tableId,
 						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 						 errmsg("index creation on system columns is not supported")));
 		}
-
-		/*
-		 * XXX Virtual generated columns in index expressions or predicates
-		 * could be supported, but it needs support in
-		 * RelationGetIndexExpressions() and RelationGetIndexPredicate().
-		 */
-		j = -1;
-		while ((j = bms_next_member(indexattrs, j)) >= 0)
-		{
-			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
-
-			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-				ereport(ERROR,
-						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-						 stmt->isconstraint ?
-						 errmsg("unique constraints on virtual generated columns are not supported") :
-						 errmsg("indexes on virtual generated columns are not supported")));
-		}
 	}
 
 	/* Is index safe for others to ignore?  See set_indexsafe_procflags() */
@@ -1307,6 +1314,7 @@ DefineIndex(Oid tableId,
 			bool		invalidate_parent = false;
 			Relation	parentIndex;
 			TupleDesc	parentDesc;
+			bool		parent_idx_virtual;
 
 			/*
 			 * Report the total number of partitions at the start of the
@@ -1353,6 +1361,8 @@ DefineIndex(Oid tableId,
 			parentIndex = index_open(indexRelationId, lockmode);
 			indexInfo = BuildIndexInfo(parentIndex);
 
+			parent_idx_virtual = IsIndexOverVirtualGenerated(indexInfo);
+
 			parentDesc = RelationGetDescr(rel);
 
 			/*
@@ -1412,6 +1422,14 @@ DefineIndex(Oid tableId,
 										  parentDesc,
 										  false);
 
+				/*
+				 * child don't have any index, but parent have index over
+				 * virtual generated column. We need ensure the indexed
+				 * generated expression on parent match with child.
+				*/
+				if (childidxs == NIL && parent_idx_virtual)
+					check_generated_indexattrs(indexInfo, rel, childrel, attmap, false);
+
 				foreach(cell, childidxs)
 				{
 					Oid			cldidxid = lfirst_oid(cell);
@@ -1481,6 +1499,23 @@ DefineIndex(Oid tableId,
 						index_close(cldidx, NoLock);
 						break;
 					}
+					else
+					{
+						bool	cldidx_virtual;
+						bool	index_virtual;
+						index_virtual = IsIndexOverVirtualGenerated(indexInfo);
+						cldidx_virtual = IsIndexOverVirtualGenerated(cldIdxInfo);
+
+						/* should fail. otherwise pg_dump won't work */
+						if (index_virtual || cldidx_virtual)
+							ereport(ERROR,
+									errcode(ERRCODE_WRONG_OBJECT_TYPE),
+									errmsg("cannot create index on partitioned table \"%s\"",
+										   RelationGetRelationName(rel)),
+									errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+											  RelationGetRelationName(rel),
+											  RelationGetRelationName(childrel)));
+					}
 
 					index_close(cldidx, lockmode);
 				}
@@ -1857,6 +1892,72 @@ CheckPredicate(Expr *predicate)
 				 errmsg("functions in index predicate must be marked IMMUTABLE")));
 }
 
+/*
+ * rel_idx_info: the IndexInfo that is associated with rel.
+ * "childrel": the relation to be attached to "rel" or the child of "rel".
+ * attmap: Attribute mapping between childrel and rel.
+ * is_attach: is this command of ALTER TABLE ATTACH PARTITION
+ *
+ * Use build_attrmap_by_name(childrel, rel) to build the attmap.
+*/
+void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+								Relation rel,
+								Relation childrel,
+								const AttrMap *attmap,
+								bool is_attach)
+{
+	int	i;
+
+	/* if parent have virtual generated column, child must also have */
+	Assert(rel->rd_att->constr->has_generated_virtual);
+	Assert(childrel->rd_att->constr->has_generated_virtual);
+
+	for (i = 0; i < rel_idx_info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(rel_idx_info->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			Node	   *node_rel;
+			Node	   *node_attach;
+			AttrNumber	attno;
+			bool		found_whole_row;
+
+			attno	= rel_idx_info->ii_IndexAttrGeneratedNumbers[i];
+
+			node_rel = 	build_generation_expression(rel, attno);
+			node_rel = map_variable_attnos(node_rel,
+										   1, 0,
+										   attmap,
+										   InvalidOid, &found_whole_row);
+			if (found_whole_row)
+				elog(ERROR, "Index contains a whole-row table reference");
+
+			node_attach = build_generation_expression(childrel,
+													  attmap->attnums[attno - 1]);
+
+			if (!equal(node_rel, node_attach))
+			{
+				if (is_attach)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+								   RelationGetRelationName(childrel),
+								   RelationGetRelationName(rel));
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+				else
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot create index on partitioned table \"%s\"",
+								   RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+			}
+		}
+	}
+}
+
 /*
  * Compute per-index-column information, including indexed column numbers
  * or index expressions, opclasses and their options. Note, all output vectors
@@ -1881,6 +1982,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 				  bool amcanorder,
 				  bool isconstraint,
 				  bool iswithoutoverlaps,
+				  bool is_primary,
 				  Oid ddl_userid,
 				  int ddl_sec_context,
 				  int *ddl_save_nestlevel)
@@ -1891,6 +1993,28 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 	int			nkeycols = indexInfo->ii_NumIndexKeyAttrs;
 	Oid			save_userid;
 	int			save_sec_context;
+	Relation	rel;
+	TupleDesc	reltupldesc;
+	List		*virtual_generated = NIL;
+
+	rel	= table_open(relId, NoLock);
+	reltupldesc = RelationGetDescr(rel);
+
+	/*
+	 * currently, we do not support virtual generated columns over expression
+	 * indexes.  we accumulate the attribute number of virtual generated columns
+	 * so we can verify it later.
+	*/
+	if (reltupldesc->constr && reltupldesc->constr->has_generated_virtual)
+	{
+		for (int i = 0; i < reltupldesc->natts; i++)
+		{
+			Form_pg_attribute attr = TupleDescAttr(reltupldesc, i);
+
+			if (attr->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				virtual_generated = lappend_int(virtual_generated, attr->attnum);
+		}
+	}
 
 	/* Allocate space for exclusion operator info, if needed */
 	if (exclusionOpNames)
@@ -1933,6 +2057,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 		IndexElem  *attribute = (IndexElem *) lfirst(lc);
 		Oid			atttype;
 		Oid			attcollation;
+		char		attgenerated = '\0';
 
 		/*
 		 * Process the column-or-expression to be indexed.
@@ -1942,6 +2067,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			/* Simple index attribute */
 			HeapTuple	atttuple;
 			Form_pg_attribute attform;
+			AttrNumber	attnum;
 
 			Assert(attribute->expr == NULL);
 			atttuple = SearchSysCacheAttName(relId, attribute->name);
@@ -1960,10 +2086,17 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 									attribute->name)));
 			}
 			attform = (Form_pg_attribute) GETSTRUCT(atttuple);
+			attnum = attform->attnum;
 			indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
 			atttype = attform->atttypid;
 			attcollation = attform->attcollation;
+			attgenerated = attform->attgenerated;
 			ReleaseSysCache(atttuple);
+
+			if (attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				compute_generated_indexattrs(indexInfo, rel, is_primary, attn, attnum);
+			else
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 		}
 		else
 		{
@@ -1986,18 +2119,42 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			while (IsA(expr, CollateExpr))
 				expr = (Node *) ((CollateExpr *) expr)->arg;
 
+			if (!IsA(expr, Var))
+			{
+				Bitmapset  *idxattrs = NULL;
+				int			j = -1;
+
+				pull_varattnos(expr, 1, &idxattrs);
+				while ((j = bms_next_member(idxattrs, j)) >= 0)
+				{
+					AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+					if (list_member_int(virtual_generated, attno))
+						ereport(ERROR,
+								errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+								errmsg("expression index over virtual generated columns are not supported"));
+				}
+			}
+
 			if (IsA(expr, Var) &&
 				((Var *) expr)->varattno != InvalidAttrNumber)
 			{
+				int			attnum = ((Var *) expr)->varattno;
+
 				/*
 				 * User wrote "(column)" or "(column COLLATE something)".
 				 * Treat it like simple attribute anyway.
 				 */
-				indexInfo->ii_IndexAttrNumbers[attn] = ((Var *) expr)->varattno;
+				indexInfo->ii_IndexAttrNumbers[attn] = attnum;
+
+				if (list_member_int(virtual_generated, attnum))
+					compute_generated_indexattrs(indexInfo, rel, is_primary, attn, attnum);
+				else
+					indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 			}
 			else
 			{
 				indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* marks expression */
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 				indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
 													expr);
 
@@ -2248,6 +2405,78 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 
 		attn++;
 	}
+	table_close(rel, NoLock);
+}
+
+/*
+ * indexInfo: this IndexInfo to be build.
+ * rel: the relation this indexInfo is based on.
+ * is_primary: is this index a primary key.
+ * attn: indices of the index key attribute, 0 based.
+ * attnum: virtual generated column attribute number.
+*/
+static void
+compute_generated_indexattrs(IndexInfo *indexInfo, Relation rel,
+							 bool is_primary, int attn, int attnum)
+{
+	Node	   *node;
+	Bitmapset  *genattrs = NULL;
+
+	if (is_primary)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("primary keys on virtual generated columns are not supported"));
+
+	if (indexInfo->ii_Unique)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("unique constraints on virtual generated columns are not supported"));
+
+	if (attn >= indexInfo->ii_NumIndexKeyAttrs)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("virtual generated column are not supported in index included columns"));
+
+	/* Fetch the GENERATED AS expression tree */
+	node = build_generation_expression(rel, attnum);
+
+	/*
+	 * if the generation expression just reference another Var node, then set
+	 * ii_IndexAttrNumbers to that Var->varattno.
+	*/
+	if (IsA(node, Var))
+	{
+		Var		   *var = (Var *) node;
+
+		Assert(var->varattno > 0);
+		indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+	}
+	else
+	{
+		/*
+		 * Strip any top-level COLLATE clause.  This ensures that we treat
+		 * "x COLLATE y" and "(x COLLATE y)" alike.
+		*/
+		while (IsA(node, CollateExpr))
+			node = (Node *) ((CollateExpr *) node)->arg;
+
+		/* generation expression are immutable, so this unlikely to happen */
+		if (contain_mutable_functions_after_planning((Expr *) node))
+			elog(ERROR,"functions in index expression must be marked IMMUTABLE");
+
+		pull_varattnos(node, 1, &genattrs);
+
+		if (genattrs == NULL)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("can not create index based on variable free generation expression"));
+
+		indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* mark as expression index */
+		indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
+											node);
+	}
+
+	indexInfo->ii_IndexAttrGeneratedNumbers[attn] = attnum;
 }
 
 /*
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index 686f1850cab..ea92b91763e 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -8652,6 +8652,32 @@ ATExecSetExpression(AlteredTableInfo *tab, Relation rel, const char *colName,
 		 */
 		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
 	}
+	else
+	{
+		Assert(attgenerated == ATTRIBUTE_GENERATED_VIRTUAL);
+
+		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
+
+		/*
+		 * Changing the generation expression of the virtual generated column
+		 * does not require table rewrite. However, if an index is built on top
+		 * of it, table rewrite is necessary. So in phase 3, index_rebuild can
+		 * successfully rebuild the index based on the new generation expression
+		*/
+		if (tab->changedIndexOids != NIL)
+		{
+			rewrite = true;
+
+			/*
+			 * Clear all the missing values if we're rewriting the table, since
+			 * this renders them pointless.
+			*/
+			RelationClearMissing(rel);
+
+			/* make sure we don't conflict with later attribute modifications */
+			CommandCounterIncrement();
+		}
+	}
 
 	/*
 	 * Drop the dependency records of the GENERATED expression, in particular
@@ -14755,6 +14781,14 @@ ATExecAlterColumnType(AlteredTableInfo *tab, Relation rel,
 	 */
 	RememberAllDependentForRebuilding(tab, AT_AlterColumnType, rel, attnum, colName);
 
+	/*
+	 * tell phase3 do table rewrite if there are any index based on virtual
+	 * generated colum.
+	*/
+	if (attTup->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL &&
+		tab->changedIndexOids != NIL)
+		tab->rewrite |= AT_REWRITE_COLUMN_REWRITE;
+
 	/*
 	 * Now scan for dependencies of this column on other things.  The only
 	 * things we should find are the dependency on the column datatype and
@@ -20521,6 +20555,7 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 		AttrMap    *attmap;
 		bool		found = false;
 		Oid			constraintOid;
+		bool		parent_idx_virtual;
 
 		/*
 		 * Ignore indexes in the partitioned table other than partitioned
@@ -20534,9 +20569,19 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 
 		/* construct an indexinfo to compare existing indexes against */
 		info = BuildIndexInfo(idxRel);
+		parent_idx_virtual = IsIndexOverVirtualGenerated(info);
 		attmap = build_attrmap_by_name(RelationGetDescr(attachrel),
 									   RelationGetDescr(rel),
 									   false);
+
+		/*
+		 * The attach partition don't have index, but parent have index over
+		 * virtual generated column. We need ensure generated expression on
+		 * parent that index was based on it match with attach partition.
+		*/
+		if (attachRelIdxs == NIL && parent_idx_virtual)
+			check_generated_indexattrs(info, rel, attachrel, attmap, true);
+
 		constraintOid = get_relation_idx_constraint_oid(RelationGetRelid(rel), idx);
 
 		/*
@@ -20595,6 +20640,22 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 				CommandCounterIncrement();
 				break;
 			}
+			else
+			{
+				bool		attach_idx_virtual;
+				attach_idx_virtual = IsIndexOverVirtualGenerated(attachInfos[i]);
+
+				/* should fail. different index definition cannot merge */
+				if (attach_idx_virtual || parent_idx_virtual)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+									RelationGetRelationName(attachrel),
+									RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									RelationGetRelationName(rel),
+									RelationGetRelationName(attachrel)));
+			}
 		}
 
 		/*
diff --git a/src/backend/parser/parse_utilcmd.c b/src/backend/parser/parse_utilcmd.c
index 62015431fdf..3c7af2605b3 100644
--- a/src/backend/parser/parse_utilcmd.c
+++ b/src/backend/parser/parse_utilcmd.c
@@ -1681,6 +1681,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	Form_pg_am	amrec;
 	oidvector  *indcollation;
 	oidvector  *indclass;
+	int2vector	*indgenkey;
 	IndexStmt  *index;
 	List	   *indexprs;
 	ListCell   *indexpr_item;
@@ -1688,6 +1689,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	int			keyno;
 	Oid			keycoltype;
 	Datum		datum;
+	Datum		indgenkeyDatum;
 	bool		isnull;
 
 	if (constraintOid)
@@ -1723,6 +1725,11 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	datum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx, Anum_pg_index_indclass);
 	indclass = (oidvector *) DatumGetPointer(datum);
 
+	/* Extract indattrgenerated from the pg_index tuple */
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* Begin building the IndexStmt */
 	index = makeNode(IndexStmt);
 	index->relation = heapRel;
@@ -1854,13 +1861,29 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	{
 		IndexElem  *iparam;
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Form_pg_attribute attr = TupleDescAttr(RelationGetDescr(source_idx),
 											   keyno);
 		int16		opt = source_idx->rd_indoption[keyno];
 
 		iparam = makeNode(IndexElem);
 
-		if (AttributeNumberIsValid(attnum))
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * index over virtual generated column was converted into a
+			 * expression index, but we need restore the original attribute
+			 * number for recreate it.
+			*/
+			char	   *virtual_attname;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			keycoltype = get_atttype(indrelid, gennum);
+
+			iparam->name = virtual_attname;
+			iparam->expr = NULL;
+		}
+		else if (AttributeNumberIsValid(attnum))
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/backend/utils/adt/ruleutils.c b/src/backend/utils/adt/ruleutils.c
index 9e90acedb91..ae3db86294d 100644
--- a/src/backend/utils/adt/ruleutils.c
+++ b/src/backend/utils/adt/ruleutils.c
@@ -1290,9 +1290,11 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	Datum		indcollDatum;
 	Datum		indclassDatum;
 	Datum		indoptionDatum;
+	Datum		indgenkeyDatum;
 	oidvector  *indcollation;
 	oidvector  *indclass;
 	int2vector *indoption;
+	int2vector *indgenkey;
 	StringInfoData buf;
 	char	   *str;
 	char	   *sep;
@@ -1325,6 +1327,10 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 											Anum_pg_index_indoption);
 	indoption = (int2vector *) DatumGetPointer(indoptionDatum);
 
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/*
 	 * Fetch the pg_class tuple of the index relation
 	 */
@@ -1398,6 +1404,7 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	for (keyno = 0; keyno < idxrec->indnatts; keyno++)
 	{
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Oid			keycoltype;
 		Oid			keycolcollation;
 
@@ -1418,7 +1425,26 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 			appendStringInfoString(&buf, sep);
 		sep = ", ";
 
-		if (attnum != 0)
+		if (!AttributeNumberIsValid(attnum) && AttributeNumberIsValid(gennum))
+			indexpr_item = lnext(indexprs, indexpr_item);
+
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * This index is created on virtual generated column
+			*/
+			char	   *virtual_attname;
+			int32		geneycoltypmod;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			if (!colno || colno == keyno + 1)
+				appendStringInfoString(&buf, quote_identifier(virtual_attname));
+
+			get_atttypetypmodcoll(indrelid, gennum,
+								  &keycoltype, &geneycoltypmod,
+								  &keycolcollation);
+		}
+		else if (attnum != 0)
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/include/catalog/index.h b/src/include/catalog/index.h
index 4daa8bef5ee..a7e93f3a107 100644
--- a/src/include/catalog/index.h
+++ b/src/include/catalog/index.h
@@ -126,6 +126,7 @@ extern IndexInfo *BuildIndexInfo(Relation index);
 
 extern IndexInfo *BuildDummyIndexInfo(Relation index);
 
+extern bool IsIndexOverVirtualGenerated(const IndexInfo *info);
 extern bool CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 							 const Oid *collations1, const Oid *collations2,
 							 const Oid *opfamilies1, const Oid *opfamilies2,
@@ -175,6 +176,11 @@ extern void RestoreReindexState(const void *reindexstate);
 
 extern void IndexSetParentIndex(Relation partitionIdx, Oid parentOid);
 
+extern void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+									   Relation rel,
+									   Relation childrel,
+									   const AttrMap *attmap,
+									   bool	is_attach);
 
 /*
  * itemptr_encode - Encode ItemPointer as int64/int8
diff --git a/src/include/catalog/pg_index.h b/src/include/catalog/pg_index.h
index 4392b9d221d..7ed74a593a4 100644
--- a/src/include/catalog/pg_index.h
+++ b/src/include/catalog/pg_index.h
@@ -54,6 +54,7 @@ CATALOG(pg_index,2610,IndexRelationId) BKI_SCHEMA_MACRO
 	oidvector	indclass BKI_LOOKUP(pg_opclass) BKI_FORCE_NOT_NULL; /* opclass identifiers */
 	int2vector	indoption BKI_FORCE_NOT_NULL;	/* per-column flags
 												 * (AM-specific meanings) */
+	int2vector	indattrgenerated BKI_FORCE_NOT_NULL; /* the attribute of virtual generated column? */
 	pg_node_tree indexprs;		/* expression trees for index attributes that
 								 * are not simple column references; one for
 								 * each zero entry in indkey[] */
diff --git a/src/include/nodes/execnodes.h b/src/include/nodes/execnodes.h
index 5b6cadb5a6c..ea4240b36e4 100644
--- a/src/include/nodes/execnodes.h
+++ b/src/include/nodes/execnodes.h
@@ -196,6 +196,7 @@ typedef struct IndexInfo
 	int			ii_NumIndexAttrs;	/* total number of columns in index */
 	int			ii_NumIndexKeyAttrs;	/* number of key columns in index */
 	AttrNumber	ii_IndexAttrNumbers[INDEX_MAX_KEYS];
+	AttrNumber	ii_IndexAttrGeneratedNumbers[INDEX_MAX_KEYS]; /* XXX more better comments */
 	List	   *ii_Expressions; /* list of Expr */
 	List	   *ii_ExpressionsState;	/* list of ExprState */
 	List	   *ii_Predicate;	/* list of Expr */
diff --git a/src/test/regress/expected/fast_default.out b/src/test/regress/expected/fast_default.out
index ccbcdf8403f..ef19f667cc1 100644
--- a/src/test/regress/expected/fast_default.out
+++ b/src/test/regress/expected/fast_default.out
@@ -70,6 +70,14 @@ NOTICE:  rewriting table has_volatile for reason 4
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 NOTICE:  rewriting table has_volatile for reason 2
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+NOTICE:  rewriting table has_volatile for reason 2
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
+NOTICE:  rewriting table has_volatile for reason 4
 -- Test a large sample of different datatypes
 CREATE TABLE T(pk INT NOT NULL PRIMARY KEY, c_int INT DEFAULT 1);
 SELECT set('t');
diff --git a/src/test/regress/expected/generated_virtual.out b/src/test/regress/expected/generated_virtual.out
index 26bbe1e9c31..25b84564b1c 100644
--- a/src/test/regress/expected/generated_virtual.out
+++ b/src/test/regress/expected/generated_virtual.out
@@ -742,30 +742,175 @@ ERROR:  primary keys on virtual generated columns are not supported
 --INSERT INTO gtest22b VALUES (2);
 --INSERT INTO gtest22b VALUES (2);
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
---CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
---CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
---SELECT * FROM gtest22c WHERE b * 3 = 6;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error. partitioned and partition have different generation expression, can not
+--build index on it.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ERROR:  cannot create index on partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart3"
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+--error. index over different generation expression should not allowed
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ERROR:  cannot attach table "gtestpart1" as partition of partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart1"
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+       relid       |    parentrelid    | isleaf | level 
+-------------------+-------------------+--------+-------
+ gtestparted_a_idx |                   | f      |     0
+ gtestpart2_a_idx  | gtestparted_a_idx | t      |     1
+(2 rows)
+
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+ERROR:  cannot attach index "gtestpart2_a_idx_copy" as a partition of index "gtestparted_a_idx"
+DETAIL:  Another index is already attached for partition "gtestpart2".
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+         relid         |     parentrelid     | isleaf | level 
+-----------------------+---------------------+--------+-------
+ gtestparted_a_idx_1   |                     | f      |     0
+ gtestpart2_a_idx_copy | gtestparted_a_idx_1 | t      |     1
+(2 rows)
+
+--create table like should work just fine
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+           Table "generated_virtual_tests.gtestparted_like"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+ a      | integer |           |          | generated always as (c + 1)
+Indexes:
+    "gtestparted_like_a_idx" btree (a)
+    "gtestparted_like_a_idx1" btree (a)
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL
+                      ,c int GENERATED ALWAYS AS (11) VIRTUAL
+                      ,d int GENERATED ALWAYS AS (a *3) VIRTUAL
+                      ,e int4range GENERATED ALWAYS AS (int4range(a, a+10)) VIRTUAL
+                      ,f int GENERATED ALWAYS AS (a) VIRTUAL);
+CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+--variable free generation expression have no pratical usage, so error out.
+CREATE INDEX gtest22c_c_idx ON gtest22c (c);
+ERROR:  can not create index based on variable free generation expression
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_idx ON gtest22c USING gist(e);
+--error. include columns are not supported.
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (b,c);
+ERROR:  virtual generated column are not supported in index included columns
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (f);
+ERROR:  virtual generated column are not supported in index included columns
+-- CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
+-- CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
+\d gtest22c
+                        Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                  Default                   
+--------+-----------+-----------+----------+--------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e      | int4range |           |          | generated always as (int4range(a, a + 10))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e_idx" gist (e)
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4;
+ a | b | c  | d |   e    | f 
+---+---+----+---+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_d_idx on gtest22c
+   Index Cond: ((a * 3) = 6)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE d = 6;
+ a | b | c  | d |   e    | f 
+---+---+----+---+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12;
+                     QUERY PLAN                     
+----------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e_idx on gtest22c
+         Index Cond: (int4range(a, (a + 10)) @> 12)
+(3 rows)
+
+SELECT count(*) from gtest22c where e @> 12;
+ count 
+-------
+     2
+(1 row)
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
+               Table "generated_virtual_tests.gtest22c"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ a      | integer |           |          | 
+ b      | integer |           |          | generated always as (a * 2)
+ c      | integer |           |          | generated always as (11)
+ d      | integer |           |          | generated always as (a * 3)
+ f      | integer |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b)
+    "gtest22c_d_idx" hash (d)
+
+-- EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
+-- SELECT * FROM gtest22c WHERE b * 3 = 6;
+-- EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
+-- SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 4) = 8)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 8;
+ a | b | c  | d | f 
+---+---+----+---+---
+ 2 | 8 | 11 | 6 | 2
+(1 row)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
 --INSERT INTO gtest23a VALUES (1, 11), (2, 22), (3, 33);
@@ -1587,3 +1732,17 @@ select * from gtest32 t group by grouping sets (a, b, c, d) having c = 20;
 (1 row)
 
 drop table gtest32;
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
+ indrelid | attnum | attname | attgenerated 
+----------+--------+---------+--------------
+(0 rows)
+
diff --git a/src/test/regress/sql/fast_default.sql b/src/test/regress/sql/fast_default.sql
index 068dd0bc8aa..b39e76bcfc3 100644
--- a/src/test/regress/sql/fast_default.sql
+++ b/src/test/regress/sql/fast_default.sql
@@ -77,6 +77,12 @@ ALTER TABLE has_volatile ALTER COLUMN col1 SET DATA TYPE float8,
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
 
 
 -- Test a large sample of different datatypes
diff --git a/src/test/regress/sql/generated_virtual.sql b/src/test/regress/sql/generated_virtual.sql
index 13cfbd76859..7fbe14d1711 100644
--- a/src/test/regress/sql/generated_virtual.sql
+++ b/src/test/regress/sql/generated_virtual.sql
@@ -1,6 +1,4 @@
 -- keep these tests aligned with generated_stored.sql
-
-
 CREATE SCHEMA generated_virtual_tests;
 GRANT USAGE ON SCHEMA generated_virtual_tests TO PUBLIC;
 SET search_path = generated_virtual_tests;
@@ -391,32 +389,86 @@ CREATE TABLE gtest22b (a int, b int GENERATED ALWAYS AS (a / 2) VIRTUAL, PRIMARY
 --INSERT INTO gtest22b VALUES (2);
 
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
---CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
---CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
-
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
---SELECT * FROM gtest22c WHERE b * 3 = 6;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
-
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error. partitioned and partition have different generation expression, can not
+--build index on it.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+
+--error. index over different generation expression should not allowed
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+
+
+--create table like should work just fine
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL
+                      ,c int GENERATED ALWAYS AS (11) VIRTUAL
+                      ,d int GENERATED ALWAYS AS (a *3) VIRTUAL
+                      ,e int4range GENERATED ALWAYS AS (int4range(a, a+10)) VIRTUAL
+                      ,f int GENERATED ALWAYS AS (a) VIRTUAL);
+CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+--variable free generation expression have no pratical usage, so error out.
+CREATE INDEX gtest22c_c_idx ON gtest22c (c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_idx ON gtest22c USING gist(e);
+--error. include columns are not supported.
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (b,c);
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (f);
+
+-- CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
+-- CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
+\d gtest22c
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+SELECT * FROM gtest22c WHERE b = 4;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+SELECT * FROM gtest22c WHERE d = 6;
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12;
+SELECT count(*) from gtest22c where e @> 12;
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
+
+-- EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
+-- SELECT * FROM gtest22c WHERE b * 3 = 6;
+-- EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
+-- SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
+
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+SELECT * FROM gtest22c WHERE b = 8;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
@@ -828,3 +880,14 @@ select * from gtest32 t group by grouping sets (a, b, c, d) having c = 20;
 select * from gtest32 t group by grouping sets (a, b, c, d) having c = 20;
 
 drop table gtest32;
+
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
-- 
2.34.1

From c3f39858798c27de7afdf5156c4174217920c676 Mon Sep 17 00:00:00 2001
From: jian he <jian.universality@gmail.com>
Date: Tue, 15 Apr 2025 16:28:46 +0800
Subject: [PATCH v3 1/1] index on virtual generated column

* internally such index transformed into expression index.
  For example, an index on (b int GENERATED ALWAYS AS (a * 2) VIRTUAL)
  internal representation: an expression index on ((a * 2)).
* in pageinspect module, add some test to check the index content of virtual generated column.
* primary key, unique index over virtual generated column are not supported.
* expression index and predicate index over virtual generated columns are
  currently not supported.
* virtual generated column can not be in "include column"
* all types of indexes are supported, hash index, gist index regress test added.
* To support ALTER TABLE SET EXPRESSION, in pg_index, we need to track the original
  virtual generated column attribute number, so ALTER TABLE SET EXPRESSION can
  identify which index needs to be rebuilt.
* ALTER COLUMN SET DATA TYPE will also cause table rewrite, so we really
  need to track the virtual generated column attribute number that index was built on.

* if the partitioned table and partition both have an index, then the index over the virtual
  generated column should be the same expression. For example, the following last
  command should error out.

    CREATE TABLE parted (b integer,c integer,a integer GENERATED ALWAYS AS (c+1)) PARTITION BY RANGE (b);
    CREATE TABLE part (b integer,c integer,a integer GENERATED ALWAYS AS (c));
    create index on part(a);
    create index on parted(a);
    alter table parted ATTACH partition part for values from (1) to (10);

discussion: https://postgr.es/m/CACJufxGao-cypdNhifHAdt8jHfK6-HX=tRBovBkgRuxw063GaA@mail.gmail.com
commitfest entry: https://commitfest.postgresql.org/patch/5667/
---
 contrib/pageinspect/expected/btree.out        |  33 ++
 contrib/pageinspect/sql/btree.sql             |  21 ++
 doc/src/sgml/catalogs.sgml                    |  15 +
 src/backend/catalog/index.c                   |  69 ++++
 src/backend/commands/indexcmds.c              | 301 +++++++++++++++---
 src/backend/commands/tablecmds.c              |  61 ++++
 src/backend/parser/parse_utilcmd.c            |  25 +-
 src/backend/utils/adt/ruleutils.c             |  28 +-
 src/include/catalog/index.h                   |   6 +
 src/include/catalog/pg_index.h                |   1 +
 src/include/nodes/execnodes.h                 |   1 +
 src/test/regress/expected/fast_default.out    |   8 +
 .../regress/expected/generated_virtual.out    | 187 ++++++++++-
 src/test/regress/sql/fast_default.sql         |   6 +
 src/test/regress/sql/generated_virtual.sql    |  94 +++++-
 15 files changed, 788 insertions(+), 68 deletions(-)

diff --git a/contrib/pageinspect/expected/btree.out b/contrib/pageinspect/expected/btree.out
index 0aa5d73322f..56d57848cf7 100644
--- a/contrib/pageinspect/expected/btree.out
+++ b/contrib/pageinspect/expected/btree.out
@@ -183,6 +183,39 @@ tids       |
 
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 ERROR:  block number 2 is out of range for relation "test1_a_idx"
+---test index over virtual generated column
+CREATE TABLE test3 (a int8, b int4range, c int8 generated always as (a+1) virtual);
+INSERT INTO test3 VALUES (72057594037927936, '[0,1)');
+CREATE INDEX test3_a_idx ON test3 USING btree (c);
+SELECT * FROM bt_page_items('test3_a_idx', 1);
+-[ RECORD 1 ]-----------------------
+itemoffset | 1
+ctid       | (0,1)
+itemlen    | 16
+nulls      | f
+vars       | f
+data       | 01 00 00 00 00 00 00 01
+dead       | f
+htid       | (0,1)
+tids       | 
+
+--expect zero row.
+SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1))
+EXCEPT ALL
+SELECT * FROM bt_page_items(get_raw_page('test3_a_idx', 1));
+(0 rows)
+
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b ON test4 USING btree (b);
+CREATE INDEX test4_c ON test4 USING btree (c);
+ALTER TABLE test4 alter column b set data type text;
+---should return zero row.
+SELECT * FROM bt_page_items('test4_b', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_c', 1);
+(0 rows)
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/contrib/pageinspect/sql/btree.sql b/contrib/pageinspect/sql/btree.sql
index 102ebdefe3c..d3392c11d5f 100644
--- a/contrib/pageinspect/sql/btree.sql
+++ b/contrib/pageinspect/sql/btree.sql
@@ -32,6 +32,27 @@ SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 0));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 
+---test index over virtual generated column
+CREATE TABLE test3 (a int8, b int4range, c int8 generated always as (a+1) virtual);
+INSERT INTO test3 VALUES (72057594037927936, '[0,1)');
+CREATE INDEX test3_a_idx ON test3 USING btree (c);
+SELECT * FROM bt_page_items('test3_a_idx', 1);
+
+--expect zero row.
+SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1))
+EXCEPT ALL
+SELECT * FROM bt_page_items(get_raw_page('test3_a_idx', 1));
+
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b ON test4 USING btree (b);
+CREATE INDEX test4_c ON test4 USING btree (c);
+ALTER TABLE test4 alter column b set data type text;
+---should return zero row.
+SELECT * FROM bt_page_items('test4_b', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_c', 1);
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/doc/src/sgml/catalogs.sgml b/doc/src/sgml/catalogs.sgml
index cbd4e40a320..d7ee73373f5 100644
--- a/doc/src/sgml/catalogs.sgml
+++ b/doc/src/sgml/catalogs.sgml
@@ -4595,6 +4595,21 @@ SCRAM-SHA-256$<replaceable>&lt;iteration count&gt;</replaceable>:<replaceable>&l
       </para></entry>
      </row>
 
+     <row>
+      <entry role="catalog_table_entry"><para role="column_definition">
+       <structfield>indattrgenerated</structfield> <type>int2vector</type>
+       (references <link linkend="catalog-pg-attribute"><structname>pg_attribute</structname></link>.<structfield>attnum</structfield>)
+      </para>
+      <para>
+       This is an array of <structfield>indnatts</structfield> values that
+       indicate which table virtual generated columns this index indexes.
+       For example, a value of <literal>1 3</literal> would mean that the first
+       and the third table columns of this index entries are virtual generated
+       column. A zero in this array indicates that the corresponding index
+       attribute is not virtual generated column reference.
+      </para></entry>
+     </row>
+
      <row>
       <entry role="catalog_table_entry"><para role="column_definition">
        <structfield>indexprs</structfield> <type>pg_node_tree</type>
diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index 739a92bdcc1..dd379c2b79c 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -584,6 +584,12 @@ UpdateIndexRelation(Oid indexoid,
 	Relation	pg_index;
 	HeapTuple	tuple;
 	int			i;
+	int2vector *indgenkey;
+	int16	   *colgenerated;
+
+	colgenerated = palloc_array(int16, indexInfo->ii_NumIndexAttrs);
+	for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+		colgenerated[i] = indexInfo->ii_IndexAttrGeneratedNumbers[i];
 
 	/*
 	 * Copy the index key, opclass, and indoption info into arrays (should we
@@ -596,6 +602,7 @@ UpdateIndexRelation(Oid indexoid,
 	indclass = buildoidvector(opclassOids, indexInfo->ii_NumIndexKeyAttrs);
 	indoption = buildint2vector(coloptions, indexInfo->ii_NumIndexKeyAttrs);
 
+	indgenkey = buildint2vector(colgenerated, indexInfo->ii_NumIndexAttrs);
 	/*
 	 * Convert the index expressions (if any) to a text datum
 	 */
@@ -653,6 +660,7 @@ UpdateIndexRelation(Oid indexoid,
 	values[Anum_pg_index_indcollation - 1] = PointerGetDatum(indcollation);
 	values[Anum_pg_index_indclass - 1] = PointerGetDatum(indclass);
 	values[Anum_pg_index_indoption - 1] = PointerGetDatum(indoption);
+	values[Anum_pg_index_indattrgenerated - 1] = PointerGetDatum(indgenkey);
 	values[Anum_pg_index_indexprs - 1] = exprsDatum;
 	if (exprsDatum == (Datum) 0)
 		nulls[Anum_pg_index_indexprs - 1] = true;
@@ -1134,6 +1142,28 @@ index_create(Relation heapRelation,
 				}
 			}
 
+			/*
+			 * Internally, we convert index of virtual generation column into an
+			 * expression index. For example, if column 'b' is defined as (b INT
+			 * GENERATED ALWAYS AS (a * 2) VIRTUAL) then index over 'b' would
+			 * transformed into an expression index as ((a * 2)). As a result,
+			 * the pg_depend refobjsubid does not retain the original attribute
+			 * number of the virtual generated column. But we need rebuild any
+			 * index that was build on virtual generated column. so we need auto
+			 * dependencies on referenced virtual generated columns.
+			*/
+			for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+			{
+				if (indexInfo->ii_IndexAttrGeneratedNumbers[i] != 0)
+				{
+					ObjectAddressSubSet(referenced, RelationRelationId,
+										heapRelationId,
+										indexInfo->ii_IndexAttrGeneratedNumbers[i]);
+					add_exact_object_address(&referenced, addrs);
+					have_simple_col = false;
+				}
+			}
+
 			/*
 			 * If there are no simply-referenced columns, give the index an
 			 * auto dependency on the whole table.  In most cases, this will
@@ -2428,9 +2458,12 @@ IndexInfo *
 BuildIndexInfo(Relation index)
 {
 	IndexInfo  *ii;
+	HeapTuple	ht_idx;
 	Form_pg_index indexStruct = index->rd_index;
 	int			i;
 	int			numAtts;
+	Datum		indgenkeyDatum;
+	int2vector *indgenkey;
 
 	/* check the number of keys, and copy attr numbers into the IndexInfo */
 	numAtts = indexStruct->indnatts;
@@ -2454,9 +2487,19 @@ BuildIndexInfo(Relation index)
 					   index->rd_indam->amsummarizing,
 					   indexStruct->indisexclusion && indexStruct->indisunique);
 
+	ht_idx = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(indexStruct->indexrelid));
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* fill in attribute numbers */
 	for (i = 0; i < numAtts; i++)
+	{
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
+		ii->ii_IndexAttrGeneratedNumbers[i] = indgenkey->values[i];
+	}
+
+	ReleaseSysCache(ht_idx);
 
 	/* fetch exclusion constraint info if any */
 	if (indexStruct->indisexclusion)
@@ -2523,6 +2566,23 @@ BuildDummyIndexInfo(Relation index)
 	return ii;
 }
 
+/*
+ * IndexOverVirtualGenerated
+ *		Return whether this index is built on virtual generated column.
+ */
+bool
+IsIndexOverVirtualGenerated(const IndexInfo *info)
+{
+	int			i;
+
+	for (i = 0; i < info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(info->ii_IndexAttrGeneratedNumbers[i]))
+			return true;
+	}
+	return false;
+}
+
 /*
  * CompareIndexInfo
  *		Return whether the properties of two indexes (in different tables)
@@ -2585,6 +2645,15 @@ CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 				return false;
 		}
 
+		if (AttributeNumberIsValid(info1->ii_IndexAttrGeneratedNumbers[i]) ||
+			AttributeNumberIsValid(info2->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			/* fail if index over virtual generated column attribute does not match */
+			if (attmap->attnums[info2->ii_IndexAttrGeneratedNumbers[i] - 1] !=
+				info1->ii_IndexAttrGeneratedNumbers[i])
+				return false;
+		}
+
 		/* collation and opfamily are not valid for included columns */
 		if (i >= info1->ii_NumIndexKeyAttrs)
 			continue;
diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 33c2106c17c..f36edaf5e38 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -54,6 +54,7 @@
 #include "parser/parse_utilcmd.h"
 #include "partitioning/partdesc.h"
 #include "pgstat.h"
+#include "rewrite/rewriteHandler.h"
 #include "rewrite/rewriteManip.h"
 #include "storage/lmgr.h"
 #include "storage/proc.h"
@@ -90,9 +91,15 @@ static void ComputeIndexAttrs(IndexInfo *indexInfo,
 							  bool amcanorder,
 							  bool isconstraint,
 							  bool iswithoutoverlaps,
+							  bool is_primary,
 							  Oid ddl_userid,
 							  int ddl_sec_context,
 							  int *ddl_save_nestlevel);
+static void compute_generated_indexattrs(IndexInfo *indexInfo,
+										 Relation rel,
+										 bool is_primary,
+										 int attn,
+										 int attnum);
 static char *ChooseIndexName(const char *tabname, Oid namespaceId,
 							 const List *colnames, const List *exclusionOpNames,
 							 bool primary, bool isconstraint);
@@ -182,6 +189,7 @@ CheckIndexCompatible(Oid oldId,
 					 bool isWithoutOverlaps)
 {
 	bool		isconstraint;
+	bool		is_primary;
 	Oid		   *typeIds;
 	Oid		   *collationIds;
 	Oid		   *opclassIds;
@@ -214,6 +222,12 @@ CheckIndexCompatible(Oid oldId,
 	 */
 	isconstraint = false;
 
+	/*
+	 * We can pretend is_primary = false unconditionally.  It only serves to
+	 * decide the text of an error message that should never happen for us.
+	 */
+	is_primary = false;
+
 	numberOfAttributes = list_length(attributeList);
 	Assert(numberOfAttributes > 0);
 	Assert(numberOfAttributes <= INDEX_MAX_KEYS);
@@ -254,7 +268,7 @@ CheckIndexCompatible(Oid oldId,
 					  coloptions, attributeList,
 					  exclusionOpNames, relationId,
 					  accessMethodName, accessMethodId,
-					  amcanorder, isconstraint, isWithoutOverlaps, InvalidOid,
+					  amcanorder, isconstraint, isWithoutOverlaps, is_primary, InvalidOid,
 					  0, NULL);
 
 	/* Get the soon-obsolete pg_index tuple. */
@@ -905,6 +919,31 @@ DefineIndex(Oid tableId,
 	if (stmt->whereClause)
 		CheckPredicate((Expr *) stmt->whereClause);
 
+	/* virtual generated column over predicate indexes are not supported */
+	if (RelationGetDescr(rel)->constr &&
+		RelationGetDescr(rel)->constr->has_generated_virtual &&
+		stmt->whereClause)
+	{
+		Bitmapset  *indexattrs_pred = NULL;
+		int			j;
+
+		pull_varattnos(stmt->whereClause, 1, &indexattrs_pred);
+
+		j = -1;
+		while ((j = bms_next_member(indexattrs_pred, j)) >= 0)
+		{
+			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+
+			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+			{
+				ereport(ERROR,
+						errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+						errmsg("partial index on virtual generated columns are not supported"));
+				break;
+			}
+		}
+	}
+
 	/*
 	 * Parse AM-specific options, convert to text array form, validate.
 	 */
@@ -941,6 +980,7 @@ DefineIndex(Oid tableId,
 					  stmt->excludeOpNames, tableId,
 					  accessMethodName, accessMethodId,
 					  amcanorder, stmt->isconstraint, stmt->iswithoutoverlaps,
+					  stmt->primary,
 					  root_save_userid, root_save_sec_context,
 					  &root_save_nestlevel);
 
@@ -1102,9 +1142,6 @@ DefineIndex(Oid tableId,
 	/*
 	 * We disallow indexes on system columns.  They would not necessarily get
 	 * updated correctly, and they don't seem useful anyway.
-	 *
-	 * Also disallow virtual generated columns in indexes (use expression
-	 * index instead).
 	 */
 	for (int i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
 	{
@@ -1114,26 +1151,14 @@ DefineIndex(Oid tableId,
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("index creation on system columns is not supported")));
-
-
-		if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-			ereport(ERROR,
-					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-					stmt->primary ?
-					errmsg("primary keys on virtual generated columns are not supported") :
-					stmt->isconstraint ?
-					errmsg("unique constraints on virtual generated columns are not supported") :
-					errmsg("indexes on virtual generated columns are not supported"));
 	}
 
 	/*
-	 * Also check for system and generated columns used in expressions or
-	 * predicates.
+	 * Also check for system columns used in expressions or predicates.
 	 */
 	if (indexInfo->ii_Expressions || indexInfo->ii_Predicate)
 	{
 		Bitmapset  *indexattrs = NULL;
-		int			j;
 
 		pull_varattnos((Node *) indexInfo->ii_Expressions, 1, &indexattrs);
 		pull_varattnos((Node *) indexInfo->ii_Predicate, 1, &indexattrs);
@@ -1146,24 +1171,6 @@ DefineIndex(Oid tableId,
 						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 						 errmsg("index creation on system columns is not supported")));
 		}
-
-		/*
-		 * XXX Virtual generated columns in index expressions or predicates
-		 * could be supported, but it needs support in
-		 * RelationGetIndexExpressions() and RelationGetIndexPredicate().
-		 */
-		j = -1;
-		while ((j = bms_next_member(indexattrs, j)) >= 0)
-		{
-			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
-
-			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-				ereport(ERROR,
-						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-						 stmt->isconstraint ?
-						 errmsg("unique constraints on virtual generated columns are not supported") :
-						 errmsg("indexes on virtual generated columns are not supported")));
-		}
 	}
 
 	/* Is index safe for others to ignore?  See set_indexsafe_procflags() */
@@ -1307,6 +1314,7 @@ DefineIndex(Oid tableId,
 			bool		invalidate_parent = false;
 			Relation	parentIndex;
 			TupleDesc	parentDesc;
+			bool		parent_idx_virtual;
 
 			/*
 			 * Report the total number of partitions at the start of the
@@ -1353,6 +1361,8 @@ DefineIndex(Oid tableId,
 			parentIndex = index_open(indexRelationId, lockmode);
 			indexInfo = BuildIndexInfo(parentIndex);
 
+			parent_idx_virtual = IsIndexOverVirtualGenerated(indexInfo);
+
 			parentDesc = RelationGetDescr(rel);
 
 			/*
@@ -1412,6 +1422,14 @@ DefineIndex(Oid tableId,
 										  parentDesc,
 										  false);
 
+				/*
+				 * child don't have any index, but parent have index over
+				 * virtual generated column. We need ensure the indexed
+				 * generated expression on parent match with child.
+				*/
+				if (childidxs == NIL && parent_idx_virtual)
+					check_generated_indexattrs(indexInfo, rel, childrel, attmap, false);
+
 				foreach(cell, childidxs)
 				{
 					Oid			cldidxid = lfirst_oid(cell);
@@ -1481,6 +1499,23 @@ DefineIndex(Oid tableId,
 						index_close(cldidx, NoLock);
 						break;
 					}
+					else
+					{
+						bool	cldidx_virtual;
+						bool	index_virtual;
+						index_virtual = IsIndexOverVirtualGenerated(indexInfo);
+						cldidx_virtual = IsIndexOverVirtualGenerated(cldIdxInfo);
+
+						/* should fail. otherwise pg_dump won't work */
+						if (index_virtual || cldidx_virtual)
+							ereport(ERROR,
+									errcode(ERRCODE_WRONG_OBJECT_TYPE),
+									errmsg("cannot create index on partitioned table \"%s\"",
+										   RelationGetRelationName(rel)),
+									errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+											  RelationGetRelationName(rel),
+											  RelationGetRelationName(childrel)));
+					}
 
 					index_close(cldidx, lockmode);
 				}
@@ -1857,6 +1892,72 @@ CheckPredicate(Expr *predicate)
 				 errmsg("functions in index predicate must be marked IMMUTABLE")));
 }
 
+/*
+ * rel_idx_info: the IndexInfo that is associated with rel.
+ * "childrel": the relation to be attached to "rel" or the child of "rel".
+ * attmap: Attribute mapping between childrel and rel.
+ * is_attach: is this command of ALTER TABLE ATTACH PARTITION
+ *
+ * Use build_attrmap_by_name(childrel, rel) to build the attmap.
+*/
+void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+								Relation rel,
+								Relation childrel,
+								const AttrMap *attmap,
+								bool is_attach)
+{
+	int	i;
+
+	/* if parent have virtual generated column, child must also have */
+	Assert(rel->rd_att->constr->has_generated_virtual);
+	Assert(childrel->rd_att->constr->has_generated_virtual);
+
+	for (i = 0; i < rel_idx_info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(rel_idx_info->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			Node	   *node_rel;
+			Node	   *node_attach;
+			AttrNumber	attno;
+			bool		found_whole_row;
+
+			attno	= rel_idx_info->ii_IndexAttrGeneratedNumbers[i];
+
+			node_rel = 	build_generation_expression(rel, attno);
+			node_rel = map_variable_attnos(node_rel,
+										   1, 0,
+										   attmap,
+										   InvalidOid, &found_whole_row);
+			if (found_whole_row)
+				elog(ERROR, "Index contains a whole-row table reference");
+
+			node_attach = build_generation_expression(childrel,
+													  attmap->attnums[attno - 1]);
+
+			if (!equal(node_rel, node_attach))
+			{
+				if (is_attach)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+								   RelationGetRelationName(childrel),
+								   RelationGetRelationName(rel));
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+				else
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot create index on partitioned table \"%s\"",
+								   RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+			}
+		}
+	}
+}
+
 /*
  * Compute per-index-column information, including indexed column numbers
  * or index expressions, opclasses and their options. Note, all output vectors
@@ -1881,6 +1982,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 				  bool amcanorder,
 				  bool isconstraint,
 				  bool iswithoutoverlaps,
+				  bool is_primary,
 				  Oid ddl_userid,
 				  int ddl_sec_context,
 				  int *ddl_save_nestlevel)
@@ -1891,6 +1993,28 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 	int			nkeycols = indexInfo->ii_NumIndexKeyAttrs;
 	Oid			save_userid;
 	int			save_sec_context;
+	Relation	rel;
+	TupleDesc	reltupldesc;
+	List		*virtual_generated = NIL;
+
+	rel	= table_open(relId, NoLock);
+	reltupldesc = RelationGetDescr(rel);
+
+	/*
+	 * currently, we do not support virtual generated columns over expression
+	 * indexes.  we accumulate the attribute number of virtual generated columns
+	 * so we can verify it later.
+	*/
+	if (reltupldesc->constr && reltupldesc->constr->has_generated_virtual)
+	{
+		for (int i = 0; i < reltupldesc->natts; i++)
+		{
+			Form_pg_attribute attr = TupleDescAttr(reltupldesc, i);
+
+			if (attr->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				virtual_generated = lappend_int(virtual_generated, attr->attnum);
+		}
+	}
 
 	/* Allocate space for exclusion operator info, if needed */
 	if (exclusionOpNames)
@@ -1933,6 +2057,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 		IndexElem  *attribute = (IndexElem *) lfirst(lc);
 		Oid			atttype;
 		Oid			attcollation;
+		char		attgenerated = '\0';
 
 		/*
 		 * Process the column-or-expression to be indexed.
@@ -1942,6 +2067,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			/* Simple index attribute */
 			HeapTuple	atttuple;
 			Form_pg_attribute attform;
+			AttrNumber	attnum;
 
 			Assert(attribute->expr == NULL);
 			atttuple = SearchSysCacheAttName(relId, attribute->name);
@@ -1960,10 +2086,17 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 									attribute->name)));
 			}
 			attform = (Form_pg_attribute) GETSTRUCT(atttuple);
+			attnum = attform->attnum;
 			indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
 			atttype = attform->atttypid;
 			attcollation = attform->attcollation;
+			attgenerated = attform->attgenerated;
 			ReleaseSysCache(atttuple);
+
+			if (attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				compute_generated_indexattrs(indexInfo, rel, is_primary, attn, attnum);
+			else
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 		}
 		else
 		{
@@ -1986,18 +2119,42 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			while (IsA(expr, CollateExpr))
 				expr = (Node *) ((CollateExpr *) expr)->arg;
 
+			if (!IsA(expr, Var))
+			{
+				Bitmapset  *idxattrs = NULL;
+				int			j = -1;
+
+				pull_varattnos(expr, 1, &idxattrs);
+				while ((j = bms_next_member(idxattrs, j)) >= 0)
+				{
+					AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+					if (list_member_int(virtual_generated, attno))
+						ereport(ERROR,
+								errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+								errmsg("expression index over virtual generated columns are not supported"));
+				}
+			}
+
 			if (IsA(expr, Var) &&
 				((Var *) expr)->varattno != InvalidAttrNumber)
 			{
+				int			attnum = ((Var *) expr)->varattno;
+
 				/*
 				 * User wrote "(column)" or "(column COLLATE something)".
 				 * Treat it like simple attribute anyway.
 				 */
-				indexInfo->ii_IndexAttrNumbers[attn] = ((Var *) expr)->varattno;
+				indexInfo->ii_IndexAttrNumbers[attn] = attnum;
+
+				if (list_member_int(virtual_generated, attnum))
+					compute_generated_indexattrs(indexInfo, rel, is_primary, attn, attnum);
+				else
+					indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 			}
 			else
 			{
 				indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* marks expression */
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 				indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
 													expr);
 
@@ -2248,6 +2405,78 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 
 		attn++;
 	}
+	table_close(rel, NoLock);
+}
+
+/*
+ * indexInfo: this IndexInfo to be build.
+ * rel: the relation this indexInfo is based on.
+ * is_primary: is this index a primary key.
+ * attn: indices of the index key attribute, 0 based.
+ * attnum: virtual generated column attribute number.
+*/
+static void
+compute_generated_indexattrs(IndexInfo *indexInfo, Relation rel,
+							 bool is_primary, int attn, int attnum)
+{
+	Node	   *node;
+	Bitmapset  *genattrs = NULL;
+
+	if (is_primary)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("primary keys on virtual generated columns are not supported"));
+
+	if (indexInfo->ii_Unique)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("unique constraints on virtual generated columns are not supported"));
+
+	if (attn >= indexInfo->ii_NumIndexKeyAttrs)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("virtual generated column are not supported in index included columns"));
+
+	/* Fetch the GENERATED AS expression tree */
+	node = build_generation_expression(rel, attnum);
+
+	/*
+	 * if the generation expression just reference another Var node, then set
+	 * ii_IndexAttrNumbers to that Var->varattno.
+	*/
+	if (IsA(node, Var))
+	{
+		Var		   *var = (Var *) node;
+
+		Assert(var->varattno > 0);
+		indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+	}
+	else
+	{
+		/*
+		 * Strip any top-level COLLATE clause.  This ensures that we treat
+		 * "x COLLATE y" and "(x COLLATE y)" alike.
+		*/
+		while (IsA(node, CollateExpr))
+			node = (Node *) ((CollateExpr *) node)->arg;
+
+		/* generation expression are immutable, so this unlikely to happen */
+		if (contain_mutable_functions_after_planning((Expr *) node))
+			elog(ERROR,"functions in index expression must be marked IMMUTABLE");
+
+		pull_varattnos(node, 1, &genattrs);
+
+		if (genattrs == NULL)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("can not create index based on variable free generation expression"));
+
+		indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* mark as expression index */
+		indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
+											node);
+	}
+
+	indexInfo->ii_IndexAttrGeneratedNumbers[attn] = attnum;
 }
 
 /*
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index b3ed69457fc..27aa3686e65 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -8652,6 +8652,32 @@ ATExecSetExpression(AlteredTableInfo *tab, Relation rel, const char *colName,
 		 */
 		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
 	}
+	else
+	{
+		Assert(attgenerated == ATTRIBUTE_GENERATED_VIRTUAL);
+
+		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
+
+		/*
+		 * Changing the generation expression of the virtual generated column
+		 * does not require table rewrite. However, if an index is built on top
+		 * of it, table rewrite is necessary. So in phase 3, index_rebuild can
+		 * successfully rebuild the index based on the new generation expression
+		*/
+		if (tab->changedIndexOids != NIL)
+		{
+			rewrite = true;
+
+			/*
+			 * Clear all the missing values if we're rewriting the table, since
+			 * this renders them pointless.
+			*/
+			RelationClearMissing(rel);
+
+			/* make sure we don't conflict with later attribute modifications */
+			CommandCounterIncrement();
+		}
+	}
 
 	/*
 	 * Drop the dependency records of the GENERATED expression, in particular
@@ -14755,6 +14781,14 @@ ATExecAlterColumnType(AlteredTableInfo *tab, Relation rel,
 	 */
 	RememberAllDependentForRebuilding(tab, AT_AlterColumnType, rel, attnum, colName);
 
+	/*
+	 * tell phase3 do table rewrite if there are any index based on virtual
+	 * generated colum.
+	*/
+	if (attTup->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL &&
+		tab->changedIndexOids != NIL)
+		tab->rewrite |= AT_REWRITE_COLUMN_REWRITE;
+
 	/*
 	 * Now scan for dependencies of this column on other things.  The only
 	 * things we should find are the dependency on the column datatype and
@@ -20521,6 +20555,7 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 		AttrMap    *attmap;
 		bool		found = false;
 		Oid			constraintOid;
+		bool		parent_idx_virtual;
 
 		/*
 		 * Ignore indexes in the partitioned table other than partitioned
@@ -20534,9 +20569,19 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 
 		/* construct an indexinfo to compare existing indexes against */
 		info = BuildIndexInfo(idxRel);
+		parent_idx_virtual = IsIndexOverVirtualGenerated(info);
 		attmap = build_attrmap_by_name(RelationGetDescr(attachrel),
 									   RelationGetDescr(rel),
 									   false);
+
+		/*
+		 * The attach partition don't have index, but parent have index over
+		 * virtual generated column. We need ensure generated expression on
+		 * parent that index was based on it match with attach partition.
+		*/
+		if (attachRelIdxs == NIL && parent_idx_virtual)
+			check_generated_indexattrs(info, rel, attachrel, attmap, true);
+
 		constraintOid = get_relation_idx_constraint_oid(RelationGetRelid(rel), idx);
 
 		/*
@@ -20595,6 +20640,22 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 				CommandCounterIncrement();
 				break;
 			}
+			else
+			{
+				bool		attach_idx_virtual;
+				attach_idx_virtual = IsIndexOverVirtualGenerated(attachInfos[i]);
+
+				/* should fail. different index definition cannot merge */
+				if (attach_idx_virtual || parent_idx_virtual)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+									RelationGetRelationName(attachrel),
+									RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									RelationGetRelationName(rel),
+									RelationGetRelationName(attachrel)));
+			}
 		}
 
 		/*
diff --git a/src/backend/parser/parse_utilcmd.c b/src/backend/parser/parse_utilcmd.c
index 62015431fdf..3c7af2605b3 100644
--- a/src/backend/parser/parse_utilcmd.c
+++ b/src/backend/parser/parse_utilcmd.c
@@ -1681,6 +1681,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	Form_pg_am	amrec;
 	oidvector  *indcollation;
 	oidvector  *indclass;
+	int2vector	*indgenkey;
 	IndexStmt  *index;
 	List	   *indexprs;
 	ListCell   *indexpr_item;
@@ -1688,6 +1689,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	int			keyno;
 	Oid			keycoltype;
 	Datum		datum;
+	Datum		indgenkeyDatum;
 	bool		isnull;
 
 	if (constraintOid)
@@ -1723,6 +1725,11 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	datum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx, Anum_pg_index_indclass);
 	indclass = (oidvector *) DatumGetPointer(datum);
 
+	/* Extract indattrgenerated from the pg_index tuple */
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* Begin building the IndexStmt */
 	index = makeNode(IndexStmt);
 	index->relation = heapRel;
@@ -1854,13 +1861,29 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	{
 		IndexElem  *iparam;
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Form_pg_attribute attr = TupleDescAttr(RelationGetDescr(source_idx),
 											   keyno);
 		int16		opt = source_idx->rd_indoption[keyno];
 
 		iparam = makeNode(IndexElem);
 
-		if (AttributeNumberIsValid(attnum))
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * index over virtual generated column was converted into a
+			 * expression index, but we need restore the original attribute
+			 * number for recreate it.
+			*/
+			char	   *virtual_attname;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			keycoltype = get_atttype(indrelid, gennum);
+
+			iparam->name = virtual_attname;
+			iparam->expr = NULL;
+		}
+		else if (AttributeNumberIsValid(attnum))
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/backend/utils/adt/ruleutils.c b/src/backend/utils/adt/ruleutils.c
index 9e90acedb91..ae3db86294d 100644
--- a/src/backend/utils/adt/ruleutils.c
+++ b/src/backend/utils/adt/ruleutils.c
@@ -1290,9 +1290,11 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	Datum		indcollDatum;
 	Datum		indclassDatum;
 	Datum		indoptionDatum;
+	Datum		indgenkeyDatum;
 	oidvector  *indcollation;
 	oidvector  *indclass;
 	int2vector *indoption;
+	int2vector *indgenkey;
 	StringInfoData buf;
 	char	   *str;
 	char	   *sep;
@@ -1325,6 +1327,10 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 											Anum_pg_index_indoption);
 	indoption = (int2vector *) DatumGetPointer(indoptionDatum);
 
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/*
 	 * Fetch the pg_class tuple of the index relation
 	 */
@@ -1398,6 +1404,7 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	for (keyno = 0; keyno < idxrec->indnatts; keyno++)
 	{
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Oid			keycoltype;
 		Oid			keycolcollation;
 
@@ -1418,7 +1425,26 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 			appendStringInfoString(&buf, sep);
 		sep = ", ";
 
-		if (attnum != 0)
+		if (!AttributeNumberIsValid(attnum) && AttributeNumberIsValid(gennum))
+			indexpr_item = lnext(indexprs, indexpr_item);
+
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * This index is created on virtual generated column
+			*/
+			char	   *virtual_attname;
+			int32		geneycoltypmod;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			if (!colno || colno == keyno + 1)
+				appendStringInfoString(&buf, quote_identifier(virtual_attname));
+
+			get_atttypetypmodcoll(indrelid, gennum,
+								  &keycoltype, &geneycoltypmod,
+								  &keycolcollation);
+		}
+		else if (attnum != 0)
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/include/catalog/index.h b/src/include/catalog/index.h
index 4daa8bef5ee..a7e93f3a107 100644
--- a/src/include/catalog/index.h
+++ b/src/include/catalog/index.h
@@ -126,6 +126,7 @@ extern IndexInfo *BuildIndexInfo(Relation index);
 
 extern IndexInfo *BuildDummyIndexInfo(Relation index);
 
+extern bool IsIndexOverVirtualGenerated(const IndexInfo *info);
 extern bool CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 							 const Oid *collations1, const Oid *collations2,
 							 const Oid *opfamilies1, const Oid *opfamilies2,
@@ -175,6 +176,11 @@ extern void RestoreReindexState(const void *reindexstate);
 
 extern void IndexSetParentIndex(Relation partitionIdx, Oid parentOid);
 
+extern void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+									   Relation rel,
+									   Relation childrel,
+									   const AttrMap *attmap,
+									   bool	is_attach);
 
 /*
  * itemptr_encode - Encode ItemPointer as int64/int8
diff --git a/src/include/catalog/pg_index.h b/src/include/catalog/pg_index.h
index 4392b9d221d..7ed74a593a4 100644
--- a/src/include/catalog/pg_index.h
+++ b/src/include/catalog/pg_index.h
@@ -54,6 +54,7 @@ CATALOG(pg_index,2610,IndexRelationId) BKI_SCHEMA_MACRO
 	oidvector	indclass BKI_LOOKUP(pg_opclass) BKI_FORCE_NOT_NULL; /* opclass identifiers */
 	int2vector	indoption BKI_FORCE_NOT_NULL;	/* per-column flags
 												 * (AM-specific meanings) */
+	int2vector	indattrgenerated BKI_FORCE_NOT_NULL; /* the attribute of virtual generated column? */
 	pg_node_tree indexprs;		/* expression trees for index attributes that
 								 * are not simple column references; one for
 								 * each zero entry in indkey[] */
diff --git a/src/include/nodes/execnodes.h b/src/include/nodes/execnodes.h
index 5b6cadb5a6c..ea4240b36e4 100644
--- a/src/include/nodes/execnodes.h
+++ b/src/include/nodes/execnodes.h
@@ -196,6 +196,7 @@ typedef struct IndexInfo
 	int			ii_NumIndexAttrs;	/* total number of columns in index */
 	int			ii_NumIndexKeyAttrs;	/* number of key columns in index */
 	AttrNumber	ii_IndexAttrNumbers[INDEX_MAX_KEYS];
+	AttrNumber	ii_IndexAttrGeneratedNumbers[INDEX_MAX_KEYS]; /* XXX more better comments */
 	List	   *ii_Expressions; /* list of Expr */
 	List	   *ii_ExpressionsState;	/* list of ExprState */
 	List	   *ii_Predicate;	/* list of Expr */
diff --git a/src/test/regress/expected/fast_default.out b/src/test/regress/expected/fast_default.out
index ccbcdf8403f..ef19f667cc1 100644
--- a/src/test/regress/expected/fast_default.out
+++ b/src/test/regress/expected/fast_default.out
@@ -70,6 +70,14 @@ NOTICE:  rewriting table has_volatile for reason 4
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 NOTICE:  rewriting table has_volatile for reason 2
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+NOTICE:  rewriting table has_volatile for reason 2
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
+NOTICE:  rewriting table has_volatile for reason 4
 -- Test a large sample of different datatypes
 CREATE TABLE T(pk INT NOT NULL PRIMARY KEY, c_int INT DEFAULT 1);
 SELECT set('t');
diff --git a/src/test/regress/expected/generated_virtual.out b/src/test/regress/expected/generated_virtual.out
index 26bbe1e9c31..d3525a1352e 100644
--- a/src/test/regress/expected/generated_virtual.out
+++ b/src/test/regress/expected/generated_virtual.out
@@ -742,30 +742,175 @@ ERROR:  primary keys on virtual generated columns are not supported
 --INSERT INTO gtest22b VALUES (2);
 --INSERT INTO gtest22b VALUES (2);
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error. partitioned and partition have different generation expression, can not
+--build index on it.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ERROR:  cannot create index on partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart3"
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+--error. index over different generation expression should not allowed
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ERROR:  cannot attach table "gtestpart1" as partition of partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart1"
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+       relid       |    parentrelid    | isleaf | level 
+-------------------+-------------------+--------+-------
+ gtestparted_a_idx |                   | f      |     0
+ gtestpart2_a_idx  | gtestparted_a_idx | t      |     1
+(2 rows)
+
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+ERROR:  cannot attach index "gtestpart2_a_idx_copy" as a partition of index "gtestparted_a_idx"
+DETAIL:  Another index is already attached for partition "gtestpart2".
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+         relid         |     parentrelid     | isleaf | level 
+-----------------------+---------------------+--------+-------
+ gtestparted_a_idx_1   |                     | f      |     0
+ gtestpart2_a_idx_copy | gtestparted_a_idx_1 | t      |     1
+(2 rows)
+
+--create table like should work just fine
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+           Table "generated_virtual_tests.gtestparted_like"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+ a      | integer |           |          | generated always as (c + 1)
+Indexes:
+    "gtestparted_like_a_idx" btree (a)
+    "gtestparted_like_a_idx1" btree (a)
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL
+                      ,c int GENERATED ALWAYS AS (11) VIRTUAL
+                      ,d int GENERATED ALWAYS AS (a *3) VIRTUAL
+                      ,e int4range GENERATED ALWAYS AS (int4range(a, a+10)) VIRTUAL
+                      ,f int GENERATED ALWAYS AS (a) VIRTUAL);
+CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+--variable free generation expression have no pratical usage, so error out.
+CREATE INDEX gtest22c_c_idx ON gtest22c (c);
+ERROR:  can not create index based on variable free generation expression
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_idx ON gtest22c USING gist(e);
+--error. include columns are not supported.
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (b,c);
+ERROR:  virtual generated column are not supported in index included columns
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (f);
+ERROR:  virtual generated column are not supported in index included columns
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
+\d gtest22c
+                        Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                  Default                   
+--------+-----------+-----------+----------+--------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e      | int4range |           |          | generated always as (int4range(a, a + 10))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e_idx" gist (e)
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4;
+ a | b | c  | d |   e    | f 
+---+---+----+---+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_d_idx on gtest22c
+   Index Cond: ((a * 3) = 6)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE d = 6;
+ a | b | c  | d |   e    | f 
+---+---+----+---+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12;
+                     QUERY PLAN                     
+----------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e_idx on gtest22c
+         Index Cond: (int4range(a, (a + 10)) @> 12)
+(3 rows)
+
+SELECT count(*) from gtest22c where e @> 12;
+ count 
+-------
+     2
+(1 row)
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
+               Table "generated_virtual_tests.gtest22c"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ a      | integer |           |          | 
+ b      | integer |           |          | generated always as (a * 2)
+ c      | integer |           |          | generated always as (11)
+ d      | integer |           |          | generated always as (a * 3)
+ f      | integer |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b)
+    "gtest22c_d_idx" hash (d)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 4) = 8)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 8;
+ a | b | c  | d | f 
+---+---+----+---+---
+ 2 | 8 | 11 | 6 | 2
+(1 row)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
 --INSERT INTO gtest23a VALUES (1, 11), (2, 22), (3, 33);
@@ -1587,3 +1732,17 @@ select * from gtest32 t group by grouping sets (a, b, c, d) having c = 20;
 (1 row)
 
 drop table gtest32;
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
+ indrelid | attnum | attname | attgenerated 
+----------+--------+---------+--------------
+(0 rows)
+
diff --git a/src/test/regress/sql/fast_default.sql b/src/test/regress/sql/fast_default.sql
index 068dd0bc8aa..b39e76bcfc3 100644
--- a/src/test/regress/sql/fast_default.sql
+++ b/src/test/regress/sql/fast_default.sql
@@ -77,6 +77,12 @@ ALTER TABLE has_volatile ALTER COLUMN col1 SET DATA TYPE float8,
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
 
 
 -- Test a large sample of different datatypes
diff --git a/src/test/regress/sql/generated_virtual.sql b/src/test/regress/sql/generated_virtual.sql
index 13cfbd76859..04dd56e58cf 100644
--- a/src/test/regress/sql/generated_virtual.sql
+++ b/src/test/regress/sql/generated_virtual.sql
@@ -1,6 +1,4 @@
 -- keep these tests aligned with generated_stored.sql
-
-
 CREATE SCHEMA generated_virtual_tests;
 GRANT USAGE ON SCHEMA generated_virtual_tests TO PUBLIC;
 SET search_path = generated_virtual_tests;
@@ -391,32 +389,85 @@ CREATE TABLE gtest22b (a int, b int GENERATED ALWAYS AS (a / 2) VIRTUAL, PRIMARY
 --INSERT INTO gtest22b VALUES (2);
 
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error. partitioned and partition have different generation expression, can not
+--build index on it.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+
+--error. index over different generation expression should not allowed
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+
+--create table like should work just fine
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL
+                      ,c int GENERATED ALWAYS AS (11) VIRTUAL
+                      ,d int GENERATED ALWAYS AS (a *3) VIRTUAL
+                      ,e int4range GENERATED ALWAYS AS (int4range(a, a+10)) VIRTUAL
+                      ,f int GENERATED ALWAYS AS (a) VIRTUAL);
+CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+--variable free generation expression have no pratical usage, so error out.
+CREATE INDEX gtest22c_c_idx ON gtest22c (c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_idx ON gtest22c USING gist(e);
+--error. include columns are not supported.
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (b,c);
+CREATE INDEX gtest22c_idx1 ON gtest22c USING btree(a) include (f);
+
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
+\d gtest22c
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+SELECT * FROM gtest22c WHERE b = 4;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+SELECT * FROM gtest22c WHERE d = 6;
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12;
+SELECT count(*) from gtest22c where e @> 12;
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
 
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+SELECT * FROM gtest22c WHERE b = 8;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
@@ -828,3 +879,14 @@ select * from gtest32 t group by grouping sets (a, b, c, d) having c = 20;
 select * from gtest32 t group by grouping sets (a, b, c, d) having c = 20;
 
 drop table gtest32;
+
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
-- 
2.34.1

From d61f21e6fc410827d152a633e5699197c802870a Mon Sep 17 00:00:00 2001
From: jian he <jian.universality@gmail.com>
Date: Tue, 8 Jul 2025 14:26:33 +0800
Subject: [PATCH v4 1/1] index on virtual generated column

* btree, hash, gist, spgist, gin, brin all are supported
* Primary key and unique indexes on virtual generated columns are not supported.
* exclusion constraint on virtual generated columns are not supported, maybe future
* Expression indexes and partial (predicate) indexes on virtual generated
  columns are currently unsupported.
* Indexes with included columns cannot use virtual generated columns.
* An index on a virtual generated column like ``(b INT GENERATED ALWAYS AS (a) VIRTUAL)``
  is effectively equivalent to an index on a.
* Internally, such indexes are transformed into expression indexes.  For
  example, an index on ``(b INT GENERATED ALWAYS AS (a * 2) VIRTUAL)``
  is internally represented as an expression index on (a * 2).
* In the pageinspect module, additional tests added for verify the index content
  for virtual generated columns.
* All index types are supported, including hash and GiST indexes, and
  corresponding regression tests have been added.
* To support ALTER TABLE ... SET EXPRESSION, the pg_index catalog tracks the
  original attribute number of the virtual generated column, allowing
  identification of indexes that require rebuilding.
* ALTER COLUMN SET DATA TYPE also triggers a table rewrite; therefore, tracking
  the attribute number of the virtual generated column used by the index is necessary.
* if the partitioned table and partition both have an index, then the index over the virtual
  generated column should be the same expression. For example, the following last
  command should error out.
    CREATE TABLE parted (b integer,c integer,a integer GENERATED ALWAYS AS (c+1)) PARTITION BY RANGE (b);
    CREATE TABLE part (b integer,c integer,a integer GENERATED ALWAYS AS (c));
    create index on part(a);
    create index on parted(a);
    alter table parted ATTACH partition part for values from (1) to (10);

discussion: https://postgr.es/m/CACJufxGao-cypdNhifHAdt8jHfK6-HX=tRBovBkgRuxw063GaA@mail.gmail.com
commitfest: https://commitfest.postgresql.org/patch/5667
---
 contrib/pageinspect/expected/btree.out        |  23 ++
 contrib/pageinspect/sql/btree.sql             |  11 +
 doc/src/sgml/catalogs.sgml                    |  15 +
 src/backend/catalog/index.c                   |  69 ++++
 src/backend/commands/indexcmds.c              | 301 +++++++++++++++---
 src/backend/commands/tablecmds.c              |  70 ++++
 src/backend/parser/parse_utilcmd.c            |  25 +-
 src/backend/utils/adt/ruleutils.c             |  30 +-
 src/include/catalog/index.h                   |   6 +
 src/include/catalog/pg_index.h                |   1 +
 src/include/nodes/execnodes.h                 |   8 +
 .../regress/expected/collate.icu.utf8.out     |  11 +
 src/test/regress/expected/fast_default.out    |   8 +
 .../regress/expected/generated_virtual.out    | 262 ++++++++++++++-
 src/test/regress/sql/collate.icu.utf8.sql     |   5 +
 src/test/regress/sql/fast_default.sql         |   6 +
 src/test/regress/sql/generated_virtual.sql    | 124 +++++++-
 17 files changed, 907 insertions(+), 68 deletions(-)

diff --git a/contrib/pageinspect/expected/btree.out b/contrib/pageinspect/expected/btree.out
index 0aa5d73322f..f985a690b72 100644
--- a/contrib/pageinspect/expected/btree.out
+++ b/contrib/pageinspect/expected/btree.out
@@ -183,6 +183,29 @@ tids       |
 
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 ERROR:  block number 2 is out of range for relation "test1_a_idx"
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+SELECT * FROM bt_page_items('test4_b_idx', 1);
+-[ RECORD 1 ]-----------------------
+itemoffset | 1
+ctid       | (16,8194)
+itemlen    | 32
+nulls      | f
+vars       | f
+data       | 0b 00 00 00 00 00 00 00
+dead       | f
+htid       | (0,1)
+tids       | {"(0,1)","(0,2)"}
+
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+(0 rows)
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/contrib/pageinspect/sql/btree.sql b/contrib/pageinspect/sql/btree.sql
index 102ebdefe3c..109e4c4466e 100644
--- a/contrib/pageinspect/sql/btree.sql
+++ b/contrib/pageinspect/sql/btree.sql
@@ -32,6 +32,17 @@ SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 0));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+SELECT * FROM bt_page_items('test4_b_idx', 1);
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/doc/src/sgml/catalogs.sgml b/doc/src/sgml/catalogs.sgml
index 4f9192316e0..2f73ac4aa3d 100644
--- a/doc/src/sgml/catalogs.sgml
+++ b/doc/src/sgml/catalogs.sgml
@@ -4589,6 +4589,21 @@ SCRAM-SHA-256$<replaceable>&lt;iteration count&gt;</replaceable>:<replaceable>&l
       </para></entry>
      </row>
 
+     <row>
+      <entry role="catalog_table_entry"><para role="column_definition">
+       <structfield>indattrgenerated</structfield> <type>int2vector</type>
+       (references <link linkend="catalog-pg-attribute"><structname>pg_attribute</structname></link>.<structfield>attnum</structfield>)
+      </para>
+      <para>
+       This is an array of <structfield>indnatts</structfield> values that
+       indicate which virtual generated columns this index indexes.
+       For example, a value of <literal>1 3</literal> would mean that the first
+       and the third table columns of this index entries are virtual generated
+       column. A zero in this array indicates that the corresponding index
+       attribute is not virtual generated column reference.
+      </para></entry>
+     </row>
+
      <row>
       <entry role="catalog_table_entry"><para role="column_definition">
        <structfield>indexprs</structfield> <type>pg_node_tree</type>
diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index aa216683b74..1fad8b4edc4 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -584,6 +584,12 @@ UpdateIndexRelation(Oid indexoid,
 	Relation	pg_index;
 	HeapTuple	tuple;
 	int			i;
+	int2vector *indgenkey;
+	int16	   *colgenerated;
+
+	colgenerated = palloc_array(int16, indexInfo->ii_NumIndexAttrs);
+	for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+		colgenerated[i] = indexInfo->ii_IndexAttrGeneratedNumbers[i];
 
 	/*
 	 * Copy the index key, opclass, and indoption info into arrays (should we
@@ -595,6 +601,7 @@ UpdateIndexRelation(Oid indexoid,
 	indcollation = buildoidvector(collationOids, indexInfo->ii_NumIndexKeyAttrs);
 	indclass = buildoidvector(opclassOids, indexInfo->ii_NumIndexKeyAttrs);
 	indoption = buildint2vector(coloptions, indexInfo->ii_NumIndexKeyAttrs);
+	indgenkey = buildint2vector(colgenerated, indexInfo->ii_NumIndexAttrs);
 
 	/*
 	 * Convert the index expressions (if any) to a text datum
@@ -653,6 +660,7 @@ UpdateIndexRelation(Oid indexoid,
 	values[Anum_pg_index_indcollation - 1] = PointerGetDatum(indcollation);
 	values[Anum_pg_index_indclass - 1] = PointerGetDatum(indclass);
 	values[Anum_pg_index_indoption - 1] = PointerGetDatum(indoption);
+	values[Anum_pg_index_indattrgenerated - 1] = PointerGetDatum(indgenkey);
 	values[Anum_pg_index_indexprs - 1] = exprsDatum;
 	if (exprsDatum == (Datum) 0)
 		nulls[Anum_pg_index_indexprs - 1] = true;
@@ -1134,6 +1142,28 @@ index_create(Relation heapRelation,
 				}
 			}
 
+			/*
+			 * Internally, we convert index of virtual generation column into an
+			 * expression index. For example, if column 'b' is defined as (b INT
+			 * GENERATED ALWAYS AS (a * 2) VIRTUAL) then index over 'b' would
+			 * transformed into an expression index as ((a * 2)). As a result,
+			 * the pg_depend refobjsubid does not retain the original attribute
+			 * number of the virtual generated column. But we need rebuild any
+			 * index that was build on virtual generated column. so we need auto
+			 * dependencies on referenced virtual generated columns.
+			*/
+			for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+			{
+				if (indexInfo->ii_IndexAttrGeneratedNumbers[i] != 0)
+				{
+					ObjectAddressSubSet(referenced, RelationRelationId,
+										heapRelationId,
+										indexInfo->ii_IndexAttrGeneratedNumbers[i]);
+					add_exact_object_address(&referenced, addrs);
+					have_simple_col = false;
+				}
+			}
+
 			/*
 			 * If there are no simply-referenced columns, give the index an
 			 * auto dependency on the whole table.  In most cases, this will
@@ -2428,9 +2458,12 @@ IndexInfo *
 BuildIndexInfo(Relation index)
 {
 	IndexInfo  *ii;
+	HeapTuple	ht_idx;
 	Form_pg_index indexStruct = index->rd_index;
 	int			i;
 	int			numAtts;
+	Datum		indgenkeyDatum;
+	int2vector *indgenkey;
 
 	/* check the number of keys, and copy attr numbers into the IndexInfo */
 	numAtts = indexStruct->indnatts;
@@ -2454,9 +2487,19 @@ BuildIndexInfo(Relation index)
 					   index->rd_indam->amsummarizing,
 					   indexStruct->indisexclusion && indexStruct->indisunique);
 
+	ht_idx = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(indexStruct->indexrelid));
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* fill in attribute numbers */
 	for (i = 0; i < numAtts; i++)
+	{
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
+		ii->ii_IndexAttrGeneratedNumbers[i] = indgenkey->values[i];
+	}
+
+	ReleaseSysCache(ht_idx);
 
 	/* fetch exclusion constraint info if any */
 	if (indexStruct->indisexclusion)
@@ -2523,6 +2566,23 @@ BuildDummyIndexInfo(Relation index)
 	return ii;
 }
 
+/*
+ * IndexOverVirtualGenerated
+ *		Return whether this index is built on virtual generated column.
+ */
+bool
+IsIndexOverVirtualGenerated(const IndexInfo *info)
+{
+	int			i;
+
+	for (i = 0; i < info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(info->ii_IndexAttrGeneratedNumbers[i]))
+			return true;
+	}
+	return false;
+}
+
 /*
  * CompareIndexInfo
  *		Return whether the properties of two indexes (in different tables)
@@ -2585,6 +2645,15 @@ CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 				return false;
 		}
 
+		if (AttributeNumberIsValid(info1->ii_IndexAttrGeneratedNumbers[i]) ||
+			AttributeNumberIsValid(info2->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			/* fail if index over virtual generated column does not match */
+			if (attmap->attnums[info2->ii_IndexAttrGeneratedNumbers[i] - 1] !=
+				info1->ii_IndexAttrGeneratedNumbers[i])
+				return false;
+		}
+
 		/* collation and opfamily are not valid for included columns */
 		if (i >= info1->ii_NumIndexKeyAttrs)
 			continue;
diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 6f753ab6d7a..c0df17f068b 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -54,6 +54,7 @@
 #include "parser/parse_utilcmd.h"
 #include "partitioning/partdesc.h"
 #include "pgstat.h"
+#include "rewrite/rewriteHandler.h"
 #include "rewrite/rewriteManip.h"
 #include "storage/lmgr.h"
 #include "storage/proc.h"
@@ -90,9 +91,15 @@ static void ComputeIndexAttrs(IndexInfo *indexInfo,
 							  bool amcanorder,
 							  bool isconstraint,
 							  bool iswithoutoverlaps,
+							  bool is_primary,
 							  Oid ddl_userid,
 							  int ddl_sec_context,
 							  int *ddl_save_nestlevel);
+static void compute_index_generatedattrs(IndexInfo *indexInfo,
+										 Relation rel,
+										 bool is_primary,
+										 int attn,
+										 int attnum);
 static char *ChooseIndexName(const char *tabname, Oid namespaceId,
 							 const List *colnames, const List *exclusionOpNames,
 							 bool primary, bool isconstraint);
@@ -182,6 +189,7 @@ CheckIndexCompatible(Oid oldId,
 					 bool isWithoutOverlaps)
 {
 	bool		isconstraint;
+	bool		is_primary;
 	Oid		   *typeIds;
 	Oid		   *collationIds;
 	Oid		   *opclassIds;
@@ -214,6 +222,12 @@ CheckIndexCompatible(Oid oldId,
 	 */
 	isconstraint = false;
 
+	/*
+	 * We can pretend is_primary = false unconditionally.  It only serves to
+	 * decide the text of an error message that should never happen for us.
+	 */
+	is_primary = false;
+
 	numberOfAttributes = list_length(attributeList);
 	Assert(numberOfAttributes > 0);
 	Assert(numberOfAttributes <= INDEX_MAX_KEYS);
@@ -254,7 +268,7 @@ CheckIndexCompatible(Oid oldId,
 					  coloptions, attributeList,
 					  exclusionOpNames, relationId,
 					  accessMethodName, accessMethodId,
-					  amcanorder, isconstraint, isWithoutOverlaps, InvalidOid,
+					  amcanorder, isconstraint, isWithoutOverlaps, is_primary, InvalidOid,
 					  0, NULL);
 
 	/* Get the soon-obsolete pg_index tuple. */
@@ -905,6 +919,31 @@ DefineIndex(Oid tableId,
 	if (stmt->whereClause)
 		CheckPredicate((Expr *) stmt->whereClause);
 
+	/* virtual generated column over predicate indexes are not supported */
+	if (RelationGetDescr(rel)->constr &&
+		RelationGetDescr(rel)->constr->has_generated_virtual &&
+		stmt->whereClause)
+	{
+		Bitmapset  *indexattrs_pred = NULL;
+		int			j;
+
+		pull_varattnos(stmt->whereClause, 1, &indexattrs_pred);
+
+		j = -1;
+		while ((j = bms_next_member(indexattrs_pred, j)) >= 0)
+		{
+			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+
+			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+			{
+				ereport(ERROR,
+						errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+						errmsg("partial index on virtual generated columns are not supported"));
+				break;
+			}
+		}
+	}
+
 	/*
 	 * Parse AM-specific options, convert to text array form, validate.
 	 */
@@ -941,6 +980,7 @@ DefineIndex(Oid tableId,
 					  stmt->excludeOpNames, tableId,
 					  accessMethodName, accessMethodId,
 					  amcanorder, stmt->isconstraint, stmt->iswithoutoverlaps,
+					  stmt->primary,
 					  root_save_userid, root_save_sec_context,
 					  &root_save_nestlevel);
 
@@ -1102,9 +1142,6 @@ DefineIndex(Oid tableId,
 	/*
 	 * We disallow indexes on system columns.  They would not necessarily get
 	 * updated correctly, and they don't seem useful anyway.
-	 *
-	 * Also disallow virtual generated columns in indexes (use expression
-	 * index instead).
 	 */
 	for (int i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
 	{
@@ -1114,26 +1151,14 @@ DefineIndex(Oid tableId,
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("index creation on system columns is not supported")));
-
-
-		if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-			ereport(ERROR,
-					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-					stmt->primary ?
-					errmsg("primary keys on virtual generated columns are not supported") :
-					stmt->isconstraint ?
-					errmsg("unique constraints on virtual generated columns are not supported") :
-					errmsg("indexes on virtual generated columns are not supported"));
 	}
 
 	/*
-	 * Also check for system and generated columns used in expressions or
-	 * predicates.
+	 * Also check for system columns used in expressions or predicates.
 	 */
 	if (indexInfo->ii_Expressions || indexInfo->ii_Predicate)
 	{
 		Bitmapset  *indexattrs = NULL;
-		int			j;
 
 		pull_varattnos((Node *) indexInfo->ii_Expressions, 1, &indexattrs);
 		pull_varattnos((Node *) indexInfo->ii_Predicate, 1, &indexattrs);
@@ -1146,24 +1171,6 @@ DefineIndex(Oid tableId,
 						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 						 errmsg("index creation on system columns is not supported")));
 		}
-
-		/*
-		 * XXX Virtual generated columns in index expressions or predicates
-		 * could be supported, but it needs support in
-		 * RelationGetIndexExpressions() and RelationGetIndexPredicate().
-		 */
-		j = -1;
-		while ((j = bms_next_member(indexattrs, j)) >= 0)
-		{
-			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
-
-			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-				ereport(ERROR,
-						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-						 stmt->isconstraint ?
-						 errmsg("unique constraints on virtual generated columns are not supported") :
-						 errmsg("indexes on virtual generated columns are not supported")));
-		}
 	}
 
 	/* Is index safe for others to ignore?  See set_indexsafe_procflags() */
@@ -1307,6 +1314,7 @@ DefineIndex(Oid tableId,
 			bool		invalidate_parent = false;
 			Relation	parentIndex;
 			TupleDesc	parentDesc;
+			bool		parent_idx_virtual;
 
 			/*
 			 * Report the total number of partitions at the start of the
@@ -1353,6 +1361,8 @@ DefineIndex(Oid tableId,
 			parentIndex = index_open(indexRelationId, lockmode);
 			indexInfo = BuildIndexInfo(parentIndex);
 
+			parent_idx_virtual = IsIndexOverVirtualGenerated(indexInfo);
+
 			parentDesc = RelationGetDescr(rel);
 
 			/*
@@ -1412,6 +1422,14 @@ DefineIndex(Oid tableId,
 										  parentDesc,
 										  false);
 
+				/*
+				 * child don't have any index, but parent have index over
+				 * virtual generated column. We need ensure the indexed
+				 * generated expression on the parent match with the child.
+				*/
+				if (childidxs == NIL && parent_idx_virtual)
+					check_generated_indexattrs(indexInfo, rel, childrel, attmap, false);
+
 				foreach(cell, childidxs)
 				{
 					Oid			cldidxid = lfirst_oid(cell);
@@ -1481,6 +1499,22 @@ DefineIndex(Oid tableId,
 						index_close(cldidx, NoLock);
 						break;
 					}
+					else
+					{
+						bool	cldidx_virtual;
+						bool	index_virtual;
+						index_virtual = IsIndexOverVirtualGenerated(indexInfo);
+						cldidx_virtual = IsIndexOverVirtualGenerated(cldIdxInfo);
+
+						if (index_virtual || cldidx_virtual)
+							ereport(ERROR,
+									errcode(ERRCODE_WRONG_OBJECT_TYPE),
+									errmsg("cannot create index on partitioned table \"%s\"",
+										   RelationGetRelationName(rel)),
+									errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+											  RelationGetRelationName(rel),
+											  RelationGetRelationName(childrel)));
+					}
 
 					index_close(cldidx, lockmode);
 				}
@@ -1857,6 +1891,73 @@ CheckPredicate(Expr *predicate)
 				 errmsg("functions in index predicate must be marked IMMUTABLE")));
 }
 
+/*
+ * Verify that the generated expression of the parent matches that of the child
+ *
+ * rel_idx_info: the IndexInfo that is associated with rel.
+ * childrel: the relation to be attached to "rel" or the child of "rel".
+ * attmap: Attribute mapping between childrel and rel.
+ * is_attach: is this command of ALTER TABLE ATTACH PARTITION
+ *
+ * Use build_attrmap_by_name(childrel, rel) to build the attmap.
+*/
+void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+								Relation rel,
+								Relation childrel,
+								const AttrMap *attmap,
+								bool is_attach)
+{
+	/* if parent have virtual generated column, child must also have */
+	Assert(rel->rd_att->constr->has_generated_virtual);
+	Assert(childrel->rd_att->constr->has_generated_virtual);
+
+	for (int i = 0; i < rel_idx_info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(rel_idx_info->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			Node	   *node_rel;
+			Node	   *node_attach;
+			AttrNumber	attno;
+			bool		found_whole_row;
+
+			attno	= rel_idx_info->ii_IndexAttrGeneratedNumbers[i];
+
+			node_rel = 	build_generation_expression(rel, attno);
+			node_rel = map_variable_attnos(node_rel,
+										   1,
+										   0,
+										   attmap,
+										   InvalidOid, &found_whole_row);
+			if (found_whole_row)
+				elog(ERROR, "Index contains a whole-row table reference");
+
+			node_attach = build_generation_expression(childrel,
+													  attmap->attnums[attno - 1]);
+
+			if (!equal(node_rel, node_attach))
+			{
+				if (is_attach)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+								   RelationGetRelationName(childrel),
+								   RelationGetRelationName(rel));
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+				else
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot create index on partitioned table \"%s\"",
+								   RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+			}
+		}
+	}
+}
+
 /*
  * Compute per-index-column information, including indexed column numbers
  * or index expressions, opclasses and their options. Note, all output vectors
@@ -1881,6 +1982,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 				  bool amcanorder,
 				  bool isconstraint,
 				  bool iswithoutoverlaps,
+				  bool is_primary,
 				  Oid ddl_userid,
 				  int ddl_sec_context,
 				  int *ddl_save_nestlevel)
@@ -1891,6 +1993,28 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 	int			nkeycols = indexInfo->ii_NumIndexKeyAttrs;
 	Oid			save_userid;
 	int			save_sec_context;
+	Relation	rel;
+	TupleDesc	reltupldesc;
+	List		*virtual_generated = NIL;
+
+	rel	= table_open(relId, NoLock);
+	reltupldesc = RelationGetDescr(rel);
+
+	/*
+	 * Currently, we do not support virtual generated columns over expression
+	 * indexes.  we accumulate the attribute number of virtual generated columns
+	 * so we can verify it later.
+	*/
+	if (reltupldesc->constr && reltupldesc->constr->has_generated_virtual)
+	{
+		for (int i = 0; i < reltupldesc->natts; i++)
+		{
+			Form_pg_attribute attr = TupleDescAttr(reltupldesc, i);
+
+			if (attr->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				virtual_generated = lappend_int(virtual_generated, attr->attnum);
+		}
+	}
 
 	/* Allocate space for exclusion operator info, if needed */
 	if (exclusionOpNames)
@@ -1963,6 +2087,12 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
 			atttype = attform->atttypid;
 			attcollation = attform->attcollation;
+
+			if (attform->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				compute_index_generatedattrs(indexInfo, rel, is_primary, attn, attform->attnum);
+			else
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
+
 			ReleaseSysCache(atttuple);
 		}
 		else
@@ -1986,18 +2116,42 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			while (IsA(expr, CollateExpr))
 				expr = (Node *) ((CollateExpr *) expr)->arg;
 
+			if (!IsA(expr, Var))
+			{
+				Bitmapset  *idxattrs = NULL;
+				int			j = -1;
+
+				pull_varattnos(expr, 1, &idxattrs);
+				while ((j = bms_next_member(idxattrs, j)) >= 0)
+				{
+					AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+					if (list_member_int(virtual_generated, attno))
+						ereport(ERROR,
+								errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+								errmsg("expression index over virtual generated columns are not supported"));
+				}
+			}
+
 			if (IsA(expr, Var) &&
 				((Var *) expr)->varattno != InvalidAttrNumber)
 			{
+				int			attnum = ((Var *) expr)->varattno;
+
 				/*
 				 * User wrote "(column)" or "(column COLLATE something)".
 				 * Treat it like simple attribute anyway.
 				 */
-				indexInfo->ii_IndexAttrNumbers[attn] = ((Var *) expr)->varattno;
+				indexInfo->ii_IndexAttrNumbers[attn] = attnum;
+
+				if (list_member_int(virtual_generated, attnum))
+					compute_index_generatedattrs(indexInfo, rel, is_primary, attn, attnum);
+				else
+					indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 			}
 			else
 			{
 				indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* marks expression */
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 				indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
 													expr);
 
@@ -2248,6 +2402,81 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 
 		attn++;
 	}
+
+	table_close(rel, NoLock);
+}
+
+/*
+ * indexInfo: this IndexInfo to be build.
+ * rel: the relation this indexInfo is based on.
+ * is_primary: is this index a primary key.
+ * attn: indices of the index key attribute, 0 based.
+ * attnum: virtual generated column attribute number.
+*/
+static void
+compute_index_generatedattrs(IndexInfo *indexInfo, Relation rel,
+							 bool is_primary, int attn, int attnum)
+{
+	Node	   *node;
+
+	if (is_primary)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("primary keys on virtual generated columns are not supported"));
+
+	if (indexInfo->ii_Unique)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("unique constraints on virtual generated columns are not supported"));
+
+	if (attn >= indexInfo->ii_NumIndexKeyAttrs)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("virtual generated column are not supported in index included columns"));
+
+	/* Fetch the GENERATED AS expression tree */
+	node = build_generation_expression(rel, attnum);
+
+	/*
+	 * if the generation expression just reference another Var node, then set
+	 * ii_IndexAttrNumbers to that Var->varattno.
+	*/
+	if (IsA(node, Var))
+	{
+		Var		   *var = (Var *) node;
+
+		if (var->varattno < 0)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("index creation on system columns is not supported"));
+
+		indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+	}
+	else
+	{
+		/*
+		 * Strip any top-level COLLATE clause in generated expression.  This
+		 * ensures that we treat "x COLLATE y" and "(x COLLATE y)" alike.
+		*/
+		while (IsA(node, CollateExpr))
+			node = (Node *) ((CollateExpr *) node)->arg;
+
+		if (IsA(node, Var))
+		{
+			Var		   *var = (Var *) node;
+
+			Assert(var->varattno > 0);
+			indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+		}
+		else
+		{
+			indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* mark as expression index */
+			indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
+												node);
+		}
+	}
+
+	indexInfo->ii_IndexAttrGeneratedNumbers[attn] = attnum;
 }
 
 /*
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index cb811520c29..169eb49251b 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -8652,6 +8652,32 @@ ATExecSetExpression(AlteredTableInfo *tab, Relation rel, const char *colName,
 		 */
 		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
 	}
+	else
+	{
+		Assert(attgenerated == ATTRIBUTE_GENERATED_VIRTUAL);
+
+		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
+
+		/*
+		 * Changing the generation expression of the virtual generated column
+		 * does not require table rewrite. However, if an index is built on top
+		 * of it, table rewrite is necessary. So in phase 3, index_rebuild can
+		 * successfully rebuild the index based on the new generation expression
+		*/
+		if (tab->changedIndexOids != NIL)
+		{
+			rewrite = true;
+
+			/*
+			 * Clear all the missing values if we're rewriting the table, since
+			 * this renders them pointless.
+			*/
+			RelationClearMissing(rel);
+
+			/* make sure we don't conflict with later attribute modifications */
+			CommandCounterIncrement();
+		}
+	}
 
 	/*
 	 * Drop the dependency records of the GENERATED expression, in particular
@@ -14804,6 +14830,23 @@ ATExecAlterColumnType(AlteredTableInfo *tab, Relation rel,
 	 */
 	RememberAllDependentForRebuilding(tab, AT_AlterColumnType, rel, attnum, colName);
 
+	/*
+	 * tell phase3 do table rewrite if there are any index based on virtual
+	 * generated colum.
+	*/
+	if (attTup->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL &&
+		tab->changedIndexOids != NIL)
+	{
+		Relation	newrel;
+
+		newrel = table_open(RelationGetRelid(rel), NoLock);
+		RelationClearMissing(newrel);
+		relation_close(newrel, NoLock);
+		/* make sure we don't conflict with later attribute modifications */
+		CommandCounterIncrement();
+		tab->rewrite |= AT_REWRITE_COLUMN_REWRITE;
+	}
+
 	/*
 	 * Now scan for dependencies of this column on other things.  The only
 	 * things we should find are the dependency on the column datatype and
@@ -20589,6 +20632,7 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 		AttrMap    *attmap;
 		bool		found = false;
 		Oid			constraintOid;
+		bool		parent_idx_virtual;
 
 		/*
 		 * Ignore indexes in the partitioned table other than partitioned
@@ -20602,9 +20646,19 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 
 		/* construct an indexinfo to compare existing indexes against */
 		info = BuildIndexInfo(idxRel);
+		parent_idx_virtual = IsIndexOverVirtualGenerated(info);
 		attmap = build_attrmap_by_name(RelationGetDescr(attachrel),
 									   RelationGetDescr(rel),
 									   false);
+
+		/*
+		 * The attach partition don't have index, but parent have index over
+		 * virtual generated column. We need ensure generated expression on
+		 * parent that index was based on it match with attach partition.
+		*/
+		if (attachRelIdxs == NIL && parent_idx_virtual)
+			check_generated_indexattrs(info, rel, attachrel, attmap, true);
+
 		constraintOid = get_relation_idx_constraint_oid(RelationGetRelid(rel), idx);
 
 		/*
@@ -20663,6 +20717,22 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 				CommandCounterIncrement();
 				break;
 			}
+			else
+			{
+				bool		attach_idx_virtual;
+				attach_idx_virtual = IsIndexOverVirtualGenerated(attachInfos[i]);
+
+				/* should fail. different index definition cannot merge */
+				if (attach_idx_virtual || parent_idx_virtual)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+									RelationGetRelationName(attachrel),
+									RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									RelationGetRelationName(rel),
+									RelationGetRelationName(attachrel)));
+			}
 		}
 
 		/*
diff --git a/src/backend/parser/parse_utilcmd.c b/src/backend/parser/parse_utilcmd.c
index afcf54169c3..a414bfd6252 100644
--- a/src/backend/parser/parse_utilcmd.c
+++ b/src/backend/parser/parse_utilcmd.c
@@ -1703,6 +1703,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	Form_pg_am	amrec;
 	oidvector  *indcollation;
 	oidvector  *indclass;
+	int2vector	*indgenkey;
 	IndexStmt  *index;
 	List	   *indexprs;
 	ListCell   *indexpr_item;
@@ -1710,6 +1711,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	int			keyno;
 	Oid			keycoltype;
 	Datum		datum;
+	Datum		indgenkeyDatum;
 	bool		isnull;
 
 	if (constraintOid)
@@ -1745,6 +1747,11 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	datum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx, Anum_pg_index_indclass);
 	indclass = (oidvector *) DatumGetPointer(datum);
 
+	/* Extract indattrgenerated from the pg_index tuple */
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* Begin building the IndexStmt */
 	index = makeNode(IndexStmt);
 	index->relation = heapRel;
@@ -1876,13 +1883,29 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	{
 		IndexElem  *iparam;
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Form_pg_attribute attr = TupleDescAttr(RelationGetDescr(source_idx),
 											   keyno);
 		int16		opt = source_idx->rd_indoption[keyno];
 
 		iparam = makeNode(IndexElem);
 
-		if (AttributeNumberIsValid(attnum))
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * index over virtual generated column was converted into a
+			 * expression index, but we need restore the original attribute
+			 * number for recreate it.
+			*/
+			char	   *virtual_attname;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			keycoltype = get_atttype(indrelid, gennum);
+
+			iparam->name = virtual_attname;
+			iparam->expr = NULL;
+		}
+		else if (AttributeNumberIsValid(attnum))
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/backend/utils/adt/ruleutils.c b/src/backend/utils/adt/ruleutils.c
index 3d6e6bdbfd2..70b52578fe2 100644
--- a/src/backend/utils/adt/ruleutils.c
+++ b/src/backend/utils/adt/ruleutils.c
@@ -1290,9 +1290,11 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	Datum		indcollDatum;
 	Datum		indclassDatum;
 	Datum		indoptionDatum;
+	Datum		indgenkeyDatum;
 	oidvector  *indcollation;
 	oidvector  *indclass;
 	int2vector *indoption;
+	int2vector *indgenkey;
 	StringInfoData buf;
 	char	   *str;
 	char	   *sep;
@@ -1325,6 +1327,10 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 											Anum_pg_index_indoption);
 	indoption = (int2vector *) DatumGetPointer(indoptionDatum);
 
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/*
 	 * Fetch the pg_class tuple of the index relation
 	 */
@@ -1398,6 +1404,7 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	for (keyno = 0; keyno < idxrec->indnatts; keyno++)
 	{
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Oid			keycoltype;
 		Oid			keycolcollation;
 
@@ -1418,7 +1425,28 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 			appendStringInfoString(&buf, sep);
 		sep = ", ";
 
-		if (attnum != 0)
+		if (!AttributeNumberIsValid(attnum) && AttributeNumberIsValid(gennum))
+			indexpr_item = lnext(indexprs, indexpr_item);
+
+		/*
+		 * we need firtst check index over virtual generated column then simple
+		 * index column. because virtual generted column can reference another
+		 * column.
+		 */
+		if (AttributeNumberIsValid(gennum))
+		{
+			char	   *virtual_attname;
+			int32		geneycoltypmod;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			if (!colno || colno == keyno + 1)
+				appendStringInfoString(&buf, quote_identifier(virtual_attname));
+
+			get_atttypetypmodcoll(indrelid, gennum,
+								  &keycoltype, &geneycoltypmod,
+								  &keycolcollation);
+		}
+		else if (attnum != 0)
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/include/catalog/index.h b/src/include/catalog/index.h
index 4daa8bef5ee..a7e93f3a107 100644
--- a/src/include/catalog/index.h
+++ b/src/include/catalog/index.h
@@ -126,6 +126,7 @@ extern IndexInfo *BuildIndexInfo(Relation index);
 
 extern IndexInfo *BuildDummyIndexInfo(Relation index);
 
+extern bool IsIndexOverVirtualGenerated(const IndexInfo *info);
 extern bool CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 							 const Oid *collations1, const Oid *collations2,
 							 const Oid *opfamilies1, const Oid *opfamilies2,
@@ -175,6 +176,11 @@ extern void RestoreReindexState(const void *reindexstate);
 
 extern void IndexSetParentIndex(Relation partitionIdx, Oid parentOid);
 
+extern void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+									   Relation rel,
+									   Relation childrel,
+									   const AttrMap *attmap,
+									   bool	is_attach);
 
 /*
  * itemptr_encode - Encode ItemPointer as int64/int8
diff --git a/src/include/catalog/pg_index.h b/src/include/catalog/pg_index.h
index 731d3938169..d00da9c4642 100644
--- a/src/include/catalog/pg_index.h
+++ b/src/include/catalog/pg_index.h
@@ -54,6 +54,7 @@ CATALOG(pg_index,2610,IndexRelationId) BKI_SCHEMA_MACRO
 	oidvector	indclass BKI_LOOKUP(pg_opclass) BKI_FORCE_NOT_NULL; /* opclass identifiers */
 	int2vector	indoption BKI_FORCE_NOT_NULL;	/* per-column flags
 												 * (AM-specific meanings) */
+	int2vector	indattrgenerated BKI_FORCE_NOT_NULL; /* the attribute of virtual generated column? */
 	pg_node_tree indexprs;		/* expression trees for index attributes that
 								 * are not simple column references; one for
 								 * each zero entry in indkey[] */
diff --git a/src/include/nodes/execnodes.h b/src/include/nodes/execnodes.h
index e107d6e5f81..7cef81050b5 100644
--- a/src/include/nodes/execnodes.h
+++ b/src/include/nodes/execnodes.h
@@ -176,6 +176,14 @@ typedef struct IndexInfo
 	 */
 	AttrNumber	ii_IndexAttrNumbers[INDEX_MAX_KEYS];
 
+	/*
+	 * Virtual generated column attribute numbers of the underlying relation
+	 * used as index keys.  A value of zero indicates either an expression or a
+	 * non-virtual generated column.  Note: Virtual generated columns cannot be
+	 * used as index key included columns.
+	*/
+	AttrNumber	ii_IndexAttrGeneratedNumbers[INDEX_MAX_KEYS];
+
 	/* expr trees for expression entries, or NIL if none */
 	List	   *ii_Expressions; /* list of Expr */
 	/* exec state for expressions, or NIL if none */
diff --git a/src/test/regress/expected/collate.icu.utf8.out b/src/test/regress/expected/collate.icu.utf8.out
index 69805d4b9ec..a9c65298dac 100644
--- a/src/test/regress/expected/collate.icu.utf8.out
+++ b/src/test/regress/expected/collate.icu.utf8.out
@@ -2690,6 +2690,17 @@ SELECT * FROM t5 ORDER BY c ASC, a ASC;
  3 | d1 | d1
 (3 rows)
 
+CREATE INDEX t5_idx1 ON t5 USING btree((c COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((c));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated, indcollation[0]::regcollation
+FROM    pg_index
+WHERE indrelid = 't5'::regclass ORDER BY indexrelid;
+ indexrelid | indrelid | indnatts | indattrgenerated | indcollation 
+------------+----------+----------+------------------+--------------
+ t5_idx1    | t5       |        1 | 3                | "POSIX"
+ t5_idx2    | t5       |        1 | 3                | "C"
+(2 rows)
+
 -- cleanup
 RESET search_path;
 SET client_min_messages TO warning;
diff --git a/src/test/regress/expected/fast_default.out b/src/test/regress/expected/fast_default.out
index ccbcdf8403f..ef19f667cc1 100644
--- a/src/test/regress/expected/fast_default.out
+++ b/src/test/regress/expected/fast_default.out
@@ -70,6 +70,14 @@ NOTICE:  rewriting table has_volatile for reason 4
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 NOTICE:  rewriting table has_volatile for reason 2
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+NOTICE:  rewriting table has_volatile for reason 2
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
+NOTICE:  rewriting table has_volatile for reason 4
 -- Test a large sample of different datatypes
 CREATE TABLE T(pk INT NOT NULL PRIMARY KEY, c_int INT DEFAULT 1);
 SELECT set('t');
diff --git a/src/test/regress/expected/generated_virtual.out b/src/test/regress/expected/generated_virtual.out
index 3b40e15a95a..9d3e86b591b 100644
--- a/src/test/regress/expected/generated_virtual.out
+++ b/src/test/regress/expected/generated_virtual.out
@@ -739,30 +739,249 @@ ERROR:  primary keys on virtual generated columns are not supported
 --INSERT INTO gtest22b VALUES (2);
 --INSERT INTO gtest22b VALUES (2);
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ERROR:  cannot create index on partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart3"
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ERROR:  cannot attach table "gtestpart1" as partition of partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart1"
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+       relid       |    parentrelid    | isleaf | level 
+-------------------+-------------------+--------+-------
+ gtestparted_a_idx |                   | f      |     0
+ gtestpart2_a_idx  | gtestparted_a_idx | t      |     1
+(2 rows)
+
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+ERROR:  cannot attach index "gtestpart2_a_idx_copy" as a partition of index "gtestparted_a_idx"
+DETAIL:  Another index is already attached for partition "gtestpart2".
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+         relid         |     parentrelid     | isleaf | level 
+-----------------------+---------------------+--------+-------
+ gtestparted_a_idx_1   |                     | f      |     0
+ gtestpart2_a_idx_copy | gtestparted_a_idx_1 | t      |     1
+(2 rows)
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+           Table "generated_virtual_tests.gtestparted_like"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+ a      | integer |           |          | generated always as (c + 1)
+Indexes:
+    "gtestparted_like_a_idx" btree (a)
+    "gtestparted_like_a_idx1" btree (a)
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2),
+                       c int GENERATED ALWAYS AS (11),
+                       d int GENERATED ALWAYS AS (a *3),
+                       e int4range GENERATED ALWAYS AS (int4range(a, a+10)),
+                       e1 int8range GENERATED ALWAYS AS (int8range(a, a+10)),
+                       f int GENERATED ALWAYS AS (a),
+                       f1 oid GENERATED ALWAYS AS (tableoid));
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+ERROR:  index creation on system columns is not supported
+CREATE INDEX gtest22c_error ON gtest22c (f1);
+ERROR:  index creation on system columns is not supported
+ALTER TABLE gtest22c DROP COLUMN f1;
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e      | int4range |           |          | generated always as (int4range(a, a + 10))
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+    "gtest22c_e_e1_idx" gist (e, e1)
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_d_idx on gtest22c
+   Index Cond: ((a * 3) = 6)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE d = 6;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 and e1 @> 12::bigint;
+                                                      QUERY PLAN                                                       
+-----------------------------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e_e1_idx on gtest22c
+         Index Cond: ((int4range(a, (a + 10)) @> 12) AND (int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint))
+(3 rows)
+
+SELECT count(*) from gtest22c where e @> 12 and e1 @> 12::bigint;
+ count 
+-------
+     2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint;
+                                    QUERY PLAN                                    
+----------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e1_idx on gtest22c
+         Index Cond: (int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint)
+(3 rows)
+
+SELECT count(*) from gtest22c where e1 @> 12::bigint;
+ count 
+-------
+     2
+(1 row)
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 4) = 8)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 8;
+ a | b | c  | d |   e1   | f 
+---+---+----+---+--------+---
+ 2 | 8 | 11 | 6 | [2,12) | 2
+(1 row)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(j jsonb, j1 jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+                f1 interval, f2 interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1)  SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX ON t2 USING brin (f1 interval_minmax_multi_ops, f2 interval_minmax_multi_ops) WITH (pages_per_range=1);
+CREATE INDEX t_gin_j1 ON t2 USING gin (j1);
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+                                           QUERY PLAN                                            
+-------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Bitmap Heap Scan on t2
+         Recheck Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+         ->  Bitmap Index Scan on t_gin_j1
+               Index Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+(5 rows)
+
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+ count 
+-------
+   141
+(1 row)
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+                                                  QUERY PLAN                                                   
+---------------------------------------------------------------------------------------------------------------
+ Bitmap Heap Scan on t2
+   Recheck Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+   ->  Bitmap Index Scan on t2_f1_f2_idx
+         Index Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+(4 rows)
+
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+ j | j1 |    f1    |    f2    
+---+----+----------+----------
+   |    | infinity | infinity
+(1 row)
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
 --INSERT INTO gtest23a VALUES (1, 11), (2, 22), (3, 33);
@@ -1292,6 +1511,7 @@ ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello2');
 DROP STATISTICS gtest31_2_stat;
 CREATE INDEX gtest31_2_y_idx ON gtest31_2(((y).b));
 ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello3');
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
 DROP TABLE gtest31_1, gtest31_2;
 -- Check it for a partitioned table, too
 CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') VIRTUAL, c text) PARTITION BY LIST (a);
@@ -1614,3 +1834,17 @@ select * from gtest32 t group by grouping sets (a, b, c, d, e) having c = 20;
 -- Ensure that the virtual generated columns in ALTER COLUMN TYPE USING expression are expanded
 alter table gtest32 alter column e type bigint using b;
 drop table gtest32;
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
+ indrelid | attnum | attname | attgenerated 
+----------+--------+---------+--------------
+(0 rows)
+
diff --git a/src/test/regress/sql/collate.icu.utf8.sql b/src/test/regress/sql/collate.icu.utf8.sql
index dbc190227d0..5492d2db438 100644
--- a/src/test/regress/sql/collate.icu.utf8.sql
+++ b/src/test/regress/sql/collate.icu.utf8.sql
@@ -997,6 +997,11 @@ INSERT INTO t5 (a, b) values (1, 'D1'), (2, 'D2'), (3, 'd1');
 -- rewriting.)
 SELECT * FROM t5 ORDER BY c ASC, a ASC;
 
+CREATE INDEX t5_idx1 ON t5 USING btree((c COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((c));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated, indcollation[0]::regcollation
+FROM    pg_index
+WHERE indrelid = 't5'::regclass ORDER BY indexrelid;
 
 -- cleanup
 RESET search_path;
diff --git a/src/test/regress/sql/fast_default.sql b/src/test/regress/sql/fast_default.sql
index 068dd0bc8aa..b39e76bcfc3 100644
--- a/src/test/regress/sql/fast_default.sql
+++ b/src/test/regress/sql/fast_default.sql
@@ -77,6 +77,12 @@ ALTER TABLE has_volatile ALTER COLUMN col1 SET DATA TYPE float8,
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
 
 
 -- Test a large sample of different datatypes
diff --git a/src/test/regress/sql/generated_virtual.sql b/src/test/regress/sql/generated_virtual.sql
index e2b31853e01..8587a5704ef 100644
--- a/src/test/regress/sql/generated_virtual.sql
+++ b/src/test/regress/sql/generated_virtual.sql
@@ -1,6 +1,4 @@
 -- keep these tests aligned with generated_stored.sql
-
-
 CREATE SCHEMA generated_virtual_tests;
 GRANT USAGE ON SCHEMA generated_virtual_tests TO PUBLIC;
 SET search_path = generated_virtual_tests;
@@ -392,32 +390,115 @@ CREATE TABLE gtest22b (a int, b int GENERATED ALWAYS AS (a / 2) VIRTUAL, PRIMARY
 --INSERT INTO gtest22b VALUES (2);
 
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2),
+                       c int GENERATED ALWAYS AS (11),
+                       d int GENERATED ALWAYS AS (a *3),
+                       e int4range GENERATED ALWAYS AS (int4range(a, a+10)),
+                       e1 int8range GENERATED ALWAYS AS (int8range(a, a+10)),
+                       f int GENERATED ALWAYS AS (a),
+                       f1 oid GENERATED ALWAYS AS (tableoid));
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+CREATE INDEX gtest22c_error ON gtest22c (f1);
+ALTER TABLE gtest22c DROP COLUMN f1;
+
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
+
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
+\d gtest22c
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+SELECT * FROM gtest22c WHERE b = 4;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+SELECT * FROM gtest22c WHERE d = 6;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 and e1 @> 12::bigint;
+SELECT count(*) from gtest22c where e @> 12 and e1 @> 12::bigint;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint;
+SELECT count(*) from gtest22c where e1 @> 12::bigint;
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
 
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+SELECT * FROM gtest22c WHERE b = 8;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(j jsonb, j1 jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+                f1 interval, f2 interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1)  SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX ON t2 USING brin (f1 interval_minmax_multi_ops, f2 interval_minmax_multi_ops) WITH (pages_per_range=1);
+CREATE INDEX t_gin_j1 ON t2 USING gin (j1);
+
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
@@ -859,3 +940,14 @@ select * from gtest32 t group by grouping sets (a, b, c, d, e) having c = 20;
 alter table gtest32 alter column e type bigint using b;
 
 drop table gtest32;
+
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
-- 
2.34.1

From 7b400c0d026bca74ecfca0873962b18af9003a09 Mon Sep 17 00:00:00 2001
From: jian he <jian.universality@gmail.com>
Date: Thu, 10 Jul 2025 11:43:40 +0800
Subject: [PATCH v5 1/1] index on virtual generated column

* btree, hash, gist, spgist, gin, brin all are supported
* Primary key and unique indexes on virtual generated columns are not supported.
* exclusion constraint on virtual generated columns are not supported, maybe future
* Expression indexes and partial (predicate) indexes on virtual generated
  columns are currently unsupported.
* Indexes with included columns cannot use virtual generated columns.
* An index on a virtual generated column like ``(b INT GENERATED ALWAYS AS (a) VIRTUAL)``
  is effectively equivalent to an index on a.
* Internally, such indexes are transformed into expression indexes.  For
  example, an index on ``(b INT GENERATED ALWAYS AS (a * 2) VIRTUAL)``
  is internally represented as an expression index on (a * 2).
* In the pageinspect module, additional tests added for verify the index content
  for virtual generated columns.
* All index types are supported, including hash and GiST indexes, and
  corresponding regression tests have been added.
* To support ALTER TABLE ... SET EXPRESSION, the pg_index catalog tracks the
  original attribute number of the virtual generated column, allowing
  identification of indexes that require rebuilding.
* ALTER COLUMN SET DATA TYPE also triggers a table rewrite; therefore, tracking
  the attribute number of the virtual generated column used by the index is necessary.
* if the partitioned table and partition both have an index, then the index over the virtual
  generated column should be the same expression. For example, the following last
  command should error out.
    CREATE TABLE parted (b integer,c integer,a integer GENERATED ALWAYS AS (c+1)) PARTITION BY RANGE (b);
    CREATE TABLE part (b integer,c integer,a integer GENERATED ALWAYS AS (c));
    create index on part(a);
    create index on parted(a);
    alter table parted ATTACH partition part for values from (1) to (10);

discussion: https://postgr.es/m/CACJufxGao-cypdNhifHAdt8jHfK6-HX=tRBovBkgRuxw063GaA@mail.gmail.com
discussion: https://postgr.es/m/CACJufxGgkH0PyyqP6ggqcEWHxZzmkV=puY8ad=s8kisss9MAwg@mail.gmail.com
commitfest: https://commitfest.postgresql.org/patch/5667
---
 contrib/pageinspect/expected/btree.out        |  11 +
 contrib/pageinspect/sql/btree.sql             |  10 +
 doc/src/sgml/catalogs.sgml                    |  15 +
 src/backend/catalog/index.c                   |  69 ++++
 src/backend/commands/indexcmds.c              | 301 +++++++++++++++---
 src/backend/commands/tablecmds.c              |  70 ++++
 src/backend/parser/parse_utilcmd.c            |  25 +-
 src/backend/utils/adt/ruleutils.c             |  30 +-
 src/include/catalog/index.h                   |   6 +
 src/include/catalog/pg_index.h                |   1 +
 src/include/nodes/execnodes.h                 |   8 +
 .../regress/expected/collate.icu.utf8.out     |  11 +
 src/test/regress/expected/fast_default.out    |   8 +
 .../regress/expected/generated_virtual.out    | 262 ++++++++++++++-
 src/test/regress/sql/collate.icu.utf8.sql     |   5 +
 src/test/regress/sql/fast_default.sql         |   6 +
 src/test/regress/sql/generated_virtual.sql    | 124 +++++++-
 17 files changed, 894 insertions(+), 68 deletions(-)

diff --git a/contrib/pageinspect/expected/btree.out b/contrib/pageinspect/expected/btree.out
index 0aa5d73322f..b7d36f7d047 100644
--- a/contrib/pageinspect/expected/btree.out
+++ b/contrib/pageinspect/expected/btree.out
@@ -183,6 +183,17 @@ tids       |
 
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 ERROR:  block number 2 is out of range for relation "test1_a_idx"
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+(0 rows)
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/contrib/pageinspect/sql/btree.sql b/contrib/pageinspect/sql/btree.sql
index 102ebdefe3c..2670f85f79a 100644
--- a/contrib/pageinspect/sql/btree.sql
+++ b/contrib/pageinspect/sql/btree.sql
@@ -32,6 +32,16 @@ SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 0));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/doc/src/sgml/catalogs.sgml b/doc/src/sgml/catalogs.sgml
index 4f9192316e0..2f73ac4aa3d 100644
--- a/doc/src/sgml/catalogs.sgml
+++ b/doc/src/sgml/catalogs.sgml
@@ -4589,6 +4589,21 @@ SCRAM-SHA-256$<replaceable>&lt;iteration count&gt;</replaceable>:<replaceable>&l
       </para></entry>
      </row>
 
+     <row>
+      <entry role="catalog_table_entry"><para role="column_definition">
+       <structfield>indattrgenerated</structfield> <type>int2vector</type>
+       (references <link linkend="catalog-pg-attribute"><structname>pg_attribute</structname></link>.<structfield>attnum</structfield>)
+      </para>
+      <para>
+       This is an array of <structfield>indnatts</structfield> values that
+       indicate which virtual generated columns this index indexes.
+       For example, a value of <literal>1 3</literal> would mean that the first
+       and the third table columns of this index entries are virtual generated
+       column. A zero in this array indicates that the corresponding index
+       attribute is not virtual generated column reference.
+      </para></entry>
+     </row>
+
      <row>
       <entry role="catalog_table_entry"><para role="column_definition">
        <structfield>indexprs</structfield> <type>pg_node_tree</type>
diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index aa216683b74..1fad8b4edc4 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -584,6 +584,12 @@ UpdateIndexRelation(Oid indexoid,
 	Relation	pg_index;
 	HeapTuple	tuple;
 	int			i;
+	int2vector *indgenkey;
+	int16	   *colgenerated;
+
+	colgenerated = palloc_array(int16, indexInfo->ii_NumIndexAttrs);
+	for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+		colgenerated[i] = indexInfo->ii_IndexAttrGeneratedNumbers[i];
 
 	/*
 	 * Copy the index key, opclass, and indoption info into arrays (should we
@@ -595,6 +601,7 @@ UpdateIndexRelation(Oid indexoid,
 	indcollation = buildoidvector(collationOids, indexInfo->ii_NumIndexKeyAttrs);
 	indclass = buildoidvector(opclassOids, indexInfo->ii_NumIndexKeyAttrs);
 	indoption = buildint2vector(coloptions, indexInfo->ii_NumIndexKeyAttrs);
+	indgenkey = buildint2vector(colgenerated, indexInfo->ii_NumIndexAttrs);
 
 	/*
 	 * Convert the index expressions (if any) to a text datum
@@ -653,6 +660,7 @@ UpdateIndexRelation(Oid indexoid,
 	values[Anum_pg_index_indcollation - 1] = PointerGetDatum(indcollation);
 	values[Anum_pg_index_indclass - 1] = PointerGetDatum(indclass);
 	values[Anum_pg_index_indoption - 1] = PointerGetDatum(indoption);
+	values[Anum_pg_index_indattrgenerated - 1] = PointerGetDatum(indgenkey);
 	values[Anum_pg_index_indexprs - 1] = exprsDatum;
 	if (exprsDatum == (Datum) 0)
 		nulls[Anum_pg_index_indexprs - 1] = true;
@@ -1134,6 +1142,28 @@ index_create(Relation heapRelation,
 				}
 			}
 
+			/*
+			 * Internally, we convert index of virtual generation column into an
+			 * expression index. For example, if column 'b' is defined as (b INT
+			 * GENERATED ALWAYS AS (a * 2) VIRTUAL) then index over 'b' would
+			 * transformed into an expression index as ((a * 2)). As a result,
+			 * the pg_depend refobjsubid does not retain the original attribute
+			 * number of the virtual generated column. But we need rebuild any
+			 * index that was build on virtual generated column. so we need auto
+			 * dependencies on referenced virtual generated columns.
+			*/
+			for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+			{
+				if (indexInfo->ii_IndexAttrGeneratedNumbers[i] != 0)
+				{
+					ObjectAddressSubSet(referenced, RelationRelationId,
+										heapRelationId,
+										indexInfo->ii_IndexAttrGeneratedNumbers[i]);
+					add_exact_object_address(&referenced, addrs);
+					have_simple_col = false;
+				}
+			}
+
 			/*
 			 * If there are no simply-referenced columns, give the index an
 			 * auto dependency on the whole table.  In most cases, this will
@@ -2428,9 +2458,12 @@ IndexInfo *
 BuildIndexInfo(Relation index)
 {
 	IndexInfo  *ii;
+	HeapTuple	ht_idx;
 	Form_pg_index indexStruct = index->rd_index;
 	int			i;
 	int			numAtts;
+	Datum		indgenkeyDatum;
+	int2vector *indgenkey;
 
 	/* check the number of keys, and copy attr numbers into the IndexInfo */
 	numAtts = indexStruct->indnatts;
@@ -2454,9 +2487,19 @@ BuildIndexInfo(Relation index)
 					   index->rd_indam->amsummarizing,
 					   indexStruct->indisexclusion && indexStruct->indisunique);
 
+	ht_idx = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(indexStruct->indexrelid));
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* fill in attribute numbers */
 	for (i = 0; i < numAtts; i++)
+	{
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
+		ii->ii_IndexAttrGeneratedNumbers[i] = indgenkey->values[i];
+	}
+
+	ReleaseSysCache(ht_idx);
 
 	/* fetch exclusion constraint info if any */
 	if (indexStruct->indisexclusion)
@@ -2523,6 +2566,23 @@ BuildDummyIndexInfo(Relation index)
 	return ii;
 }
 
+/*
+ * IndexOverVirtualGenerated
+ *		Return whether this index is built on virtual generated column.
+ */
+bool
+IsIndexOverVirtualGenerated(const IndexInfo *info)
+{
+	int			i;
+
+	for (i = 0; i < info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(info->ii_IndexAttrGeneratedNumbers[i]))
+			return true;
+	}
+	return false;
+}
+
 /*
  * CompareIndexInfo
  *		Return whether the properties of two indexes (in different tables)
@@ -2585,6 +2645,15 @@ CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 				return false;
 		}
 
+		if (AttributeNumberIsValid(info1->ii_IndexAttrGeneratedNumbers[i]) ||
+			AttributeNumberIsValid(info2->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			/* fail if index over virtual generated column does not match */
+			if (attmap->attnums[info2->ii_IndexAttrGeneratedNumbers[i] - 1] !=
+				info1->ii_IndexAttrGeneratedNumbers[i])
+				return false;
+		}
+
 		/* collation and opfamily are not valid for included columns */
 		if (i >= info1->ii_NumIndexKeyAttrs)
 			continue;
diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 6f753ab6d7a..c0df17f068b 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -54,6 +54,7 @@
 #include "parser/parse_utilcmd.h"
 #include "partitioning/partdesc.h"
 #include "pgstat.h"
+#include "rewrite/rewriteHandler.h"
 #include "rewrite/rewriteManip.h"
 #include "storage/lmgr.h"
 #include "storage/proc.h"
@@ -90,9 +91,15 @@ static void ComputeIndexAttrs(IndexInfo *indexInfo,
 							  bool amcanorder,
 							  bool isconstraint,
 							  bool iswithoutoverlaps,
+							  bool is_primary,
 							  Oid ddl_userid,
 							  int ddl_sec_context,
 							  int *ddl_save_nestlevel);
+static void compute_index_generatedattrs(IndexInfo *indexInfo,
+										 Relation rel,
+										 bool is_primary,
+										 int attn,
+										 int attnum);
 static char *ChooseIndexName(const char *tabname, Oid namespaceId,
 							 const List *colnames, const List *exclusionOpNames,
 							 bool primary, bool isconstraint);
@@ -182,6 +189,7 @@ CheckIndexCompatible(Oid oldId,
 					 bool isWithoutOverlaps)
 {
 	bool		isconstraint;
+	bool		is_primary;
 	Oid		   *typeIds;
 	Oid		   *collationIds;
 	Oid		   *opclassIds;
@@ -214,6 +222,12 @@ CheckIndexCompatible(Oid oldId,
 	 */
 	isconstraint = false;
 
+	/*
+	 * We can pretend is_primary = false unconditionally.  It only serves to
+	 * decide the text of an error message that should never happen for us.
+	 */
+	is_primary = false;
+
 	numberOfAttributes = list_length(attributeList);
 	Assert(numberOfAttributes > 0);
 	Assert(numberOfAttributes <= INDEX_MAX_KEYS);
@@ -254,7 +268,7 @@ CheckIndexCompatible(Oid oldId,
 					  coloptions, attributeList,
 					  exclusionOpNames, relationId,
 					  accessMethodName, accessMethodId,
-					  amcanorder, isconstraint, isWithoutOverlaps, InvalidOid,
+					  amcanorder, isconstraint, isWithoutOverlaps, is_primary, InvalidOid,
 					  0, NULL);
 
 	/* Get the soon-obsolete pg_index tuple. */
@@ -905,6 +919,31 @@ DefineIndex(Oid tableId,
 	if (stmt->whereClause)
 		CheckPredicate((Expr *) stmt->whereClause);
 
+	/* virtual generated column over predicate indexes are not supported */
+	if (RelationGetDescr(rel)->constr &&
+		RelationGetDescr(rel)->constr->has_generated_virtual &&
+		stmt->whereClause)
+	{
+		Bitmapset  *indexattrs_pred = NULL;
+		int			j;
+
+		pull_varattnos(stmt->whereClause, 1, &indexattrs_pred);
+
+		j = -1;
+		while ((j = bms_next_member(indexattrs_pred, j)) >= 0)
+		{
+			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+
+			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+			{
+				ereport(ERROR,
+						errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+						errmsg("partial index on virtual generated columns are not supported"));
+				break;
+			}
+		}
+	}
+
 	/*
 	 * Parse AM-specific options, convert to text array form, validate.
 	 */
@@ -941,6 +980,7 @@ DefineIndex(Oid tableId,
 					  stmt->excludeOpNames, tableId,
 					  accessMethodName, accessMethodId,
 					  amcanorder, stmt->isconstraint, stmt->iswithoutoverlaps,
+					  stmt->primary,
 					  root_save_userid, root_save_sec_context,
 					  &root_save_nestlevel);
 
@@ -1102,9 +1142,6 @@ DefineIndex(Oid tableId,
 	/*
 	 * We disallow indexes on system columns.  They would not necessarily get
 	 * updated correctly, and they don't seem useful anyway.
-	 *
-	 * Also disallow virtual generated columns in indexes (use expression
-	 * index instead).
 	 */
 	for (int i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
 	{
@@ -1114,26 +1151,14 @@ DefineIndex(Oid tableId,
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("index creation on system columns is not supported")));
-
-
-		if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-			ereport(ERROR,
-					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-					stmt->primary ?
-					errmsg("primary keys on virtual generated columns are not supported") :
-					stmt->isconstraint ?
-					errmsg("unique constraints on virtual generated columns are not supported") :
-					errmsg("indexes on virtual generated columns are not supported"));
 	}
 
 	/*
-	 * Also check for system and generated columns used in expressions or
-	 * predicates.
+	 * Also check for system columns used in expressions or predicates.
 	 */
 	if (indexInfo->ii_Expressions || indexInfo->ii_Predicate)
 	{
 		Bitmapset  *indexattrs = NULL;
-		int			j;
 
 		pull_varattnos((Node *) indexInfo->ii_Expressions, 1, &indexattrs);
 		pull_varattnos((Node *) indexInfo->ii_Predicate, 1, &indexattrs);
@@ -1146,24 +1171,6 @@ DefineIndex(Oid tableId,
 						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 						 errmsg("index creation on system columns is not supported")));
 		}
-
-		/*
-		 * XXX Virtual generated columns in index expressions or predicates
-		 * could be supported, but it needs support in
-		 * RelationGetIndexExpressions() and RelationGetIndexPredicate().
-		 */
-		j = -1;
-		while ((j = bms_next_member(indexattrs, j)) >= 0)
-		{
-			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
-
-			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-				ereport(ERROR,
-						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-						 stmt->isconstraint ?
-						 errmsg("unique constraints on virtual generated columns are not supported") :
-						 errmsg("indexes on virtual generated columns are not supported")));
-		}
 	}
 
 	/* Is index safe for others to ignore?  See set_indexsafe_procflags() */
@@ -1307,6 +1314,7 @@ DefineIndex(Oid tableId,
 			bool		invalidate_parent = false;
 			Relation	parentIndex;
 			TupleDesc	parentDesc;
+			bool		parent_idx_virtual;
 
 			/*
 			 * Report the total number of partitions at the start of the
@@ -1353,6 +1361,8 @@ DefineIndex(Oid tableId,
 			parentIndex = index_open(indexRelationId, lockmode);
 			indexInfo = BuildIndexInfo(parentIndex);
 
+			parent_idx_virtual = IsIndexOverVirtualGenerated(indexInfo);
+
 			parentDesc = RelationGetDescr(rel);
 
 			/*
@@ -1412,6 +1422,14 @@ DefineIndex(Oid tableId,
 										  parentDesc,
 										  false);
 
+				/*
+				 * child don't have any index, but parent have index over
+				 * virtual generated column. We need ensure the indexed
+				 * generated expression on the parent match with the child.
+				*/
+				if (childidxs == NIL && parent_idx_virtual)
+					check_generated_indexattrs(indexInfo, rel, childrel, attmap, false);
+
 				foreach(cell, childidxs)
 				{
 					Oid			cldidxid = lfirst_oid(cell);
@@ -1481,6 +1499,22 @@ DefineIndex(Oid tableId,
 						index_close(cldidx, NoLock);
 						break;
 					}
+					else
+					{
+						bool	cldidx_virtual;
+						bool	index_virtual;
+						index_virtual = IsIndexOverVirtualGenerated(indexInfo);
+						cldidx_virtual = IsIndexOverVirtualGenerated(cldIdxInfo);
+
+						if (index_virtual || cldidx_virtual)
+							ereport(ERROR,
+									errcode(ERRCODE_WRONG_OBJECT_TYPE),
+									errmsg("cannot create index on partitioned table \"%s\"",
+										   RelationGetRelationName(rel)),
+									errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+											  RelationGetRelationName(rel),
+											  RelationGetRelationName(childrel)));
+					}
 
 					index_close(cldidx, lockmode);
 				}
@@ -1857,6 +1891,73 @@ CheckPredicate(Expr *predicate)
 				 errmsg("functions in index predicate must be marked IMMUTABLE")));
 }
 
+/*
+ * Verify that the generated expression of the parent matches that of the child
+ *
+ * rel_idx_info: the IndexInfo that is associated with rel.
+ * childrel: the relation to be attached to "rel" or the child of "rel".
+ * attmap: Attribute mapping between childrel and rel.
+ * is_attach: is this command of ALTER TABLE ATTACH PARTITION
+ *
+ * Use build_attrmap_by_name(childrel, rel) to build the attmap.
+*/
+void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+								Relation rel,
+								Relation childrel,
+								const AttrMap *attmap,
+								bool is_attach)
+{
+	/* if parent have virtual generated column, child must also have */
+	Assert(rel->rd_att->constr->has_generated_virtual);
+	Assert(childrel->rd_att->constr->has_generated_virtual);
+
+	for (int i = 0; i < rel_idx_info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(rel_idx_info->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			Node	   *node_rel;
+			Node	   *node_attach;
+			AttrNumber	attno;
+			bool		found_whole_row;
+
+			attno	= rel_idx_info->ii_IndexAttrGeneratedNumbers[i];
+
+			node_rel = 	build_generation_expression(rel, attno);
+			node_rel = map_variable_attnos(node_rel,
+										   1,
+										   0,
+										   attmap,
+										   InvalidOid, &found_whole_row);
+			if (found_whole_row)
+				elog(ERROR, "Index contains a whole-row table reference");
+
+			node_attach = build_generation_expression(childrel,
+													  attmap->attnums[attno - 1]);
+
+			if (!equal(node_rel, node_attach))
+			{
+				if (is_attach)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+								   RelationGetRelationName(childrel),
+								   RelationGetRelationName(rel));
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+				else
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot create index on partitioned table \"%s\"",
+								   RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+			}
+		}
+	}
+}
+
 /*
  * Compute per-index-column information, including indexed column numbers
  * or index expressions, opclasses and their options. Note, all output vectors
@@ -1881,6 +1982,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 				  bool amcanorder,
 				  bool isconstraint,
 				  bool iswithoutoverlaps,
+				  bool is_primary,
 				  Oid ddl_userid,
 				  int ddl_sec_context,
 				  int *ddl_save_nestlevel)
@@ -1891,6 +1993,28 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 	int			nkeycols = indexInfo->ii_NumIndexKeyAttrs;
 	Oid			save_userid;
 	int			save_sec_context;
+	Relation	rel;
+	TupleDesc	reltupldesc;
+	List		*virtual_generated = NIL;
+
+	rel	= table_open(relId, NoLock);
+	reltupldesc = RelationGetDescr(rel);
+
+	/*
+	 * Currently, we do not support virtual generated columns over expression
+	 * indexes.  we accumulate the attribute number of virtual generated columns
+	 * so we can verify it later.
+	*/
+	if (reltupldesc->constr && reltupldesc->constr->has_generated_virtual)
+	{
+		for (int i = 0; i < reltupldesc->natts; i++)
+		{
+			Form_pg_attribute attr = TupleDescAttr(reltupldesc, i);
+
+			if (attr->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				virtual_generated = lappend_int(virtual_generated, attr->attnum);
+		}
+	}
 
 	/* Allocate space for exclusion operator info, if needed */
 	if (exclusionOpNames)
@@ -1963,6 +2087,12 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
 			atttype = attform->atttypid;
 			attcollation = attform->attcollation;
+
+			if (attform->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				compute_index_generatedattrs(indexInfo, rel, is_primary, attn, attform->attnum);
+			else
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
+
 			ReleaseSysCache(atttuple);
 		}
 		else
@@ -1986,18 +2116,42 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			while (IsA(expr, CollateExpr))
 				expr = (Node *) ((CollateExpr *) expr)->arg;
 
+			if (!IsA(expr, Var))
+			{
+				Bitmapset  *idxattrs = NULL;
+				int			j = -1;
+
+				pull_varattnos(expr, 1, &idxattrs);
+				while ((j = bms_next_member(idxattrs, j)) >= 0)
+				{
+					AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+					if (list_member_int(virtual_generated, attno))
+						ereport(ERROR,
+								errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+								errmsg("expression index over virtual generated columns are not supported"));
+				}
+			}
+
 			if (IsA(expr, Var) &&
 				((Var *) expr)->varattno != InvalidAttrNumber)
 			{
+				int			attnum = ((Var *) expr)->varattno;
+
 				/*
 				 * User wrote "(column)" or "(column COLLATE something)".
 				 * Treat it like simple attribute anyway.
 				 */
-				indexInfo->ii_IndexAttrNumbers[attn] = ((Var *) expr)->varattno;
+				indexInfo->ii_IndexAttrNumbers[attn] = attnum;
+
+				if (list_member_int(virtual_generated, attnum))
+					compute_index_generatedattrs(indexInfo, rel, is_primary, attn, attnum);
+				else
+					indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 			}
 			else
 			{
 				indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* marks expression */
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 				indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
 													expr);
 
@@ -2248,6 +2402,81 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 
 		attn++;
 	}
+
+	table_close(rel, NoLock);
+}
+
+/*
+ * indexInfo: this IndexInfo to be build.
+ * rel: the relation this indexInfo is based on.
+ * is_primary: is this index a primary key.
+ * attn: indices of the index key attribute, 0 based.
+ * attnum: virtual generated column attribute number.
+*/
+static void
+compute_index_generatedattrs(IndexInfo *indexInfo, Relation rel,
+							 bool is_primary, int attn, int attnum)
+{
+	Node	   *node;
+
+	if (is_primary)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("primary keys on virtual generated columns are not supported"));
+
+	if (indexInfo->ii_Unique)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("unique constraints on virtual generated columns are not supported"));
+
+	if (attn >= indexInfo->ii_NumIndexKeyAttrs)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("virtual generated column are not supported in index included columns"));
+
+	/* Fetch the GENERATED AS expression tree */
+	node = build_generation_expression(rel, attnum);
+
+	/*
+	 * if the generation expression just reference another Var node, then set
+	 * ii_IndexAttrNumbers to that Var->varattno.
+	*/
+	if (IsA(node, Var))
+	{
+		Var		   *var = (Var *) node;
+
+		if (var->varattno < 0)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("index creation on system columns is not supported"));
+
+		indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+	}
+	else
+	{
+		/*
+		 * Strip any top-level COLLATE clause in generated expression.  This
+		 * ensures that we treat "x COLLATE y" and "(x COLLATE y)" alike.
+		*/
+		while (IsA(node, CollateExpr))
+			node = (Node *) ((CollateExpr *) node)->arg;
+
+		if (IsA(node, Var))
+		{
+			Var		   *var = (Var *) node;
+
+			Assert(var->varattno > 0);
+			indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+		}
+		else
+		{
+			indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* mark as expression index */
+			indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
+												node);
+		}
+	}
+
+	indexInfo->ii_IndexAttrGeneratedNumbers[attn] = attnum;
 }
 
 /*
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index cb811520c29..169eb49251b 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -8652,6 +8652,32 @@ ATExecSetExpression(AlteredTableInfo *tab, Relation rel, const char *colName,
 		 */
 		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
 	}
+	else
+	{
+		Assert(attgenerated == ATTRIBUTE_GENERATED_VIRTUAL);
+
+		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
+
+		/*
+		 * Changing the generation expression of the virtual generated column
+		 * does not require table rewrite. However, if an index is built on top
+		 * of it, table rewrite is necessary. So in phase 3, index_rebuild can
+		 * successfully rebuild the index based on the new generation expression
+		*/
+		if (tab->changedIndexOids != NIL)
+		{
+			rewrite = true;
+
+			/*
+			 * Clear all the missing values if we're rewriting the table, since
+			 * this renders them pointless.
+			*/
+			RelationClearMissing(rel);
+
+			/* make sure we don't conflict with later attribute modifications */
+			CommandCounterIncrement();
+		}
+	}
 
 	/*
 	 * Drop the dependency records of the GENERATED expression, in particular
@@ -14804,6 +14830,23 @@ ATExecAlterColumnType(AlteredTableInfo *tab, Relation rel,
 	 */
 	RememberAllDependentForRebuilding(tab, AT_AlterColumnType, rel, attnum, colName);
 
+	/*
+	 * tell phase3 do table rewrite if there are any index based on virtual
+	 * generated colum.
+	*/
+	if (attTup->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL &&
+		tab->changedIndexOids != NIL)
+	{
+		Relation	newrel;
+
+		newrel = table_open(RelationGetRelid(rel), NoLock);
+		RelationClearMissing(newrel);
+		relation_close(newrel, NoLock);
+		/* make sure we don't conflict with later attribute modifications */
+		CommandCounterIncrement();
+		tab->rewrite |= AT_REWRITE_COLUMN_REWRITE;
+	}
+
 	/*
 	 * Now scan for dependencies of this column on other things.  The only
 	 * things we should find are the dependency on the column datatype and
@@ -20589,6 +20632,7 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 		AttrMap    *attmap;
 		bool		found = false;
 		Oid			constraintOid;
+		bool		parent_idx_virtual;
 
 		/*
 		 * Ignore indexes in the partitioned table other than partitioned
@@ -20602,9 +20646,19 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 
 		/* construct an indexinfo to compare existing indexes against */
 		info = BuildIndexInfo(idxRel);
+		parent_idx_virtual = IsIndexOverVirtualGenerated(info);
 		attmap = build_attrmap_by_name(RelationGetDescr(attachrel),
 									   RelationGetDescr(rel),
 									   false);
+
+		/*
+		 * The attach partition don't have index, but parent have index over
+		 * virtual generated column. We need ensure generated expression on
+		 * parent that index was based on it match with attach partition.
+		*/
+		if (attachRelIdxs == NIL && parent_idx_virtual)
+			check_generated_indexattrs(info, rel, attachrel, attmap, true);
+
 		constraintOid = get_relation_idx_constraint_oid(RelationGetRelid(rel), idx);
 
 		/*
@@ -20663,6 +20717,22 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 				CommandCounterIncrement();
 				break;
 			}
+			else
+			{
+				bool		attach_idx_virtual;
+				attach_idx_virtual = IsIndexOverVirtualGenerated(attachInfos[i]);
+
+				/* should fail. different index definition cannot merge */
+				if (attach_idx_virtual || parent_idx_virtual)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+									RelationGetRelationName(attachrel),
+									RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									RelationGetRelationName(rel),
+									RelationGetRelationName(attachrel)));
+			}
 		}
 
 		/*
diff --git a/src/backend/parser/parse_utilcmd.c b/src/backend/parser/parse_utilcmd.c
index afcf54169c3..a414bfd6252 100644
--- a/src/backend/parser/parse_utilcmd.c
+++ b/src/backend/parser/parse_utilcmd.c
@@ -1703,6 +1703,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	Form_pg_am	amrec;
 	oidvector  *indcollation;
 	oidvector  *indclass;
+	int2vector	*indgenkey;
 	IndexStmt  *index;
 	List	   *indexprs;
 	ListCell   *indexpr_item;
@@ -1710,6 +1711,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	int			keyno;
 	Oid			keycoltype;
 	Datum		datum;
+	Datum		indgenkeyDatum;
 	bool		isnull;
 
 	if (constraintOid)
@@ -1745,6 +1747,11 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	datum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx, Anum_pg_index_indclass);
 	indclass = (oidvector *) DatumGetPointer(datum);
 
+	/* Extract indattrgenerated from the pg_index tuple */
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* Begin building the IndexStmt */
 	index = makeNode(IndexStmt);
 	index->relation = heapRel;
@@ -1876,13 +1883,29 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	{
 		IndexElem  *iparam;
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Form_pg_attribute attr = TupleDescAttr(RelationGetDescr(source_idx),
 											   keyno);
 		int16		opt = source_idx->rd_indoption[keyno];
 
 		iparam = makeNode(IndexElem);
 
-		if (AttributeNumberIsValid(attnum))
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * index over virtual generated column was converted into a
+			 * expression index, but we need restore the original attribute
+			 * number for recreate it.
+			*/
+			char	   *virtual_attname;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			keycoltype = get_atttype(indrelid, gennum);
+
+			iparam->name = virtual_attname;
+			iparam->expr = NULL;
+		}
+		else if (AttributeNumberIsValid(attnum))
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/backend/utils/adt/ruleutils.c b/src/backend/utils/adt/ruleutils.c
index 3d6e6bdbfd2..70b52578fe2 100644
--- a/src/backend/utils/adt/ruleutils.c
+++ b/src/backend/utils/adt/ruleutils.c
@@ -1290,9 +1290,11 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	Datum		indcollDatum;
 	Datum		indclassDatum;
 	Datum		indoptionDatum;
+	Datum		indgenkeyDatum;
 	oidvector  *indcollation;
 	oidvector  *indclass;
 	int2vector *indoption;
+	int2vector *indgenkey;
 	StringInfoData buf;
 	char	   *str;
 	char	   *sep;
@@ -1325,6 +1327,10 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 											Anum_pg_index_indoption);
 	indoption = (int2vector *) DatumGetPointer(indoptionDatum);
 
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/*
 	 * Fetch the pg_class tuple of the index relation
 	 */
@@ -1398,6 +1404,7 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	for (keyno = 0; keyno < idxrec->indnatts; keyno++)
 	{
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Oid			keycoltype;
 		Oid			keycolcollation;
 
@@ -1418,7 +1425,28 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 			appendStringInfoString(&buf, sep);
 		sep = ", ";
 
-		if (attnum != 0)
+		if (!AttributeNumberIsValid(attnum) && AttributeNumberIsValid(gennum))
+			indexpr_item = lnext(indexprs, indexpr_item);
+
+		/*
+		 * we need firtst check index over virtual generated column then simple
+		 * index column. because virtual generted column can reference another
+		 * column.
+		 */
+		if (AttributeNumberIsValid(gennum))
+		{
+			char	   *virtual_attname;
+			int32		geneycoltypmod;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			if (!colno || colno == keyno + 1)
+				appendStringInfoString(&buf, quote_identifier(virtual_attname));
+
+			get_atttypetypmodcoll(indrelid, gennum,
+								  &keycoltype, &geneycoltypmod,
+								  &keycolcollation);
+		}
+		else if (attnum != 0)
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/include/catalog/index.h b/src/include/catalog/index.h
index 4daa8bef5ee..a7e93f3a107 100644
--- a/src/include/catalog/index.h
+++ b/src/include/catalog/index.h
@@ -126,6 +126,7 @@ extern IndexInfo *BuildIndexInfo(Relation index);
 
 extern IndexInfo *BuildDummyIndexInfo(Relation index);
 
+extern bool IsIndexOverVirtualGenerated(const IndexInfo *info);
 extern bool CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 							 const Oid *collations1, const Oid *collations2,
 							 const Oid *opfamilies1, const Oid *opfamilies2,
@@ -175,6 +176,11 @@ extern void RestoreReindexState(const void *reindexstate);
 
 extern void IndexSetParentIndex(Relation partitionIdx, Oid parentOid);
 
+extern void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+									   Relation rel,
+									   Relation childrel,
+									   const AttrMap *attmap,
+									   bool	is_attach);
 
 /*
  * itemptr_encode - Encode ItemPointer as int64/int8
diff --git a/src/include/catalog/pg_index.h b/src/include/catalog/pg_index.h
index 731d3938169..d00da9c4642 100644
--- a/src/include/catalog/pg_index.h
+++ b/src/include/catalog/pg_index.h
@@ -54,6 +54,7 @@ CATALOG(pg_index,2610,IndexRelationId) BKI_SCHEMA_MACRO
 	oidvector	indclass BKI_LOOKUP(pg_opclass) BKI_FORCE_NOT_NULL; /* opclass identifiers */
 	int2vector	indoption BKI_FORCE_NOT_NULL;	/* per-column flags
 												 * (AM-specific meanings) */
+	int2vector	indattrgenerated BKI_FORCE_NOT_NULL; /* the attribute of virtual generated column? */
 	pg_node_tree indexprs;		/* expression trees for index attributes that
 								 * are not simple column references; one for
 								 * each zero entry in indkey[] */
diff --git a/src/include/nodes/execnodes.h b/src/include/nodes/execnodes.h
index e107d6e5f81..7cef81050b5 100644
--- a/src/include/nodes/execnodes.h
+++ b/src/include/nodes/execnodes.h
@@ -176,6 +176,14 @@ typedef struct IndexInfo
 	 */
 	AttrNumber	ii_IndexAttrNumbers[INDEX_MAX_KEYS];
 
+	/*
+	 * Virtual generated column attribute numbers of the underlying relation
+	 * used as index keys.  A value of zero indicates either an expression or a
+	 * non-virtual generated column.  Note: Virtual generated columns cannot be
+	 * used as index key included columns.
+	*/
+	AttrNumber	ii_IndexAttrGeneratedNumbers[INDEX_MAX_KEYS];
+
 	/* expr trees for expression entries, or NIL if none */
 	List	   *ii_Expressions; /* list of Expr */
 	/* exec state for expressions, or NIL if none */
diff --git a/src/test/regress/expected/collate.icu.utf8.out b/src/test/regress/expected/collate.icu.utf8.out
index 69805d4b9ec..a9c65298dac 100644
--- a/src/test/regress/expected/collate.icu.utf8.out
+++ b/src/test/regress/expected/collate.icu.utf8.out
@@ -2690,6 +2690,17 @@ SELECT * FROM t5 ORDER BY c ASC, a ASC;
  3 | d1 | d1
 (3 rows)
 
+CREATE INDEX t5_idx1 ON t5 USING btree((c COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((c));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated, indcollation[0]::regcollation
+FROM    pg_index
+WHERE indrelid = 't5'::regclass ORDER BY indexrelid;
+ indexrelid | indrelid | indnatts | indattrgenerated | indcollation 
+------------+----------+----------+------------------+--------------
+ t5_idx1    | t5       |        1 | 3                | "POSIX"
+ t5_idx2    | t5       |        1 | 3                | "C"
+(2 rows)
+
 -- cleanup
 RESET search_path;
 SET client_min_messages TO warning;
diff --git a/src/test/regress/expected/fast_default.out b/src/test/regress/expected/fast_default.out
index ccbcdf8403f..ef19f667cc1 100644
--- a/src/test/regress/expected/fast_default.out
+++ b/src/test/regress/expected/fast_default.out
@@ -70,6 +70,14 @@ NOTICE:  rewriting table has_volatile for reason 4
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 NOTICE:  rewriting table has_volatile for reason 2
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+NOTICE:  rewriting table has_volatile for reason 2
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
+NOTICE:  rewriting table has_volatile for reason 4
 -- Test a large sample of different datatypes
 CREATE TABLE T(pk INT NOT NULL PRIMARY KEY, c_int INT DEFAULT 1);
 SELECT set('t');
diff --git a/src/test/regress/expected/generated_virtual.out b/src/test/regress/expected/generated_virtual.out
index 3b40e15a95a..9d3e86b591b 100644
--- a/src/test/regress/expected/generated_virtual.out
+++ b/src/test/regress/expected/generated_virtual.out
@@ -739,30 +739,249 @@ ERROR:  primary keys on virtual generated columns are not supported
 --INSERT INTO gtest22b VALUES (2);
 --INSERT INTO gtest22b VALUES (2);
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ERROR:  cannot create index on partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart3"
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ERROR:  cannot attach table "gtestpart1" as partition of partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart1"
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+       relid       |    parentrelid    | isleaf | level 
+-------------------+-------------------+--------+-------
+ gtestparted_a_idx |                   | f      |     0
+ gtestpart2_a_idx  | gtestparted_a_idx | t      |     1
+(2 rows)
+
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+ERROR:  cannot attach index "gtestpart2_a_idx_copy" as a partition of index "gtestparted_a_idx"
+DETAIL:  Another index is already attached for partition "gtestpart2".
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+         relid         |     parentrelid     | isleaf | level 
+-----------------------+---------------------+--------+-------
+ gtestparted_a_idx_1   |                     | f      |     0
+ gtestpart2_a_idx_copy | gtestparted_a_idx_1 | t      |     1
+(2 rows)
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+           Table "generated_virtual_tests.gtestparted_like"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+ a      | integer |           |          | generated always as (c + 1)
+Indexes:
+    "gtestparted_like_a_idx" btree (a)
+    "gtestparted_like_a_idx1" btree (a)
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2),
+                       c int GENERATED ALWAYS AS (11),
+                       d int GENERATED ALWAYS AS (a *3),
+                       e int4range GENERATED ALWAYS AS (int4range(a, a+10)),
+                       e1 int8range GENERATED ALWAYS AS (int8range(a, a+10)),
+                       f int GENERATED ALWAYS AS (a),
+                       f1 oid GENERATED ALWAYS AS (tableoid));
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+ERROR:  index creation on system columns is not supported
+CREATE INDEX gtest22c_error ON gtest22c (f1);
+ERROR:  index creation on system columns is not supported
+ALTER TABLE gtest22c DROP COLUMN f1;
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e      | int4range |           |          | generated always as (int4range(a, a + 10))
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+    "gtest22c_e_e1_idx" gist (e, e1)
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_d_idx on gtest22c
+   Index Cond: ((a * 3) = 6)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE d = 6;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 and e1 @> 12::bigint;
+                                                      QUERY PLAN                                                       
+-----------------------------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e_e1_idx on gtest22c
+         Index Cond: ((int4range(a, (a + 10)) @> 12) AND (int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint))
+(3 rows)
+
+SELECT count(*) from gtest22c where e @> 12 and e1 @> 12::bigint;
+ count 
+-------
+     2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint;
+                                    QUERY PLAN                                    
+----------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e1_idx on gtest22c
+         Index Cond: (int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint)
+(3 rows)
+
+SELECT count(*) from gtest22c where e1 @> 12::bigint;
+ count 
+-------
+     2
+(1 row)
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 4) = 8)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 8;
+ a | b | c  | d |   e1   | f 
+---+---+----+---+--------+---
+ 2 | 8 | 11 | 6 | [2,12) | 2
+(1 row)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(j jsonb, j1 jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+                f1 interval, f2 interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1)  SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX ON t2 USING brin (f1 interval_minmax_multi_ops, f2 interval_minmax_multi_ops) WITH (pages_per_range=1);
+CREATE INDEX t_gin_j1 ON t2 USING gin (j1);
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+                                           QUERY PLAN                                            
+-------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Bitmap Heap Scan on t2
+         Recheck Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+         ->  Bitmap Index Scan on t_gin_j1
+               Index Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+(5 rows)
+
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+ count 
+-------
+   141
+(1 row)
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+                                                  QUERY PLAN                                                   
+---------------------------------------------------------------------------------------------------------------
+ Bitmap Heap Scan on t2
+   Recheck Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+   ->  Bitmap Index Scan on t2_f1_f2_idx
+         Index Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+(4 rows)
+
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+ j | j1 |    f1    |    f2    
+---+----+----------+----------
+   |    | infinity | infinity
+(1 row)
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
 --INSERT INTO gtest23a VALUES (1, 11), (2, 22), (3, 33);
@@ -1292,6 +1511,7 @@ ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello2');
 DROP STATISTICS gtest31_2_stat;
 CREATE INDEX gtest31_2_y_idx ON gtest31_2(((y).b));
 ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello3');
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
 DROP TABLE gtest31_1, gtest31_2;
 -- Check it for a partitioned table, too
 CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') VIRTUAL, c text) PARTITION BY LIST (a);
@@ -1614,3 +1834,17 @@ select * from gtest32 t group by grouping sets (a, b, c, d, e) having c = 20;
 -- Ensure that the virtual generated columns in ALTER COLUMN TYPE USING expression are expanded
 alter table gtest32 alter column e type bigint using b;
 drop table gtest32;
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
+ indrelid | attnum | attname | attgenerated 
+----------+--------+---------+--------------
+(0 rows)
+
diff --git a/src/test/regress/sql/collate.icu.utf8.sql b/src/test/regress/sql/collate.icu.utf8.sql
index dbc190227d0..5492d2db438 100644
--- a/src/test/regress/sql/collate.icu.utf8.sql
+++ b/src/test/regress/sql/collate.icu.utf8.sql
@@ -997,6 +997,11 @@ INSERT INTO t5 (a, b) values (1, 'D1'), (2, 'D2'), (3, 'd1');
 -- rewriting.)
 SELECT * FROM t5 ORDER BY c ASC, a ASC;
 
+CREATE INDEX t5_idx1 ON t5 USING btree((c COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((c));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated, indcollation[0]::regcollation
+FROM    pg_index
+WHERE indrelid = 't5'::regclass ORDER BY indexrelid;
 
 -- cleanup
 RESET search_path;
diff --git a/src/test/regress/sql/fast_default.sql b/src/test/regress/sql/fast_default.sql
index 068dd0bc8aa..b39e76bcfc3 100644
--- a/src/test/regress/sql/fast_default.sql
+++ b/src/test/regress/sql/fast_default.sql
@@ -77,6 +77,12 @@ ALTER TABLE has_volatile ALTER COLUMN col1 SET DATA TYPE float8,
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
 
 
 -- Test a large sample of different datatypes
diff --git a/src/test/regress/sql/generated_virtual.sql b/src/test/regress/sql/generated_virtual.sql
index e2b31853e01..8587a5704ef 100644
--- a/src/test/regress/sql/generated_virtual.sql
+++ b/src/test/regress/sql/generated_virtual.sql
@@ -1,6 +1,4 @@
 -- keep these tests aligned with generated_stored.sql
-
-
 CREATE SCHEMA generated_virtual_tests;
 GRANT USAGE ON SCHEMA generated_virtual_tests TO PUBLIC;
 SET search_path = generated_virtual_tests;
@@ -392,32 +390,115 @@ CREATE TABLE gtest22b (a int, b int GENERATED ALWAYS AS (a / 2) VIRTUAL, PRIMARY
 --INSERT INTO gtest22b VALUES (2);
 
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2),
+                       c int GENERATED ALWAYS AS (11),
+                       d int GENERATED ALWAYS AS (a *3),
+                       e int4range GENERATED ALWAYS AS (int4range(a, a+10)),
+                       e1 int8range GENERATED ALWAYS AS (int8range(a, a+10)),
+                       f int GENERATED ALWAYS AS (a),
+                       f1 oid GENERATED ALWAYS AS (tableoid));
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+CREATE INDEX gtest22c_error ON gtest22c (f1);
+ALTER TABLE gtest22c DROP COLUMN f1;
+
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
+
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
+\d gtest22c
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+SELECT * FROM gtest22c WHERE b = 4;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+SELECT * FROM gtest22c WHERE d = 6;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 and e1 @> 12::bigint;
+SELECT count(*) from gtest22c where e @> 12 and e1 @> 12::bigint;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint;
+SELECT count(*) from gtest22c where e1 @> 12::bigint;
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
 
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+SELECT * FROM gtest22c WHERE b = 8;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(j jsonb, j1 jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+                f1 interval, f2 interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1)  SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX ON t2 USING brin (f1 interval_minmax_multi_ops, f2 interval_minmax_multi_ops) WITH (pages_per_range=1);
+CREATE INDEX t_gin_j1 ON t2 USING gin (j1);
+
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
@@ -859,3 +940,14 @@ select * from gtest32 t group by grouping sets (a, b, c, d, e) having c = 20;
 alter table gtest32 alter column e type bigint using b;
 
 drop table gtest32;
+
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
-- 
2.34.1

From bbc6f3bd7daf53fe97e72bf92a6f9e1f1d71e736 Mon Sep 17 00:00:00 2001
From: jian he <jian.universality@gmail.com>
Date: Thu, 24 Jul 2025 18:33:33 +0800
Subject: [PATCH v6 1/1] index on virtual generated column

* btree, hash, gist, spgist, gin, brin all are supported
* Primary key and unique indexes on virtual generated columns are not supported.
* exclusion constraint on virtual generated columns are not supported, maybe future
* Expression indexes and partial (predicate) indexes on virtual generated
  columns are currently unsupported.
* Indexes with included columns cannot use virtual generated columns.
* An index on a virtual generated column like ``(b INT GENERATED ALWAYS AS (a) VIRTUAL)``
  is effectively equivalent to an index on a.
* Internally, such indexes are transformed into expression indexes.  For
  example, an index on ``(b INT GENERATED ALWAYS AS (a * 2) VIRTUAL)``
  is internally represented as an expression index on (a * 2).
* In the pageinspect module, additional tests added for verify the index content
  for virtual generated columns.
* All index types are supported, including hash and GiST indexes, and
  corresponding regression tests have been added.
* To support ALTER TABLE ... SET EXPRESSION, the pg_index catalog tracks the
  original attribute number of the virtual generated column, allowing
  identification of indexes that require rebuilding.
* ALTER COLUMN SET DATA TYPE also triggers a table rewrite; therefore, tracking
  the attribute number of the virtual generated column used by the index is necessary.
* if the partitioned table and partition both have an index, then the index over the virtual
  generated column should be the same expression. For example, the following last
  command should error out.
    CREATE TABLE parted (b integer,c integer,a integer GENERATED ALWAYS AS (c+1)) PARTITION BY RANGE (b);
    CREATE TABLE part (b integer,c integer,a integer GENERATED ALWAYS AS (c));
    create index on part(a);
    create index on parted(a);
    alter table parted ATTACH partition part for values from (1) to (10);

discussion: https://postgr.es/m/CACJufxGao-cypdNhifHAdt8jHfK6-HX=tRBovBkgRuxw063GaA@mail.gmail.com
discussion: https://postgr.es/m/CACJufxGgkH0PyyqP6ggqcEWHxZzmkV=puY8ad=s8kisss9MAwg@mail.gmail.com
commitfest: https://commitfest.postgresql.org/patch/5667
---
 contrib/pageinspect/expected/btree.out        |  11 +
 contrib/pageinspect/sql/btree.sql             |  10 +
 doc/src/sgml/catalogs.sgml                    |  15 +
 src/backend/catalog/index.c                   |  77 +++++
 src/backend/commands/indexcmds.c              | 314 +++++++++++++++---
 src/backend/commands/tablecmds.c              |  72 ++++
 src/backend/parser/parse_utilcmd.c            |  25 +-
 src/backend/utils/adt/ruleutils.c             |  34 +-
 src/include/catalog/index.h                   |   6 +
 src/include/catalog/pg_index.h                |   1 +
 src/include/nodes/execnodes.h                 |   8 +
 .../regress/expected/collate.icu.utf8.out     |  11 +
 src/test/regress/expected/fast_default.out    |   8 +
 .../regress/expected/generated_virtual.out    | 262 ++++++++++++++-
 src/test/regress/sql/collate.icu.utf8.sql     |   5 +
 src/test/regress/sql/fast_default.sql         |   6 +
 src/test/regress/sql/generated_virtual.sql    | 124 ++++++-
 17 files changed, 916 insertions(+), 73 deletions(-)

diff --git a/contrib/pageinspect/expected/btree.out b/contrib/pageinspect/expected/btree.out
index 0aa5d73322f..b7d36f7d047 100644
--- a/contrib/pageinspect/expected/btree.out
+++ b/contrib/pageinspect/expected/btree.out
@@ -183,6 +183,17 @@ tids       |
 
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 ERROR:  block number 2 is out of range for relation "test1_a_idx"
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+(0 rows)
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/contrib/pageinspect/sql/btree.sql b/contrib/pageinspect/sql/btree.sql
index 102ebdefe3c..2670f85f79a 100644
--- a/contrib/pageinspect/sql/btree.sql
+++ b/contrib/pageinspect/sql/btree.sql
@@ -32,6 +32,16 @@ SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 0));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/doc/src/sgml/catalogs.sgml b/doc/src/sgml/catalogs.sgml
index 97f547b3cc4..455c27c1617 100644
--- a/doc/src/sgml/catalogs.sgml
+++ b/doc/src/sgml/catalogs.sgml
@@ -4589,6 +4589,21 @@ SCRAM-SHA-256$<replaceable>&lt;iteration count&gt;</replaceable>:<replaceable>&l
       </para></entry>
      </row>
 
+     <row>
+      <entry role="catalog_table_entry"><para role="column_definition">
+       <structfield>indattrgenerated</structfield> <type>int2vector</type>
+       (references <link linkend="catalog-pg-attribute"><structname>pg_attribute</structname></link>.<structfield>attnum</structfield>)
+      </para>
+      <para>
+       This is an array of <structfield>indnatts</structfield> values that
+       indicate which virtual generated columns this index indexes.
+       For example, a value of <literal>1 3</literal> would mean that the first
+       and the third table columns of this index entries are virtual generated
+       column. A zero in this array indicates that the corresponding index
+       attribute is not virtual generated column reference.
+      </para></entry>
+     </row>
+
      <row>
       <entry role="catalog_table_entry"><para role="column_definition">
        <structfield>indexprs</structfield> <type>pg_node_tree</type>
diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index c4029a4f3d3..db067d2788f 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -584,6 +584,12 @@ UpdateIndexRelation(Oid indexoid,
 	Relation	pg_index;
 	HeapTuple	tuple;
 	int			i;
+	int2vector *indgenkey;
+	int16	   *colgenerated;
+
+	colgenerated = palloc_array(int16, indexInfo->ii_NumIndexAttrs);
+	for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+		colgenerated[i] = indexInfo->ii_IndexAttrGeneratedNumbers[i];
 
 	/*
 	 * Copy the index key, opclass, and indoption info into arrays (should we
@@ -595,6 +601,7 @@ UpdateIndexRelation(Oid indexoid,
 	indcollation = buildoidvector(collationOids, indexInfo->ii_NumIndexKeyAttrs);
 	indclass = buildoidvector(opclassOids, indexInfo->ii_NumIndexKeyAttrs);
 	indoption = buildint2vector(coloptions, indexInfo->ii_NumIndexKeyAttrs);
+	indgenkey = buildint2vector(colgenerated, indexInfo->ii_NumIndexAttrs);
 
 	/*
 	 * Convert the index expressions (if any) to a text datum
@@ -653,6 +660,7 @@ UpdateIndexRelation(Oid indexoid,
 	values[Anum_pg_index_indcollation - 1] = PointerGetDatum(indcollation);
 	values[Anum_pg_index_indclass - 1] = PointerGetDatum(indclass);
 	values[Anum_pg_index_indoption - 1] = PointerGetDatum(indoption);
+	values[Anum_pg_index_indattrgenerated - 1] = PointerGetDatum(indgenkey);
 	values[Anum_pg_index_indexprs - 1] = exprsDatum;
 	if (exprsDatum == (Datum) 0)
 		nulls[Anum_pg_index_indexprs - 1] = true;
@@ -1134,6 +1142,28 @@ index_create(Relation heapRelation,
 				}
 			}
 
+			/*
+			 * Internally, we convert index of virtual generation column into an
+			 * expression index. For example, if column 'b' is defined as (b INT
+			 * GENERATED ALWAYS AS (a * 2) VIRTUAL) then index over 'b' would
+			 * transformed into an expression index as ((a * 2)). As a result,
+			 * the pg_depend refobjsubid does not retain the original attribute
+			 * number of the virtual generated column. But we need rebuild any
+			 * index that was build on virtual generated column. so we need auto
+			 * dependencies on referenced virtual generated columns.
+			*/
+			for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+			{
+				if (indexInfo->ii_IndexAttrGeneratedNumbers[i] != 0)
+				{
+					ObjectAddressSubSet(referenced, RelationRelationId,
+										heapRelationId,
+										indexInfo->ii_IndexAttrGeneratedNumbers[i]);
+					add_exact_object_address(&referenced, addrs);
+					have_simple_col = false;
+				}
+			}
+
 			/*
 			 * If there are no simply-referenced columns, give the index an
 			 * auto dependency on the whole table.  In most cases, this will
@@ -1411,6 +1441,7 @@ index_concurrently_create_copy(Relation heapRelation, Oid oldIndexId,
 
 		indexColNames = lappend(indexColNames, NameStr(att->attname));
 		newInfo->ii_IndexAttrNumbers[i] = oldInfo->ii_IndexAttrNumbers[i];
+		newInfo->ii_IndexAttrGeneratedNumbers[i] = oldInfo->ii_IndexAttrGeneratedNumbers[i];
 	}
 
 	/* Extract opclass options for each attribute */
@@ -2428,9 +2459,12 @@ IndexInfo *
 BuildIndexInfo(Relation index)
 {
 	IndexInfo  *ii;
+	HeapTuple	ht_idx;
 	Form_pg_index indexStruct = index->rd_index;
 	int			i;
 	int			numAtts;
+	Datum		indgenkeyDatum;
+	int2vector *indgenkey;
 
 	/* check the number of keys, and copy attr numbers into the IndexInfo */
 	numAtts = indexStruct->indnatts;
@@ -2454,9 +2488,19 @@ BuildIndexInfo(Relation index)
 					   index->rd_indam->amsummarizing,
 					   indexStruct->indisexclusion && indexStruct->indisunique);
 
+	ht_idx = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(indexStruct->indexrelid));
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* fill in attribute numbers */
 	for (i = 0; i < numAtts; i++)
+	{
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
+		ii->ii_IndexAttrGeneratedNumbers[i] = indgenkey->values[i];
+	}
+
+	ReleaseSysCache(ht_idx);
 
 	/* fetch exclusion constraint info if any */
 	if (indexStruct->indisexclusion)
@@ -2518,11 +2562,35 @@ BuildDummyIndexInfo(Relation index)
 	for (i = 0; i < numAtts; i++)
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
 
+	/*
+	 * Index expressions or predicates are skipped here, see above comments. If
+	 * virtual generated columns references another column, ii_IndexAttrNumbers
+	 * will set to that referenced column. So do nothing for
+	 * ii_IndexAttrGeneratedNumbers here.
+	*/
+
 	/* We ignore the exclusion constraint if any */
 
 	return ii;
 }
 
+/*
+ * IndexOverVirtualGenerated
+ *		Return whether this index was built on virtual generated column.
+ */
+bool
+IsIndexOverVirtualGenerated(const IndexInfo *info)
+{
+	int			i;
+
+	for (i = 0; i < info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(info->ii_IndexAttrGeneratedNumbers[i]))
+			return true;
+	}
+	return false;
+}
+
 /*
  * CompareIndexInfo
  *		Return whether the properties of two indexes (in different tables)
@@ -2585,6 +2653,15 @@ CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 				return false;
 		}
 
+		if (AttributeNumberIsValid(info1->ii_IndexAttrGeneratedNumbers[i]) ||
+			AttributeNumberIsValid(info2->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			/* fail if index over virtual generated column does not match */
+			if (attmap->attnums[info2->ii_IndexAttrGeneratedNumbers[i] - 1] !=
+				info1->ii_IndexAttrGeneratedNumbers[i])
+				return false;
+		}
+
 		/* collation and opfamily are not valid for included columns */
 		if (i >= info1->ii_NumIndexKeyAttrs)
 			continue;
diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 6f753ab6d7a..c1ddad07888 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -54,6 +54,7 @@
 #include "parser/parse_utilcmd.h"
 #include "partitioning/partdesc.h"
 #include "pgstat.h"
+#include "rewrite/rewriteHandler.h"
 #include "rewrite/rewriteManip.h"
 #include "storage/lmgr.h"
 #include "storage/proc.h"
@@ -90,9 +91,15 @@ static void ComputeIndexAttrs(IndexInfo *indexInfo,
 							  bool amcanorder,
 							  bool isconstraint,
 							  bool iswithoutoverlaps,
+							  bool is_primary,
 							  Oid ddl_userid,
 							  int ddl_sec_context,
 							  int *ddl_save_nestlevel);
+static void compute_index_generatedattrs(IndexInfo *indexInfo,
+										 Relation rel,
+										 bool is_primary,
+										 int attn,
+										 int attnum);
 static char *ChooseIndexName(const char *tabname, Oid namespaceId,
 							 const List *colnames, const List *exclusionOpNames,
 							 bool primary, bool isconstraint);
@@ -182,6 +189,7 @@ CheckIndexCompatible(Oid oldId,
 					 bool isWithoutOverlaps)
 {
 	bool		isconstraint;
+	bool		is_primary;
 	Oid		   *typeIds;
 	Oid		   *collationIds;
 	Oid		   *opclassIds;
@@ -214,6 +222,12 @@ CheckIndexCompatible(Oid oldId,
 	 */
 	isconstraint = false;
 
+	/*
+	 * We can pretend is_primary = false unconditionally.  It only serves to
+	 * decide the text of an error message that should never happen for us.
+	 */
+	is_primary = false;
+
 	numberOfAttributes = list_length(attributeList);
 	Assert(numberOfAttributes > 0);
 	Assert(numberOfAttributes <= INDEX_MAX_KEYS);
@@ -254,7 +268,7 @@ CheckIndexCompatible(Oid oldId,
 					  coloptions, attributeList,
 					  exclusionOpNames, relationId,
 					  accessMethodName, accessMethodId,
-					  amcanorder, isconstraint, isWithoutOverlaps, InvalidOid,
+					  amcanorder, isconstraint, isWithoutOverlaps, is_primary, InvalidOid,
 					  0, NULL);
 
 	/* Get the soon-obsolete pg_index tuple. */
@@ -905,6 +919,31 @@ DefineIndex(Oid tableId,
 	if (stmt->whereClause)
 		CheckPredicate((Expr *) stmt->whereClause);
 
+	/* virtual generated column over predicate indexes are not supported */
+	if (RelationGetDescr(rel)->constr &&
+		RelationGetDescr(rel)->constr->has_generated_virtual &&
+		stmt->whereClause)
+	{
+		Bitmapset  *indexattrs_pred = NULL;
+		int			j;
+
+		pull_varattnos(stmt->whereClause, 1, &indexattrs_pred);
+
+		j = -1;
+		while ((j = bms_next_member(indexattrs_pred, j)) >= 0)
+		{
+			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+
+			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+			{
+				ereport(ERROR,
+						errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+						errmsg("partial index on virtual generated columns are not supported"));
+				break;
+			}
+		}
+	}
+
 	/*
 	 * Parse AM-specific options, convert to text array form, validate.
 	 */
@@ -941,6 +980,7 @@ DefineIndex(Oid tableId,
 					  stmt->excludeOpNames, tableId,
 					  accessMethodName, accessMethodId,
 					  amcanorder, stmt->isconstraint, stmt->iswithoutoverlaps,
+					  stmt->primary,
 					  root_save_userid, root_save_sec_context,
 					  &root_save_nestlevel);
 
@@ -1102,9 +1142,6 @@ DefineIndex(Oid tableId,
 	/*
 	 * We disallow indexes on system columns.  They would not necessarily get
 	 * updated correctly, and they don't seem useful anyway.
-	 *
-	 * Also disallow virtual generated columns in indexes (use expression
-	 * index instead).
 	 */
 	for (int i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
 	{
@@ -1114,26 +1151,14 @@ DefineIndex(Oid tableId,
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("index creation on system columns is not supported")));
-
-
-		if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-			ereport(ERROR,
-					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-					stmt->primary ?
-					errmsg("primary keys on virtual generated columns are not supported") :
-					stmt->isconstraint ?
-					errmsg("unique constraints on virtual generated columns are not supported") :
-					errmsg("indexes on virtual generated columns are not supported"));
 	}
 
 	/*
-	 * Also check for system and generated columns used in expressions or
-	 * predicates.
+	 * Also check for system columns used in expressions or predicates.
 	 */
 	if (indexInfo->ii_Expressions || indexInfo->ii_Predicate)
 	{
 		Bitmapset  *indexattrs = NULL;
-		int			j;
 
 		pull_varattnos((Node *) indexInfo->ii_Expressions, 1, &indexattrs);
 		pull_varattnos((Node *) indexInfo->ii_Predicate, 1, &indexattrs);
@@ -1146,24 +1171,6 @@ DefineIndex(Oid tableId,
 						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 						 errmsg("index creation on system columns is not supported")));
 		}
-
-		/*
-		 * XXX Virtual generated columns in index expressions or predicates
-		 * could be supported, but it needs support in
-		 * RelationGetIndexExpressions() and RelationGetIndexPredicate().
-		 */
-		j = -1;
-		while ((j = bms_next_member(indexattrs, j)) >= 0)
-		{
-			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
-
-			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-				ereport(ERROR,
-						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-						 stmt->isconstraint ?
-						 errmsg("unique constraints on virtual generated columns are not supported") :
-						 errmsg("indexes on virtual generated columns are not supported")));
-		}
 	}
 
 	/* Is index safe for others to ignore?  See set_indexsafe_procflags() */
@@ -1307,6 +1314,7 @@ DefineIndex(Oid tableId,
 			bool		invalidate_parent = false;
 			Relation	parentIndex;
 			TupleDesc	parentDesc;
+			bool		parent_idx_virtual;
 
 			/*
 			 * Report the total number of partitions at the start of the
@@ -1353,6 +1361,8 @@ DefineIndex(Oid tableId,
 			parentIndex = index_open(indexRelationId, lockmode);
 			indexInfo = BuildIndexInfo(parentIndex);
 
+			parent_idx_virtual = IsIndexOverVirtualGenerated(indexInfo);
+
 			parentDesc = RelationGetDescr(rel);
 
 			/*
@@ -1412,6 +1422,14 @@ DefineIndex(Oid tableId,
 										  parentDesc,
 										  false);
 
+				/*
+				 * child don't have any index, but parent have index over
+				 * virtual generated column. We need ensure the indexed
+				 * generated expression on the parent match with the child.
+				*/
+				if (childidxs == NIL && parent_idx_virtual)
+					check_generated_indexattrs(indexInfo, rel, childrel, attmap, false);
+
 				foreach(cell, childidxs)
 				{
 					Oid			cldidxid = lfirst_oid(cell);
@@ -1481,6 +1499,22 @@ DefineIndex(Oid tableId,
 						index_close(cldidx, NoLock);
 						break;
 					}
+					else
+					{
+						bool	cldidx_virtual;
+						bool	index_virtual;
+						index_virtual = IsIndexOverVirtualGenerated(indexInfo);
+						cldidx_virtual = IsIndexOverVirtualGenerated(cldIdxInfo);
+
+						if (index_virtual || cldidx_virtual)
+							ereport(ERROR,
+									errcode(ERRCODE_WRONG_OBJECT_TYPE),
+									errmsg("cannot create index on partitioned table \"%s\"",
+										   RelationGetRelationName(rel)),
+									errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+											  RelationGetRelationName(rel),
+											  RelationGetRelationName(childrel)));
+					}
 
 					index_close(cldidx, lockmode);
 				}
@@ -1857,6 +1891,73 @@ CheckPredicate(Expr *predicate)
 				 errmsg("functions in index predicate must be marked IMMUTABLE")));
 }
 
+/*
+ * Verify that the generated expression of the parent matches the child
+ *
+ * indexinfo: the IndexInfo that is associated with relation "rel".
+ * childrel: the relation to be attached to "rel" or the child of "rel".
+ * attmap: Attribute mapping between childrel and rel.
+ * is_attach: is this command of ALTER TABLE ATTACH PARTITION
+ *
+ * Use build_attrmap_by_name(childrel, rel) to build the attmap.
+*/
+void check_generated_indexattrs(const IndexInfo *indexinfo,
+								Relation rel,
+								Relation childrel,
+								const AttrMap *attmap,
+								bool is_attach)
+{
+	/* if parent have virtual generated column, child must also have */
+	Assert(rel->rd_att->constr->has_generated_virtual);
+	Assert(childrel->rd_att->constr->has_generated_virtual);
+
+	for (int i = 0; i < indexinfo->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(indexinfo->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			Node	   *node_rel;
+			Node	   *node_attach;
+			AttrNumber	attno;
+			bool		found_whole_row;
+
+			attno	= indexinfo->ii_IndexAttrGeneratedNumbers[i];
+
+			node_rel = 	build_generation_expression(rel, attno);
+			node_rel = map_variable_attnos(node_rel,
+										   1,
+										   0,
+										   attmap,
+										   InvalidOid, &found_whole_row);
+			if (found_whole_row)
+				elog(ERROR, "Index contains a whole-row table reference");
+
+			node_attach = build_generation_expression(childrel,
+													  attmap->attnums[attno - 1]);
+
+			if (!equal(node_rel, node_attach))
+			{
+				if (is_attach)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+								   RelationGetRelationName(childrel),
+								   RelationGetRelationName(rel));
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+				else
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot create index on partitioned table \"%s\"",
+								   RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									  RelationGetRelationName(rel),
+									  RelationGetRelationName(childrel)));
+			}
+		}
+	}
+}
+
 /*
  * Compute per-index-column information, including indexed column numbers
  * or index expressions, opclasses and their options. Note, all output vectors
@@ -1881,6 +1982,7 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 				  bool amcanorder,
 				  bool isconstraint,
 				  bool iswithoutoverlaps,
+				  bool is_primary,
 				  Oid ddl_userid,
 				  int ddl_sec_context,
 				  int *ddl_save_nestlevel)
@@ -1891,6 +1993,28 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 	int			nkeycols = indexInfo->ii_NumIndexKeyAttrs;
 	Oid			save_userid;
 	int			save_sec_context;
+	Relation	rel;
+	TupleDesc	reltupldesc;
+	List		*virtual_generated = NIL;
+
+	rel	= table_open(relId, NoLock);
+	reltupldesc = RelationGetDescr(rel);
+
+	/*
+	 * Currently, we do not support virtual generated columns over expression
+	 * indexes. We accumulate the attribute number of virtual generated columns
+	 * for expression attribute verification.
+	*/
+	if (reltupldesc->constr && reltupldesc->constr->has_generated_virtual)
+	{
+		for (int i = 0; i < reltupldesc->natts; i++)
+		{
+			Form_pg_attribute attr = TupleDescAttr(reltupldesc, i);
+
+			if (attr->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				virtual_generated = lappend_int(virtual_generated, attr->attnum);
+		}
+	}
 
 	/* Allocate space for exclusion operator info, if needed */
 	if (exclusionOpNames)
@@ -1960,7 +2084,13 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 									attribute->name)));
 			}
 			attform = (Form_pg_attribute) GETSTRUCT(atttuple);
-			indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
+			if (attform->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				compute_index_generatedattrs(indexInfo, rel, is_primary, attn, attform->attnum);
+			else
+			{
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
+				indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
+			}
 			atttype = attform->atttypid;
 			attcollation = attform->attcollation;
 			ReleaseSysCache(atttuple);
@@ -1986,18 +2116,43 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 			while (IsA(expr, CollateExpr))
 				expr = (Node *) ((CollateExpr *) expr)->arg;
 
+			if (!IsA(expr, Var))
+			{
+				Bitmapset  *idxattrs = NULL;
+				int			j = -1;
+
+				pull_varattnos(expr, 1, &idxattrs);
+				while ((j = bms_next_member(idxattrs, j)) >= 0)
+				{
+					AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+					if (list_member_int(virtual_generated, attno))
+						ereport(ERROR,
+								errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+								errmsg("expression index over virtual generated columns are not supported"));
+				}
+			}
+
 			if (IsA(expr, Var) &&
 				((Var *) expr)->varattno != InvalidAttrNumber)
 			{
-				/*
-				 * User wrote "(column)" or "(column COLLATE something)".
-				 * Treat it like simple attribute anyway.
-				 */
-				indexInfo->ii_IndexAttrNumbers[attn] = ((Var *) expr)->varattno;
+				int			attnum = ((Var *) expr)->varattno;
+
+				if (list_member_int(virtual_generated, attnum))
+					compute_index_generatedattrs(indexInfo, rel, is_primary, attn, attnum);
+				else
+				{
+					/*
+					 * User wrote "(column)" or "(column COLLATE something)".
+					 * Treat it like simple attribute anyway.
+					 */
+					indexInfo->ii_IndexAttrNumbers[attn] = attnum;
+					indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
+				}
 			}
 			else
 			{
 				indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* marks expression */
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 				indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
 													expr);
 
@@ -2248,6 +2403,83 @@ ComputeIndexAttrs(IndexInfo *indexInfo,
 
 		attn++;
 	}
+
+	table_close(rel, NoLock);
+}
+
+/*
+ * compute IndexInfo ii_IndexAttrNumbers, ii_IndexAttrGeneratedNumbers, ii_Expressions
+ *
+ * indexInfo: this IndexInfo to be build.
+ * rel: the relation this indexInfo is based on.
+ * is_primary: is this index a primary key.
+ * attn: indices of the index key attribute, 0 based.
+ * attnum: virtual generated column attribute number.
+*/
+static void
+compute_index_generatedattrs(IndexInfo *indexInfo, Relation rel,
+							 bool is_primary, int attn, int attnum)
+{
+	Node	   *node;
+
+	if (is_primary)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("primary keys on virtual generated columns are not supported"));
+
+	if (indexInfo->ii_Unique)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("unique constraints on virtual generated columns are not supported"));
+
+	if (attn >= indexInfo->ii_NumIndexKeyAttrs)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("virtual generated column are not supported in index included columns"));
+
+	/* Fetch the GENERATED AS expression tree */
+	node = build_generation_expression(rel, attnum);
+
+	/*
+	 * if the generation expression just reference another column, then set
+	 * ii_IndexAttrNumbers to that column attribute number.
+	*/
+	if (IsA(node, Var))
+	{
+		Var		   *var = (Var *) node;
+
+		if (var->varattno < 0)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("index creation on system columns is not supported"));
+
+		indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+	}
+	else
+	{
+		/*
+		 * Strip any top-level COLLATE clause in generated expression.  This
+		 * ensures that we treat "x COLLATE y" and "(x COLLATE y)" alike.
+		*/
+		while (IsA(node, CollateExpr))
+			node = (Node *) ((CollateExpr *) node)->arg;
+
+		if (IsA(node, Var))
+		{
+			Var		   *var = (Var *) node;
+
+			Assert(var->varattno > 0);
+			indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+		}
+		else
+		{
+			indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* mark as expression index */
+			indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
+												node);
+		}
+	}
+
+	indexInfo->ii_IndexAttrGeneratedNumbers[attn] = attnum;
 }
 
 /*
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index cb811520c29..ce669028f79 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -8652,6 +8652,33 @@ ATExecSetExpression(AlteredTableInfo *tab, Relation rel, const char *colName,
 		 */
 		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
 	}
+	else
+	{
+		Assert(attgenerated == ATTRIBUTE_GENERATED_VIRTUAL);
+
+		/*
+		 * Changing virtual generated column generation expression does not
+		 * require table rewrite. However, if any index is built on top of it,
+		 * table rewrite is necessary.
+		 * Record enough information to let us rebuild index after rewrite in
+		 * Phase3.
+		*/
+		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
+
+		if (tab->changedIndexOids != NIL)
+		{
+			rewrite = true;
+
+			/*
+			 * Clear all the missing values if we're rewriting the table, since
+			 * this renders them pointless.
+			*/
+			RelationClearMissing(rel);
+
+			/* make sure we don't conflict with later attribute modifications */
+			CommandCounterIncrement();
+		}
+	}
 
 	/*
 	 * Drop the dependency records of the GENERATED expression, in particular
@@ -14804,6 +14831,24 @@ ATExecAlterColumnType(AlteredTableInfo *tab, Relation rel,
 	 */
 	RememberAllDependentForRebuilding(tab, AT_AlterColumnType, rel, attnum, colName);
 
+	/*
+	 * Tell phase3 do table rewrite if there are any index based on virtual
+	 * generated colum.
+	*/
+	if (attTup->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL &&
+		tab->changedIndexOids != NIL)
+	{
+		Relation	newrel;
+
+		newrel = table_open(RelationGetRelid(rel), NoLock);
+		RelationClearMissing(newrel);
+		relation_close(newrel, NoLock);
+		/* make sure we don't conflict with later attribute modifications */
+		CommandCounterIncrement();
+
+		tab->rewrite |= AT_REWRITE_COLUMN_REWRITE;
+	}
+
 	/*
 	 * Now scan for dependencies of this column on other things.  The only
 	 * things we should find are the dependency on the column datatype and
@@ -20589,6 +20634,7 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 		AttrMap    *attmap;
 		bool		found = false;
 		Oid			constraintOid;
+		bool		parent_idx_virtual;
 
 		/*
 		 * Ignore indexes in the partitioned table other than partitioned
@@ -20602,9 +20648,19 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 
 		/* construct an indexinfo to compare existing indexes against */
 		info = BuildIndexInfo(idxRel);
+		parent_idx_virtual = IsIndexOverVirtualGenerated(info);
 		attmap = build_attrmap_by_name(RelationGetDescr(attachrel),
 									   RelationGetDescr(rel),
 									   false);
+
+		/*
+		 * The attach partition don't have index, but parent have index over
+		 * virtual generated column. We need ensure generated expression on
+		 * parent that index was based on it match with attach partition.
+		*/
+		if (attachRelIdxs == NIL && parent_idx_virtual)
+			check_generated_indexattrs(info, rel, attachrel, attmap, true);
+
 		constraintOid = get_relation_idx_constraint_oid(RelationGetRelid(rel), idx);
 
 		/*
@@ -20663,6 +20719,22 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 				CommandCounterIncrement();
 				break;
 			}
+			else
+			{
+				bool		attach_idx_virtual;
+				attach_idx_virtual = IsIndexOverVirtualGenerated(attachInfos[i]);
+
+				/* should fail. different index definition cannot merge */
+				if (attach_idx_virtual || parent_idx_virtual)
+					ereport(ERROR,
+							errcode(ERRCODE_WRONG_OBJECT_TYPE),
+							errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+									RelationGetRelationName(attachrel),
+									RelationGetRelationName(rel)),
+							errdetail("The index definition of partitioned table \"%s\" does not match table \"%s\"",
+									RelationGetRelationName(rel),
+									RelationGetRelationName(attachrel)));
+			}
 		}
 
 		/*
diff --git a/src/backend/parser/parse_utilcmd.c b/src/backend/parser/parse_utilcmd.c
index afcf54169c3..a414bfd6252 100644
--- a/src/backend/parser/parse_utilcmd.c
+++ b/src/backend/parser/parse_utilcmd.c
@@ -1703,6 +1703,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	Form_pg_am	amrec;
 	oidvector  *indcollation;
 	oidvector  *indclass;
+	int2vector	*indgenkey;
 	IndexStmt  *index;
 	List	   *indexprs;
 	ListCell   *indexpr_item;
@@ -1710,6 +1711,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	int			keyno;
 	Oid			keycoltype;
 	Datum		datum;
+	Datum		indgenkeyDatum;
 	bool		isnull;
 
 	if (constraintOid)
@@ -1745,6 +1747,11 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	datum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx, Anum_pg_index_indclass);
 	indclass = (oidvector *) DatumGetPointer(datum);
 
+	/* Extract indattrgenerated from the pg_index tuple */
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* Begin building the IndexStmt */
 	index = makeNode(IndexStmt);
 	index->relation = heapRel;
@@ -1876,13 +1883,29 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	{
 		IndexElem  *iparam;
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Form_pg_attribute attr = TupleDescAttr(RelationGetDescr(source_idx),
 											   keyno);
 		int16		opt = source_idx->rd_indoption[keyno];
 
 		iparam = makeNode(IndexElem);
 
-		if (AttributeNumberIsValid(attnum))
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * index over virtual generated column was converted into a
+			 * expression index, but we need restore the original attribute
+			 * number for recreate it.
+			*/
+			char	   *virtual_attname;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			keycoltype = get_atttype(indrelid, gennum);
+
+			iparam->name = virtual_attname;
+			iparam->expr = NULL;
+		}
+		else if (AttributeNumberIsValid(attnum))
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/backend/utils/adt/ruleutils.c b/src/backend/utils/adt/ruleutils.c
index 3d6e6bdbfd2..98fd300c35a 100644
--- a/src/backend/utils/adt/ruleutils.c
+++ b/src/backend/utils/adt/ruleutils.c
@@ -1290,9 +1290,11 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	Datum		indcollDatum;
 	Datum		indclassDatum;
 	Datum		indoptionDatum;
+	Datum		indgenkeyDatum;
 	oidvector  *indcollation;
 	oidvector  *indclass;
 	int2vector *indoption;
+	int2vector *indgenkey;
 	StringInfoData buf;
 	char	   *str;
 	char	   *sep;
@@ -1325,6 +1327,10 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 											Anum_pg_index_indoption);
 	indoption = (int2vector *) DatumGetPointer(indoptionDatum);
 
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/*
 	 * Fetch the pg_class tuple of the index relation
 	 */
@@ -1398,6 +1404,7 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	for (keyno = 0; keyno < idxrec->indnatts; keyno++)
 	{
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Oid			keycoltype;
 		Oid			keycolcollation;
 
@@ -1418,7 +1425,32 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 			appendStringInfoString(&buf, sep);
 		sep = ", ";
 
-		if (attnum != 0)
+		/*
+		 * We need firtst check index over virtual generated column then simple
+		 * index column. Because virtual generted column can reference another
+		 * column.
+		 */
+		if (AttributeNumberIsValid(gennum))
+		{
+			char	   *virtual_attname;
+			int32		geneycoltypmod;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			if (!colno || colno == keyno + 1)
+				appendStringInfoString(&buf, quote_identifier(virtual_attname));
+
+			get_atttypetypmodcoll(indrelid, gennum,
+								  &keycoltype, &geneycoltypmod,
+								  &keycolcollation);
+
+			/*
+			 * We alerady printed the indexing generated column, therefore the
+			 * associated generation expression should not printed.
+			 */
+			if (!AttributeNumberIsValid(attnum))
+				indexpr_item = lnext(indexprs, indexpr_item);
+		}
+		else if (attnum != 0)
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/include/catalog/index.h b/src/include/catalog/index.h
index 4daa8bef5ee..a7e93f3a107 100644
--- a/src/include/catalog/index.h
+++ b/src/include/catalog/index.h
@@ -126,6 +126,7 @@ extern IndexInfo *BuildIndexInfo(Relation index);
 
 extern IndexInfo *BuildDummyIndexInfo(Relation index);
 
+extern bool IsIndexOverVirtualGenerated(const IndexInfo *info);
 extern bool CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 							 const Oid *collations1, const Oid *collations2,
 							 const Oid *opfamilies1, const Oid *opfamilies2,
@@ -175,6 +176,11 @@ extern void RestoreReindexState(const void *reindexstate);
 
 extern void IndexSetParentIndex(Relation partitionIdx, Oid parentOid);
 
+extern void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+									   Relation rel,
+									   Relation childrel,
+									   const AttrMap *attmap,
+									   bool	is_attach);
 
 /*
  * itemptr_encode - Encode ItemPointer as int64/int8
diff --git a/src/include/catalog/pg_index.h b/src/include/catalog/pg_index.h
index 731d3938169..d00da9c4642 100644
--- a/src/include/catalog/pg_index.h
+++ b/src/include/catalog/pg_index.h
@@ -54,6 +54,7 @@ CATALOG(pg_index,2610,IndexRelationId) BKI_SCHEMA_MACRO
 	oidvector	indclass BKI_LOOKUP(pg_opclass) BKI_FORCE_NOT_NULL; /* opclass identifiers */
 	int2vector	indoption BKI_FORCE_NOT_NULL;	/* per-column flags
 												 * (AM-specific meanings) */
+	int2vector	indattrgenerated BKI_FORCE_NOT_NULL; /* the attribute of virtual generated column? */
 	pg_node_tree indexprs;		/* expression trees for index attributes that
 								 * are not simple column references; one for
 								 * each zero entry in indkey[] */
diff --git a/src/include/nodes/execnodes.h b/src/include/nodes/execnodes.h
index e107d6e5f81..7cef81050b5 100644
--- a/src/include/nodes/execnodes.h
+++ b/src/include/nodes/execnodes.h
@@ -176,6 +176,14 @@ typedef struct IndexInfo
 	 */
 	AttrNumber	ii_IndexAttrNumbers[INDEX_MAX_KEYS];
 
+	/*
+	 * Virtual generated column attribute numbers of the underlying relation
+	 * used as index keys.  A value of zero indicates either an expression or a
+	 * non-virtual generated column.  Note: Virtual generated columns cannot be
+	 * used as index key included columns.
+	*/
+	AttrNumber	ii_IndexAttrGeneratedNumbers[INDEX_MAX_KEYS];
+
 	/* expr trees for expression entries, or NIL if none */
 	List	   *ii_Expressions; /* list of Expr */
 	/* exec state for expressions, or NIL if none */
diff --git a/src/test/regress/expected/collate.icu.utf8.out b/src/test/regress/expected/collate.icu.utf8.out
index 69805d4b9ec..4b1ccb7c072 100644
--- a/src/test/regress/expected/collate.icu.utf8.out
+++ b/src/test/regress/expected/collate.icu.utf8.out
@@ -2690,6 +2690,17 @@ SELECT * FROM t5 ORDER BY c ASC, a ASC;
  3 | d1 | d1
 (3 rows)
 
+CREATE INDEX t5_idx1 ON t5 USING btree((c COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((c));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated, indcollation[0]::regcollation
+FROM    pg_index
+WHERE   indrelid = 't5'::regclass ORDER BY indexrelid;
+ indexrelid | indrelid | indnatts | indattrgenerated | indcollation 
+------------+----------+----------+------------------+--------------
+ t5_idx1    | t5       |        1 | 3                | "POSIX"
+ t5_idx2    | t5       |        1 | 3                | "C"
+(2 rows)
+
 -- cleanup
 RESET search_path;
 SET client_min_messages TO warning;
diff --git a/src/test/regress/expected/fast_default.out b/src/test/regress/expected/fast_default.out
index ccbcdf8403f..ef19f667cc1 100644
--- a/src/test/regress/expected/fast_default.out
+++ b/src/test/regress/expected/fast_default.out
@@ -70,6 +70,14 @@ NOTICE:  rewriting table has_volatile for reason 4
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 NOTICE:  rewriting table has_volatile for reason 2
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+NOTICE:  rewriting table has_volatile for reason 2
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
+NOTICE:  rewriting table has_volatile for reason 4
 -- Test a large sample of different datatypes
 CREATE TABLE T(pk INT NOT NULL PRIMARY KEY, c_int INT DEFAULT 1);
 SELECT set('t');
diff --git a/src/test/regress/expected/generated_virtual.out b/src/test/regress/expected/generated_virtual.out
index aca6347babe..3ce22db95fc 100644
--- a/src/test/regress/expected/generated_virtual.out
+++ b/src/test/regress/expected/generated_virtual.out
@@ -739,30 +739,249 @@ ERROR:  primary keys on virtual generated columns are not supported
 --INSERT INTO gtest22b VALUES (2);
 --INSERT INTO gtest22b VALUES (2);
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ERROR:  cannot create index on partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart3"
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ERROR:  cannot attach table "gtestpart1" as partition of partitioned table "gtestparted"
+DETAIL:  The index definition of partitioned table "gtestparted" does not match table "gtestpart1"
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+       relid       |    parentrelid    | isleaf | level 
+-------------------+-------------------+--------+-------
+ gtestparted_a_idx |                   | f      |     0
+ gtestpart2_a_idx  | gtestparted_a_idx | t      |     1
+(2 rows)
+
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+ERROR:  cannot attach index "gtestpart2_a_idx_copy" as a partition of index "gtestparted_a_idx"
+DETAIL:  Another index is already attached for partition "gtestpart2".
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+         relid         |     parentrelid     | isleaf | level 
+-----------------------+---------------------+--------+-------
+ gtestparted_a_idx_1   |                     | f      |     0
+ gtestpart2_a_idx_copy | gtestparted_a_idx_1 | t      |     1
+(2 rows)
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+           Table "generated_virtual_tests.gtestparted_like"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+ a      | integer |           |          | generated always as (c + 1)
+Indexes:
+    "gtestparted_like_a_idx" btree (a)
+    "gtestparted_like_a_idx1" btree (a)
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2),
+                       c int GENERATED ALWAYS AS (11),
+                       d int GENERATED ALWAYS AS (a *3),
+                       e int4range GENERATED ALWAYS AS (int4range(a, a+10)),
+                       e1 int8range GENERATED ALWAYS AS (int8range(a, a+10)),
+                       f int GENERATED ALWAYS AS (a),
+                       f1 oid GENERATED ALWAYS AS (tableoid));
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+ERROR:  index creation on system columns is not supported
+CREATE INDEX gtest22c_error ON gtest22c (f1);
+ERROR:  index creation on system columns is not supported
+ALTER TABLE gtest22c DROP COLUMN f1;
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e      | int4range |           |          | generated always as (int4range(a, a + 10))
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+    "gtest22c_e_e1_idx" gist (e, e1)
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_d_idx on gtest22c
+   Index Cond: ((a * 3) = 6)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE d = 6;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 and e1 @> 12::bigint;
+                                                      QUERY PLAN                                                       
+-----------------------------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e_e1_idx on gtest22c
+         Index Cond: ((int4range(a, (a + 10)) @> 12) AND (int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint))
+(3 rows)
+
+SELECT count(*) from gtest22c where e @> 12 and e1 @> 12::bigint;
+ count 
+-------
+     2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint;
+                                    QUERY PLAN                                    
+----------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e1_idx on gtest22c
+         Index Cond: (int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint)
+(3 rows)
+
+SELECT count(*) from gtest22c where e1 @> 12::bigint;
+ count 
+-------
+     2
+(1 row)
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 4) = 8)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 8;
+ a | b | c  | d |   e1   | f 
+---+---+----+---+--------+---
+ 2 | 8 | 11 | 6 | [2,12) | 2
+(1 row)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(j jsonb, j1 jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+                f1 interval, f2 interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1)  SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX ON t2 USING brin (f1 interval_minmax_multi_ops, f2 interval_minmax_multi_ops) WITH (pages_per_range=1);
+CREATE INDEX t_gin_j1 ON t2 USING gin (j1);
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+                                           QUERY PLAN                                            
+-------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Bitmap Heap Scan on t2
+         Recheck Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+         ->  Bitmap Index Scan on t_gin_j1
+               Index Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+(5 rows)
+
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+ count 
+-------
+   141
+(1 row)
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+                                                  QUERY PLAN                                                   
+---------------------------------------------------------------------------------------------------------------
+ Bitmap Heap Scan on t2
+   Recheck Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+   ->  Bitmap Index Scan on t2_f1_f2_idx
+         Index Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+(4 rows)
+
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+ j | j1 |    f1    |    f2    
+---+----+----------+----------
+   |    | infinity | infinity
+(1 row)
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
 --INSERT INTO gtest23a VALUES (1, 11), (2, 22), (3, 33);
@@ -1292,6 +1511,7 @@ ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello2');
 DROP STATISTICS gtest31_2_stat;
 CREATE INDEX gtest31_2_y_idx ON gtest31_2(((y).b));
 ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello3');
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
 DROP TABLE gtest31_1, gtest31_2;
 -- Check it for a partitioned table, too
 CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') VIRTUAL, c text) PARTITION BY LIST (a);
@@ -1636,3 +1856,17 @@ select 1 from gtest32 t1 where exists
 (1 row)
 
 drop table gtest32;
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
+ indrelid | attnum | attname | attgenerated 
+----------+--------+---------+--------------
+(0 rows)
+
diff --git a/src/test/regress/sql/collate.icu.utf8.sql b/src/test/regress/sql/collate.icu.utf8.sql
index dbc190227d0..7b2725f8ba5 100644
--- a/src/test/regress/sql/collate.icu.utf8.sql
+++ b/src/test/regress/sql/collate.icu.utf8.sql
@@ -997,6 +997,11 @@ INSERT INTO t5 (a, b) values (1, 'D1'), (2, 'D2'), (3, 'd1');
 -- rewriting.)
 SELECT * FROM t5 ORDER BY c ASC, a ASC;
 
+CREATE INDEX t5_idx1 ON t5 USING btree((c COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((c));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated, indcollation[0]::regcollation
+FROM    pg_index
+WHERE   indrelid = 't5'::regclass ORDER BY indexrelid;
 
 -- cleanup
 RESET search_path;
diff --git a/src/test/regress/sql/fast_default.sql b/src/test/regress/sql/fast_default.sql
index 068dd0bc8aa..b39e76bcfc3 100644
--- a/src/test/regress/sql/fast_default.sql
+++ b/src/test/regress/sql/fast_default.sql
@@ -77,6 +77,12 @@ ALTER TABLE has_volatile ALTER COLUMN col1 SET DATA TYPE float8,
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
 
 
 -- Test a large sample of different datatypes
diff --git a/src/test/regress/sql/generated_virtual.sql b/src/test/regress/sql/generated_virtual.sql
index ba19bc4c701..76a6b70739e 100644
--- a/src/test/regress/sql/generated_virtual.sql
+++ b/src/test/regress/sql/generated_virtual.sql
@@ -1,6 +1,4 @@
 -- keep these tests aligned with generated_stored.sql
-
-
 CREATE SCHEMA generated_virtual_tests;
 GRANT USAGE ON SCHEMA generated_virtual_tests TO PUBLIC;
 SET search_path = generated_virtual_tests;
@@ -392,32 +390,115 @@ CREATE TABLE gtest22b (a int, b int GENERATED ALWAYS AS (a / 2) VIRTUAL, PRIMARY
 --INSERT INTO gtest22b VALUES (2);
 
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer,a integer GENERATED ALWAYS AS (c+1))PARTITION BY RANGE (b);
+CREATE TABLE gtestpart1 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE TABLE gtestpart3 (b integer, c integer, a integer GENERATED ALWAYS AS (c));
+
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 for values from (1) to (10);
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a); --error
+ALTER TABLE gtestparted DETACH PARTITION gtestpart3;
+
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+
+--error: index cannot be created if the partitioned table and its partitions have differing generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 for values from (1) to (10); --error
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 for values from (1) to (10); --ok
+
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree.
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted including all);
+\d gtestparted_like
+
+CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2),
+                       c int GENERATED ALWAYS AS (11),
+                       d int GENERATED ALWAYS AS (a *3),
+                       e int4range GENERATED ALWAYS AS (int4range(a, a+10)),
+                       e1 int8range GENERATED ALWAYS AS (int8range(a, a+10)),
+                       f int GENERATED ALWAYS AS (a),
+                       f1 oid GENERATED ALWAYS AS (tableoid));
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+CREATE INDEX gtest22c_error ON gtest22c (f1);
+ALTER TABLE gtest22c DROP COLUMN f1;
+
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
+
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
+\d gtest22c
+
+INSERT INTO gtest22c(a) VALUES (1), (2), (3), (10);
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+SELECT * FROM gtest22c WHERE b = 4;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+SELECT * FROM gtest22c WHERE b = 4 and c = 11;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+SELECT * FROM gtest22c WHERE d = 6;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 and e1 @> 12::bigint;
+SELECT count(*) from gtest22c where e @> 12 and e1 @> 12::bigint;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint;
+SELECT count(*) from gtest22c where e1 @> 12::bigint;
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+\d gtest22c
 
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+SELECT * FROM gtest22c WHERE b = 8;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(j jsonb, j1 jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+                f1 interval, f2 interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1)  SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX ON t2 USING brin (f1 interval_minmax_multi_ops, f2 interval_minmax_multi_ops) WITH (pages_per_range=1);
+CREATE INDEX t_gin_j1 ON t2 USING gin (j1);
+
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
@@ -868,3 +949,14 @@ select 1 from gtest32 t1 where exists
   (select 1 from gtest32 t2 where t1.a > t2.a and t2.b = 2);
 
 drop table gtest32;
+
+-- sanity check of system catalog
+-- If the index is based on a virtual generated column, then the corresponding
+-- attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
-- 
2.34.1

From 0047c05725121fcb8e241a9edb4bd2983fd4dad2 Mon Sep 17 00:00:00 2001
From: jian he <jian.universality@gmail.com>
Date: Thu, 8 Jan 2026 14:11:30 +0800
Subject: [PATCH v7 1/1] index on virtual generated column

* All index access methods, including btree, hash, GiST, SP-GiST, GIN, and BRIN, are supported.
* Primary key and unique indexes on virtual generated columns are not supported.
* Exclusion constraints on virtual generated columns are not supported at present and maybe in the future.
* Expression indexes and partial (predicate) indexes on virtual generated columns are currently unsupported.
* Indexes with INCLUDED columns cannot reference virtual generated columns.
* An index on a virtual generated column such as (b INT GENERATED ALWAYS AS (a) VIRTUAL)
    is effectively equivalent to an index on column a.
* Internally, indexes on virtual generated columns are implemented as expression
  indexes. For example, an index on ``(b INT GENERATED ALWAYS AS (a * 2) VIRTUAL)``
  is internally represented as an expression index on ``(a * 2)``.
* Additional tests have been added to the pageinspect module to verify index
  contents for virtual generated columns.
* To support ALTER TABLE ... SET EXPRESSION, the pg_index catalog records the
  the attribute number of the virtual generated column, this is need for indexes
  rebuilt.
  ALTER COLUMN SET DATA TYPE triggers table rewrite too; therefore, tracking the
  attribute number of the virtual generated column referenced by an index is
  really needed.
* if the partitioned table and partition both have an index, then the index over the virtual
    generated column should be the same expression. For example, the following last
    command should error out.
CREATE TABLE parted (b integer,c integer,a integer GENERATED ALWAYS AS (c+1)) PARTITION BY RANGE (b);
CREATE TABLE part (b integer,c integer,a integer GENERATED ALWAYS AS (c));
create index on part(a);
create index on parted(a);
alter table parted ATTACH partition part for values from (1) to (10);

discussion: https://postgr.es/m/CACJufxGao-cypdNhifHAdt8jHfK6-HX=tRBovBkgRuxw063GaA@mail.gmail.com
discussion: https://postgr.es/m/CACJufxGgkH0PyyqP6ggqcEWHxZzmkV=puY8ad=s8kisss9MAwg@mail.gmail.com
related thread: https://postgr.es/m/18970-a7d1cfe1f8d5d8d9@postgresql.org
commitfest: https://commitfest.postgresql.org/patch/5667
---
 contrib/pageinspect/expected/btree.out        |  11 +
 contrib/pageinspect/sql/btree.sql             |  10 +
 doc/src/sgml/catalogs.sgml                    |  15 +
 src/backend/catalog/index.c                   |  85 +++++
 src/backend/commands/indexcmds.c              | 310 +++++++++++++---
 src/backend/commands/tablecmds.c              |  47 ++-
 src/backend/executor/execIndexing.c           |  12 +
 src/backend/executor/execPartition.c          |   5 +
 src/backend/parser/parse_utilcmd.c            |  29 +-
 src/backend/utils/adt/ruleutils.c             |  34 +-
 src/include/catalog/index.h                   |   6 +
 src/include/catalog/pg_index.h                |   3 +
 src/include/nodes/execnodes.h                 |   8 +
 src/test/regress/expected/alter_table.out     |  20 ++
 .../regress/expected/collate.icu.utf8.out     |  13 +
 src/test/regress/expected/fast_default.out    |   8 +
 .../regress/expected/generated_virtual.out    | 334 +++++++++++++++++-
 src/test/regress/expected/indexing.out        |  45 +++
 src/test/regress/sql/alter_table.sql          |   9 +
 src/test/regress/sql/collate.icu.utf8.sql     |   8 +
 src/test/regress/sql/fast_default.sql         |   6 +
 src/test/regress/sql/generated_virtual.sql    | 146 +++++++-
 src/test/regress/sql/indexing.sql             |  30 ++
 23 files changed, 1114 insertions(+), 80 deletions(-)

diff --git a/contrib/pageinspect/expected/btree.out b/contrib/pageinspect/expected/btree.out
index 0aa5d73322f..b7d36f7d047 100644
--- a/contrib/pageinspect/expected/btree.out
+++ b/contrib/pageinspect/expected/btree.out
@@ -183,6 +183,17 @@ tids       |
 
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 ERROR:  block number 2 is out of range for relation "test1_a_idx"
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+(0 rows)
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/contrib/pageinspect/sql/btree.sql b/contrib/pageinspect/sql/btree.sql
index 102ebdefe3c..2670f85f79a 100644
--- a/contrib/pageinspect/sql/btree.sql
+++ b/contrib/pageinspect/sql/btree.sql
@@ -32,6 +32,16 @@ SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 0));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 1));
 SELECT * FROM bt_page_items(get_raw_page('test1_a_idx', 2));
 
+---test index over virtual generated column
+CREATE TABLE test4(a int, b int GENERATED ALWAYS AS (a + 1), c text);
+INSERT INTO test4(a,c) VALUES (10,11), (10,11);
+CREATE INDEX test4_b_idx ON test4 USING btree (b);
+CREATE INDEX test4_a_1_idx ON test4 USING btree ((a+1));
+--expect return zero row
+SELECT * FROM bt_page_items('test4_b_idx', 1)
+EXCEPT ALL
+SELECT * FROM bt_page_items('test4_a_1_idx', 1);
+
 -- Failure when using a non-btree index.
 CREATE INDEX test1_a_hash ON test1 USING hash(a);
 SELECT bt_metap('test1_a_hash');
diff --git a/doc/src/sgml/catalogs.sgml b/doc/src/sgml/catalogs.sgml
index 2fc63442980..1405ac8424f 100644
--- a/doc/src/sgml/catalogs.sgml
+++ b/doc/src/sgml/catalogs.sgml
@@ -4592,6 +4592,21 @@ SCRAM-SHA-256$<replaceable>&lt;iteration count&gt;</replaceable>:<replaceable>&l
       </para></entry>
      </row>
 
+     <row>
+      <entry role="catalog_table_entry"><para role="column_definition">
+       <structfield>indattrgenerated</structfield> <type>int2vector</type>
+       (references <link linkend="catalog-pg-attribute"><structname>pg_attribute</structname></link>.<structfield>attnum</structfield>)
+      </para>
+      <para>
+       This is an array of <structfield>indnatts</structfield> values that
+       indicate which virtual generated columns this index indexes.
+       For example, a value of <literal>1 3</literal> would mean that the first
+       and the third table columns of this index entries are virtual generated
+       column. A zero in this array indicates that the corresponding index
+       attribute is not virtual generated column reference.
+      </para></entry>
+     </row>
+
      <row>
       <entry role="catalog_table_entry"><para role="column_definition">
        <structfield>indexprs</structfield> <type>pg_node_tree</type>
diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index 43de42ce39e..7b1d8e69c57 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -245,6 +245,16 @@ index_check_primary_key(Relation heapRel,
 		HeapTuple	atttuple;
 		Form_pg_attribute attform;
 
+		/*
+		 * Unique constraints and primary keys based on virtual generated
+		 * columns are not supported. Nevertheless, it is still prudent to
+		 * perform the check.
+		 */
+		if (indexInfo->ii_IndexAttrGeneratedNumbers[i] != 0)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("primary keys on virtual generated columns are not supported"));
+
 		if (attnum == 0)
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
@@ -582,6 +592,12 @@ UpdateIndexRelation(Oid indexoid,
 	Relation	pg_index;
 	HeapTuple	tuple;
 	int			i;
+	int2vector *indgenkey;
+
+	int16	   *colgenerated = palloc_array(int16, indexInfo->ii_NumIndexAttrs);
+
+	for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+		colgenerated[i] = indexInfo->ii_IndexAttrGeneratedNumbers[i];
 
 	/*
 	 * Copy the index key, opclass, and indoption info into arrays (should we
@@ -593,6 +609,7 @@ UpdateIndexRelation(Oid indexoid,
 	indcollation = buildoidvector(collationOids, indexInfo->ii_NumIndexKeyAttrs);
 	indclass = buildoidvector(opclassOids, indexInfo->ii_NumIndexKeyAttrs);
 	indoption = buildint2vector(coloptions, indexInfo->ii_NumIndexKeyAttrs);
+	indgenkey = buildint2vector(colgenerated, indexInfo->ii_NumIndexAttrs);
 
 	/*
 	 * Convert the index expressions (if any) to a text datum
@@ -651,6 +668,7 @@ UpdateIndexRelation(Oid indexoid,
 	values[Anum_pg_index_indcollation - 1] = PointerGetDatum(indcollation);
 	values[Anum_pg_index_indclass - 1] = PointerGetDatum(indclass);
 	values[Anum_pg_index_indoption - 1] = PointerGetDatum(indoption);
+	values[Anum_pg_index_indattrgenerated - 1] = PointerGetDatum(indgenkey);
 	values[Anum_pg_index_indexprs - 1] = exprsDatum;
 	if (exprsDatum == (Datum) 0)
 		nulls[Anum_pg_index_indexprs - 1] = true;
@@ -1132,6 +1150,28 @@ index_create(Relation heapRelation,
 				}
 			}
 
+			/*
+			 * Internally, we convert index of virtual generation column into
+			 * an expression index. For example, if column 'b' is defined as
+			 * (b INT GENERATED ALWAYS AS (a * 2) VIRTUAL) then index over 'b'
+			 * would transformed into an expression index as ((a * 2)). As a
+			 * result, the pg_depend refobjsubid does not retain the original
+			 * attribute number of the virtual generated column. But rebuild
+			 * index need these original virtual generated column. Thus we
+			 * need auto dependencies on referenced virtual generated columns.
+			 */
+			for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
+			{
+				if (indexInfo->ii_IndexAttrGeneratedNumbers[i] != 0)
+				{
+					ObjectAddressSubSet(referenced, RelationRelationId,
+										heapRelationId,
+										indexInfo->ii_IndexAttrGeneratedNumbers[i]);
+					add_exact_object_address(&referenced, addrs);
+					have_simple_col = false;
+				}
+			}
+
 			/*
 			 * If there are no simply-referenced columns, give the index an
 			 * auto dependency on the whole table.  In most cases, this will
@@ -1409,6 +1449,7 @@ index_concurrently_create_copy(Relation heapRelation, Oid oldIndexId,
 
 		indexColNames = lappend(indexColNames, NameStr(att->attname));
 		newInfo->ii_IndexAttrNumbers[i] = oldInfo->ii_IndexAttrNumbers[i];
+		newInfo->ii_IndexAttrGeneratedNumbers[i] = oldInfo->ii_IndexAttrGeneratedNumbers[i];
 	}
 
 	/* Extract opclass options for each attribute */
@@ -2426,9 +2467,12 @@ IndexInfo *
 BuildIndexInfo(Relation index)
 {
 	IndexInfo  *ii;
+	HeapTuple	ht_idx;
 	Form_pg_index indexStruct = index->rd_index;
 	int			i;
 	int			numAtts;
+	Datum		indgenkeyDatum;
+	int2vector *indgenkey;
 
 	/* check the number of keys, and copy attr numbers into the IndexInfo */
 	numAtts = indexStruct->indnatts;
@@ -2452,9 +2496,18 @@ BuildIndexInfo(Relation index)
 					   index->rd_indam->amsummarizing,
 					   indexStruct->indisexclusion && indexStruct->indisunique);
 
+	ht_idx = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(indexStruct->indexrelid));
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* fill in attribute numbers */
 	for (i = 0; i < numAtts; i++)
+	{
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
+		ii->ii_IndexAttrGeneratedNumbers[i] = indgenkey->values[i];
+	}
+	ReleaseSysCache(ht_idx);
 
 	/* fetch exclusion constraint info if any */
 	if (indexStruct->indisexclusion)
@@ -2516,11 +2569,34 @@ BuildDummyIndexInfo(Relation index)
 	for (i = 0; i < numAtts; i++)
 		ii->ii_IndexAttrNumbers[i] = indexStruct->indkey.values[i];
 
+	/*
+	 * Index expressions or predicates are skipped here, see above comments.
+	 * If virtual generated columns references another column,
+	 * ii_IndexAttrNumbers will set to that referenced column. So do nothing
+	 * for ii_IndexAttrGeneratedNumbers here.
+	 */
+
 	/* We ignore the exclusion constraint if any */
 
 	return ii;
 }
 
+/*
+ * indexContainVirtual
+ *		Return true if this index contains a reference to a virtual generated
+ *		column.
+ */
+bool
+indexContainVirtual(const IndexInfo *info)
+{
+	for (int i = 0; i < info->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(info->ii_IndexAttrGeneratedNumbers[i]))
+			return true;
+	}
+	return false;
+}
+
 /*
  * CompareIndexInfo
  *		Return whether the properties of two indexes (in different tables)
@@ -2568,6 +2644,15 @@ CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 		if (attmap->maplen < info2->ii_IndexAttrNumbers[i])
 			elog(ERROR, "incorrect attribute map");
 
+		if (AttributeNumberIsValid(info1->ii_IndexAttrGeneratedNumbers[i]) ||
+			AttributeNumberIsValid(info2->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			/* fail if index over virtual generated column does not match */
+			if (attmap->attnums[info2->ii_IndexAttrGeneratedNumbers[i] - 1] !=
+				info1->ii_IndexAttrGeneratedNumbers[i])
+				return false;
+		}
+
 		/* ignore expressions for now (but check their collation/opfamily) */
 		if (!(info1->ii_IndexAttrNumbers[i] == InvalidAttrNumber &&
 			  info2->ii_IndexAttrNumbers[i] == InvalidAttrNumber))
diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 755dc00c86f..5b677483be2 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -53,6 +53,7 @@
 #include "parser/parse_utilcmd.h"
 #include "partitioning/partdesc.h"
 #include "pgstat.h"
+#include "rewrite/rewriteHandler.h"
 #include "rewrite/rewriteManip.h"
 #include "storage/lmgr.h"
 #include "storage/proc.h"
@@ -90,9 +91,17 @@ static void ComputeIndexAttrs(ParseState *pstate,
 							  bool amcanorder,
 							  bool isconstraint,
 							  bool iswithoutoverlaps,
+							  bool is_primary,
 							  Oid ddl_userid,
 							  int ddl_sec_context,
 							  int *ddl_save_nestlevel);
+static void ComputeIndexGeneratedAttrs(ParseState *pstate,
+									   IndexInfo *indexInfo,
+									   Relation rel,
+									   bool is_primary,
+									   int attn,
+									   int attnum,
+									   int location);
 static char *ChooseIndexName(const char *tabname, Oid namespaceId,
 							 const List *colnames, const List *exclusionOpNames,
 							 bool primary, bool isconstraint);
@@ -182,6 +191,7 @@ CheckIndexCompatible(Oid oldId,
 					 bool isWithoutOverlaps)
 {
 	bool		isconstraint;
+	bool		is_primary;
 	Oid		   *typeIds;
 	Oid		   *collationIds;
 	Oid		   *opclassIds;
@@ -214,6 +224,12 @@ CheckIndexCompatible(Oid oldId,
 	 */
 	isconstraint = false;
 
+	/*
+	 * We can pretend is_primary = false unconditionally.  It only serves to
+	 * decide the text of an error message that should never happen for us.
+	 */
+	is_primary = false;
+
 	numberOfAttributes = list_length(attributeList);
 	Assert(numberOfAttributes > 0);
 	Assert(numberOfAttributes <= INDEX_MAX_KEYS);
@@ -254,7 +270,7 @@ CheckIndexCompatible(Oid oldId,
 					  coloptions, attributeList,
 					  exclusionOpNames, relationId,
 					  accessMethodName, accessMethodId,
-					  amcanorder, isconstraint, isWithoutOverlaps, InvalidOid,
+					  amcanorder, isconstraint, isWithoutOverlaps, is_primary, InvalidOid,
 					  0, NULL);
 
 	/* Get the soon-obsolete pg_index tuple. */
@@ -907,6 +923,27 @@ DefineIndex(ParseState *pstate,
 	if (stmt->whereClause)
 		CheckPredicate((Expr *) stmt->whereClause);
 
+	/* virtual generated column over predicate indexes are not supported */
+	if (RelationGetDescr(rel)->constr &&
+		RelationGetDescr(rel)->constr->has_generated_virtual &&
+		stmt->whereClause)
+	{
+		Bitmapset  *indexattrs_pred = NULL;
+		int			j = -1;
+
+		pull_varattnos(stmt->whereClause, 1, &indexattrs_pred);
+
+		while ((j = bms_next_member(indexattrs_pred, j)) >= 0)
+		{
+			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
+
+			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				ereport(ERROR,
+						errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+						errmsg("partial index on virtual generated columns are not supported"));
+		}
+	}
+
 	/*
 	 * Parse AM-specific options, convert to text array form, validate.
 	 */
@@ -944,6 +981,7 @@ DefineIndex(ParseState *pstate,
 					  stmt->excludeOpNames, tableId,
 					  accessMethodName, accessMethodId,
 					  amcanorder, stmt->isconstraint, stmt->iswithoutoverlaps,
+					  stmt->primary,
 					  root_save_userid, root_save_sec_context,
 					  &root_save_nestlevel);
 
@@ -1025,6 +1063,11 @@ DefineIndex(ParseState *pstate,
 								   constraint_type)));
 
 			/* Search the index column(s) for a match */
+
+			/*
+			 * Unique constraints and primary keys based on virtual generated
+			 * columns are not supported. So no need worry about it here.
+			 */
 			for (j = 0; j < indexInfo->ii_NumIndexKeyAttrs; j++)
 			{
 				if (key->partattrs[i] == indexInfo->ii_IndexAttrNumbers[j])
@@ -1105,9 +1148,6 @@ DefineIndex(ParseState *pstate,
 	/*
 	 * We disallow indexes on system columns.  They would not necessarily get
 	 * updated correctly, and they don't seem useful anyway.
-	 *
-	 * Also disallow virtual generated columns in indexes (use expression
-	 * index instead).
 	 */
 	for (int i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
 	{
@@ -1117,26 +1157,14 @@ DefineIndex(ParseState *pstate,
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("index creation on system columns is not supported")));
-
-
-		if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-			ereport(ERROR,
-					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-					stmt->primary ?
-					errmsg("primary keys on virtual generated columns are not supported") :
-					stmt->isconstraint ?
-					errmsg("unique constraints on virtual generated columns are not supported") :
-					errmsg("indexes on virtual generated columns are not supported"));
 	}
 
 	/*
-	 * Also check for system and generated columns used in expressions or
-	 * predicates.
+	 * Also check for system columns used in expressions or predicates.
 	 */
 	if (indexInfo->ii_Expressions || indexInfo->ii_Predicate)
 	{
 		Bitmapset  *indexattrs = NULL;
-		int			j;
 
 		pull_varattnos((Node *) indexInfo->ii_Expressions, 1, &indexattrs);
 		pull_varattnos((Node *) indexInfo->ii_Predicate, 1, &indexattrs);
@@ -1149,24 +1177,6 @@ DefineIndex(ParseState *pstate,
 						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 						 errmsg("index creation on system columns is not supported")));
 		}
-
-		/*
-		 * XXX Virtual generated columns in index expressions or predicates
-		 * could be supported, but it needs support in
-		 * RelationGetIndexExpressions() and RelationGetIndexPredicate().
-		 */
-		j = -1;
-		while ((j = bms_next_member(indexattrs, j)) >= 0)
-		{
-			AttrNumber	attno = j + FirstLowInvalidHeapAttributeNumber;
-
-			if (TupleDescAttr(RelationGetDescr(rel), attno - 1)->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
-				ereport(ERROR,
-						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-						 stmt->isconstraint ?
-						 errmsg("unique constraints on virtual generated columns are not supported") :
-						 errmsg("indexes on virtual generated columns are not supported")));
-		}
 	}
 
 	/* Is index safe for others to ignore?  See set_indexsafe_procflags() */
@@ -1310,6 +1320,7 @@ DefineIndex(ParseState *pstate,
 			bool		invalidate_parent = false;
 			Relation	parentIndex;
 			TupleDesc	parentDesc;
+			bool		parent_idx_virtual;
 
 			/*
 			 * Report the total number of partitions at the start of the
@@ -1355,6 +1366,7 @@ DefineIndex(ParseState *pstate,
 			 */
 			parentIndex = index_open(indexRelationId, lockmode);
 			indexInfo = BuildIndexInfo(parentIndex);
+			parent_idx_virtual = indexContainVirtual(indexInfo);
 
 			parentDesc = RelationGetDescr(rel);
 
@@ -1415,6 +1427,15 @@ DefineIndex(ParseState *pstate,
 										  parentDesc,
 										  false);
 
+				/*
+				 * If parent has an index on a virtual generated column, we
+				 * must ensure that the indexed generated expression on the
+				 * parent matches that of the child.
+				 */
+				if (parent_idx_virtual)
+					check_generated_indexattrs(indexInfo, rel,
+											   childrel, attmap, false);
+
 				foreach(cell, childidxs)
 				{
 					Oid			cldidxid = lfirst_oid(cell);
@@ -1862,6 +1883,66 @@ CheckPredicate(Expr *predicate)
 				 errmsg("functions in index predicate must be marked IMMUTABLE")));
 }
 
+/*
+ * Verify that the generated expression of the parent matches the child
+ *
+ * indexinfo: the IndexInfo that is associated with relation "rel".
+ * childrel : the relation to be attached to "rel" or the child of "rel".
+ * attmap   : Attribute mapping between childrel and rel.
+ * is_attach: is this command of ALTER TABLE ATTACH PARTITION
+ *
+ * Use build_attrmap_by_name(childrel, rel) to build the attmap.
+*/
+void
+check_generated_indexattrs(const IndexInfo *indexinfo,
+						   Relation rel,
+						   Relation childrel,
+						   const AttrMap *attmap,
+						   bool is_attach)
+{
+	/* if parent have virtual generated column, child must also have */
+	Assert(rel->rd_att->constr->has_generated_virtual);
+	Assert(childrel->rd_att->constr->has_generated_virtual);
+
+	for (int i = 0; i < indexinfo->ii_NumIndexAttrs; i++)
+	{
+		if (AttributeNumberIsValid(indexinfo->ii_IndexAttrGeneratedNumbers[i]))
+		{
+			Node	   *node_parent;
+			Node	   *node_child;
+			bool		found_whole_row;
+
+			AttrNumber	attno = indexinfo->ii_IndexAttrGeneratedNumbers[i];
+
+			node_parent = build_generation_expression(rel, attno);
+
+			node_parent = map_variable_attnos(node_parent,
+											  1,
+											  0,
+											  attmap,
+											  InvalidOid, &found_whole_row);
+			if (found_whole_row)
+				elog(ERROR, "Index contains a whole-row table reference");
+
+			node_child = build_generation_expression(childrel,
+													 attmap->attnums[attno - 1]);
+
+			if (!equal(node_parent, node_child))
+				ereport(ERROR,
+						errcode(ERRCODE_WRONG_OBJECT_TYPE),
+						is_attach ?
+						errmsg("cannot attach table \"%s\" as partition of partitioned table \"%s\"",
+							   RelationGetRelationName(childrel),
+							   RelationGetRelationName(rel)) :
+						errmsg("cannot create index on partitioned table \"%s\"",
+							   RelationGetRelationName(rel)),
+						errdetail("The virtual generated column expression of partitioned table \"%s\" does not match that of table \"%s\"",
+								  RelationGetRelationName(rel),
+								  RelationGetRelationName(childrel)));
+		}
+	}
+}
+
 /*
  * Compute per-index-column information, including indexed column numbers
  * or index expressions, opclasses and their options. Note, all output vectors
@@ -1887,6 +1968,7 @@ ComputeIndexAttrs(ParseState *pstate,
 				  bool amcanorder,
 				  bool isconstraint,
 				  bool iswithoutoverlaps,
+				  bool is_primary,
 				  Oid ddl_userid,
 				  int ddl_sec_context,
 				  int *ddl_save_nestlevel)
@@ -1897,6 +1979,25 @@ ComputeIndexAttrs(ParseState *pstate,
 	int			nkeycols = indexInfo->ii_NumIndexKeyAttrs;
 	Oid			save_userid;
 	int			save_sec_context;
+	List	   *virtual_generated = NIL;
+	Relation	rel = table_open(relId, NoLock);
+	TupleDesc	reltupldesc = RelationGetDescr(rel);
+
+	/*
+	 * Virtual generated columns are not currently supported in expression
+	 * indexes. We therefore collect the virtual generated columns attribute
+	 * number for subsequent verification of expression attributes.
+	 */
+	if (reltupldesc->constr && reltupldesc->constr->has_generated_virtual)
+	{
+		for (int i = 0; i < reltupldesc->natts; i++)
+		{
+			Form_pg_attribute attr = TupleDescAttr(reltupldesc, i);
+
+			if (!attr->attisdropped && attr->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				virtual_generated = lappend_int(virtual_generated, attr->attnum);
+		}
+	}
 
 	/* Allocate space for exclusion operator info, if needed */
 	if (exclusionOpNames)
@@ -1968,7 +2069,19 @@ ComputeIndexAttrs(ParseState *pstate,
 							 parser_errposition(pstate, attribute->location)));
 			}
 			attform = (Form_pg_attribute) GETSTRUCT(atttuple);
-			indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
+
+			if (attform->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
+				ComputeIndexGeneratedAttrs(pstate, indexInfo, rel,
+										   is_primary,
+										   attn,
+										   attform->attnum,
+										   attribute->location);
+			else
+			{
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
+				indexInfo->ii_IndexAttrNumbers[attn] = attform->attnum;
+			}
+
 			atttype = attform->atttypid;
 			attcollation = attform->attcollation;
 			ReleaseSysCache(atttuple);
@@ -1995,18 +2108,47 @@ ComputeIndexAttrs(ParseState *pstate,
 			while (IsA(expr, CollateExpr))
 				expr = (Node *) ((CollateExpr *) expr)->arg;
 
+			if (!IsA(expr, Var))
+			{
+				Bitmapset  *idxattrs = NULL;
+				int			j = -1;
+
+				pull_varattnos(expr, 1, &idxattrs);
+				while ((j = bms_next_member(idxattrs, j)) >= 0)
+				{
+					if (list_member_int(virtual_generated, j + FirstLowInvalidHeapAttributeNumber))
+						ereport(ERROR,
+								errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+								errmsg("expression index over virtual generated columns are not supported"),
+								parser_errposition(pstate, attribute->location));
+				}
+			}
+
 			if (IsA(expr, Var) &&
 				((Var *) expr)->varattno != InvalidAttrNumber)
 			{
-				/*
-				 * User wrote "(column)" or "(column COLLATE something)".
-				 * Treat it like simple attribute anyway.
-				 */
-				indexInfo->ii_IndexAttrNumbers[attn] = ((Var *) expr)->varattno;
+				int			attnum = ((Var *) expr)->varattno;
+
+				if (list_member_int(virtual_generated, attnum))
+					ComputeIndexGeneratedAttrs(pstate, indexInfo, rel,
+											   is_primary,
+											   attn,
+											   attnum,
+											   attribute->location);
+				else
+				{
+					/*
+					 * User wrote "(column)" or "(column COLLATE something)".
+					 * Treat it like simple attribute anyway.
+					 */
+					indexInfo->ii_IndexAttrNumbers[attn] = attnum;
+					indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
+				}
 			}
 			else
 			{
 				indexInfo->ii_IndexAttrNumbers[attn] = 0;	/* marks expression */
+				indexInfo->ii_IndexAttrGeneratedNumbers[attn] = 0;
 				indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
 													expr);
 
@@ -2268,6 +2410,92 @@ ComputeIndexAttrs(ParseState *pstate,
 
 		attn++;
 	}
+
+	table_close(rel, NoLock);
+}
+
+/*
+ * Compute IndexInfo fields: ii_IndexAttrNumbers, ii_IndexAttrGeneratedNumbers,
+ * and ii_Expressions.
+ *
+ * pstate:     ParseState struct (used only for error reports; pass NULL if not available)
+ * indexInfo:  the IndexInfo structure to be built.
+ * rel:        the relation on which this IndexInfo is based.
+ * is_primary: indicates whether this index is a primary key.
+ * attn:       zero-based indexes of the index key attributes.
+ * attnum:     attribute number of the virtual generated column.
+ * location:   index key location.
+ */
+static void
+ComputeIndexGeneratedAttrs(ParseState *pstate,
+						   IndexInfo *indexInfo, Relation rel,
+						   bool is_primary, int attn, int attnum,
+						   int location)
+{
+	Node	   *node;
+
+	if (is_primary)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("primary keys on virtual generated columns are not supported"),
+				parser_errposition(pstate, location));
+
+	if (indexInfo->ii_Unique)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("unique constraints on virtual generated columns are not supported"),
+				parser_errposition(pstate, location));
+
+	if (attn >= indexInfo->ii_NumIndexKeyAttrs)
+		ereport(ERROR,
+				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				errmsg("virtual generated column are not supported in index included columns"),
+				parser_errposition(pstate, location));
+
+	/* Fetch the GENERATED AS expression tree */
+	node = build_generation_expression(rel, attnum);
+
+	/*
+	 * if the generation expression just reference another column, then set
+	 * ii_IndexAttrNumbers to that column attribute number.
+	 */
+	if (IsA(node, Var))
+	{
+		Var		   *var = (Var *) node;
+
+		if (var->varattno < 0)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("index creation on system columns is not supported"),
+					parser_errposition(pstate, location));
+
+		indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+	}
+	else
+	{
+		/*
+		 * Strip any top-level COLLATE clause in generated expression.  This
+		 * ensures that we treat "x COLLATE y" and "(x COLLATE y)" alike.
+		 */
+		while (IsA(node, CollateExpr))
+			node = (Node *) ((CollateExpr *) node)->arg;
+
+		if (IsA(node, Var))
+		{
+			Var		   *var = (Var *) node;
+
+			Assert(var->varattno > 0);
+			indexInfo->ii_IndexAttrNumbers[attn] = var->varattno;
+		}
+		else
+		{
+			/* mark as expression index */
+			indexInfo->ii_IndexAttrNumbers[attn] = 0;
+			indexInfo->ii_Expressions = lappend(indexInfo->ii_Expressions,
+												node);
+		}
+	}
+	indexInfo->ii_IndexAttrGeneratedNumbers[attn] = attnum;
 }
 
 /*
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index f976c0e5c7e..6cc296b2957 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -8699,6 +8699,21 @@ ATExecSetExpression(AlteredTableInfo *tab, Relation rel, const char *colName,
 
 	ReleaseSysCache(tuple);
 
+	/*
+	 * Find everything that depends on the column (constraints, indexes, etc),
+	 * and record enough information to let us recreate the objects after
+	 * rewrite.
+	 */
+	RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
+
+	/*
+	 * Changing virtual geneeration expression does not require table rewrite.
+	 * However, if any index is built on top of it, table rewrite is
+	 * necessary.
+	 */
+	if (tab->changedIndexOids != NIL)
+		rewrite = true;
+
 	if (rewrite)
 	{
 		/*
@@ -8709,13 +8724,6 @@ ATExecSetExpression(AlteredTableInfo *tab, Relation rel, const char *colName,
 
 		/* make sure we don't conflict with later attribute modifications */
 		CommandCounterIncrement();
-
-		/*
-		 * Find everything that depends on the column (constraints, indexes,
-		 * etc), and record enough information to let us recreate the objects
-		 * after rewrite.
-		 */
-		RememberAllDependentForRebuilding(tab, AT_SetExpression, rel, attnum, colName);
 	}
 
 	/*
@@ -14870,6 +14878,27 @@ ATExecAlterColumnType(AlteredTableInfo *tab, Relation rel,
 	 */
 	RememberAllDependentForRebuilding(tab, AT_AlterColumnType, rel, attnum, colName);
 
+	/*
+	 * Tell phase3 do table rewrite if there are any index based on virtual
+	 * generated colum.
+	 */
+	if (attTup->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL &&
+		tab->changedIndexOids != NIL)
+	{
+		Relation	newrel;
+
+		newrel = table_open(RelationGetRelid(rel), NoLock);
+
+		RelationClearMissing(newrel);
+
+		relation_close(newrel, NoLock);
+
+		/* make sure we don't conflict with later attribute modifications */
+		CommandCounterIncrement();
+
+		tab->rewrite |= AT_REWRITE_COLUMN_REWRITE;
+	}
+
 	/*
 	 * Now scan for dependencies of this column on other things.  The only
 	 * things we should find are the dependency on the column datatype and
@@ -20699,6 +20728,10 @@ AttachPartitionEnsureIndexes(List **wqueue, Relation rel, Relation attachrel)
 		attmap = build_attrmap_by_name(RelationGetDescr(attachrel),
 									   RelationGetDescr(rel),
 									   false);
+
+		if (indexContainVirtual(info))
+			check_generated_indexattrs(info, rel, attachrel, attmap, true);
+
 		constraintOid = get_relation_idx_constraint_oid(RelationGetRelid(rel), idx);
 
 		/*
diff --git a/src/backend/executor/execIndexing.c b/src/backend/executor/execIndexing.c
index 6ae0f959592..06329347a30 100644
--- a/src/backend/executor/execIndexing.c
+++ b/src/backend/executor/execIndexing.c
@@ -1039,6 +1039,18 @@ index_unchanged_by_update(ResultRelInfo *resultRelInfo, EState *estate,
 	for (int attr = 0; attr < indexInfo->ii_NumIndexKeyAttrs; attr++)
 	{
 		int			keycol = indexInfo->ii_IndexAttrNumbers[attr];
+		int			vkeycol = indexInfo->ii_IndexAttrGeneratedNumbers[attr];
+
+		if (vkeycol > 0 &&
+			(bms_is_member(vkeycol - FirstLowInvalidHeapAttributeNumber,
+						   updatedCols) ||
+			 bms_is_member(vkeycol - FirstLowInvalidHeapAttributeNumber,
+						   extraUpdatedCols)))
+		{
+			/* Changed key column -- don't hint for this index */
+			indexInfo->ii_IndexUnchanged = false;
+			return false;
+		}
 
 		if (keycol <= 0)
 		{
diff --git a/src/backend/executor/execPartition.c b/src/backend/executor/execPartition.c
index 55bdf5c4835..439d85fedcb 100644
--- a/src/backend/executor/execPartition.c
+++ b/src/backend/executor/execPartition.c
@@ -538,6 +538,11 @@ IsIndexCompatibleAsArbiter(Relation arbiterIndexRelation,
 		if (arbiterIndexRelation->rd_index->indkey.values[i] !=
 			indexRelation->rd_index->indkey.values[i])
 			return false;
+
+		/*
+		 * Unique indexes on virtual generated columns are not supported, no
+		 * need to worry about indattrgenerated here.
+		 */
 	}
 
 	if (list_difference(RelationGetIndexExpressions(arbiterIndexRelation),
diff --git a/src/backend/parser/parse_utilcmd.c b/src/backend/parser/parse_utilcmd.c
index 652f7538c37..48fd08e428d 100644
--- a/src/backend/parser/parse_utilcmd.c
+++ b/src/backend/parser/parse_utilcmd.c
@@ -1705,6 +1705,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	Form_pg_am	amrec;
 	oidvector  *indcollation;
 	oidvector  *indclass;
+	int2vector *indgenkey;
 	IndexStmt  *index;
 	List	   *indexprs;
 	ListCell   *indexpr_item;
@@ -1712,6 +1713,7 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	int			keyno;
 	Oid			keycoltype;
 	Datum		datum;
+	Datum		indgenkeyDatum;
 	bool		isnull;
 
 	if (constraintOid)
@@ -1747,6 +1749,11 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	datum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx, Anum_pg_index_indclass);
 	indclass = (oidvector *) DatumGetPointer(datum);
 
+	/* Extract indattrgenerated from the pg_index tuple */
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/* Begin building the IndexStmt */
 	index = makeNode(IndexStmt);
 	index->relation = heapRel;
@@ -1878,13 +1885,26 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 	{
 		IndexElem  *iparam;
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Form_pg_attribute attr = TupleDescAttr(RelationGetDescr(source_idx),
 											   keyno);
 		int16		opt = source_idx->rd_indoption[keyno];
 
 		iparam = makeNode(IndexElem);
 
-		if (AttributeNumberIsValid(attnum))
+		if (AttributeNumberIsValid(gennum))
+		{
+			/*
+			 * An index on a virtual generated column was converted into an
+			 * expression index, but here we need the original attribute
+			 * number.
+			 */
+			keycoltype = get_atttype(indrelid, gennum);
+
+			iparam->name = get_attname(indrelid, gennum, false);;
+			iparam->expr = NULL;
+		}
+		else if (AttributeNumberIsValid(attnum))
 		{
 			/* Simple index column */
 			char	   *attname;
@@ -1977,6 +1997,10 @@ generateClonedIndexStmt(RangeVar *heapRel, Relation source_idx,
 
 		iparam = makeNode(IndexElem);
 
+		/*
+		 * INCLUDED COLUMNS based on virtual generated columns are not
+		 * supported. So no need worry about it here.
+		 */
 		if (AttributeNumberIsValid(attnum))
 		{
 			/* Simple index column */
@@ -2528,6 +2552,9 @@ transformIndexConstraint(Constraint *constraint, CreateStmtContext *cxt)
 			 * We shouldn't see attnum == 0 here, since we already rejected
 			 * expression indexes.  If we do, SystemAttributeDefinition will
 			 * throw an error.
+			 *
+			 * Unique constraints and primary keys based on virtual generated
+			 * columns are not supported. So no need worry about it here.
 			 */
 			if (attnum > 0)
 			{
diff --git a/src/backend/utils/adt/ruleutils.c b/src/backend/utils/adt/ruleutils.c
index 416f1a21ae4..2fd1b334a08 100644
--- a/src/backend/utils/adt/ruleutils.c
+++ b/src/backend/utils/adt/ruleutils.c
@@ -1290,9 +1290,11 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	Datum		indcollDatum;
 	Datum		indclassDatum;
 	Datum		indoptionDatum;
+	Datum		indgenkeyDatum;
 	oidvector  *indcollation;
 	oidvector  *indclass;
 	int2vector *indoption;
+	int2vector *indgenkey;
 	StringInfoData buf;
 	char	   *str;
 	char	   *sep;
@@ -1325,6 +1327,10 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 											Anum_pg_index_indoption);
 	indoption = (int2vector *) DatumGetPointer(indoptionDatum);
 
+	indgenkeyDatum = SysCacheGetAttrNotNull(INDEXRELID, ht_idx,
+											Anum_pg_index_indattrgenerated);
+	indgenkey = (int2vector *) DatumGetPointer(indgenkeyDatum);
+
 	/*
 	 * Fetch the pg_class tuple of the index relation
 	 */
@@ -1398,6 +1404,7 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 	for (keyno = 0; keyno < idxrec->indnatts; keyno++)
 	{
 		AttrNumber	attnum = idxrec->indkey.values[keyno];
+		AttrNumber	gennum = indgenkey->values[keyno];
 		Oid			keycoltype;
 		Oid			keycolcollation;
 
@@ -1418,7 +1425,32 @@ pg_get_indexdef_worker(Oid indexrelid, int colno,
 			appendStringInfoString(&buf, sep);
 		sep = ", ";
 
-		if (attnum != 0)
+		/*
+		 * We must first check indexes on virtual generated columns, and then
+		 * simple index columns, since a virtual generated column can
+		 * reference another regular column.
+		 */
+		if (AttributeNumberIsValid(gennum))
+		{
+			char	   *virtual_attname;
+			int32		geneycoltypmod;
+
+			virtual_attname = get_attname(indrelid, gennum, false);
+			if (!colno || colno == keyno + 1)
+				appendStringInfoString(&buf, quote_identifier(virtual_attname));
+
+			get_atttypetypmodcoll(indrelid, gennum,
+								  &keycoltype, &geneycoltypmod,
+								  &keycolcollation);
+
+			/*
+			 * The virtual generated column has already been printed, so its
+			 * generation expression should not be emitted again.
+			 */
+			if (!AttributeNumberIsValid(attnum))
+				indexpr_item = lnext(indexprs, indexpr_item);
+		}
+		else if (attnum != 0)
 		{
 			/* Simple index column */
 			char	   *attname;
diff --git a/src/include/catalog/index.h b/src/include/catalog/index.h
index b259c4141ed..e9519a3cafd 100644
--- a/src/include/catalog/index.h
+++ b/src/include/catalog/index.h
@@ -126,6 +126,7 @@ extern IndexInfo *BuildIndexInfo(Relation index);
 
 extern IndexInfo *BuildDummyIndexInfo(Relation index);
 
+extern bool indexContainVirtual(const IndexInfo *info);
 extern bool CompareIndexInfo(const IndexInfo *info1, const IndexInfo *info2,
 							 const Oid *collations1, const Oid *collations2,
 							 const Oid *opfamilies1, const Oid *opfamilies2,
@@ -175,6 +176,11 @@ extern void RestoreReindexState(const void *reindexstate);
 
 extern void IndexSetParentIndex(Relation partitionIdx, Oid parentOid);
 
+extern void check_generated_indexattrs(const IndexInfo *rel_idx_info,
+									   Relation rel,
+									   Relation childrel,
+									   const AttrMap *attmap,
+									   bool is_attach);
 
 /*
  * itemptr_encode - Encode ItemPointer as int64/int8
diff --git a/src/include/catalog/pg_index.h b/src/include/catalog/pg_index.h
index 02c99d70faf..e3097106d8e 100644
--- a/src/include/catalog/pg_index.h
+++ b/src/include/catalog/pg_index.h
@@ -54,6 +54,9 @@ CATALOG(pg_index,2610,IndexRelationId) BKI_SCHEMA_MACRO
 	oidvector	indclass BKI_LOOKUP(pg_opclass) BKI_FORCE_NOT_NULL; /* opclass identifiers */
 	int2vector	indoption BKI_FORCE_NOT_NULL;	/* per-column flags
 												 * (AM-specific meanings) */
+	int2vector	indattrgenerated BKI_FORCE_NOT_NULL;	/* the attribute of
+														 * virtual generated
+														 * column? */
 	pg_node_tree indexprs;		/* expression trees for index attributes that
 								 * are not simple column references; one for
 								 * each zero entry in indkey[] */
diff --git a/src/include/nodes/execnodes.h b/src/include/nodes/execnodes.h
index 02265456978..58079e49f7a 100644
--- a/src/include/nodes/execnodes.h
+++ b/src/include/nodes/execnodes.h
@@ -174,6 +174,14 @@ typedef struct IndexInfo
 	 */
 	AttrNumber	ii_IndexAttrNumbers[INDEX_MAX_KEYS];
 
+	/*
+	 * Underlying-rel virtual generated attribute numbers used as keys. A
+	 * value of zero indicates that the index key does not reference a virtual
+	 * generated column. Note: Virtual generated columns cannot be used in
+	 * INCLUDED index columns.
+	 */
+	AttrNumber	ii_IndexAttrGeneratedNumbers[INDEX_MAX_KEYS];
+
 	/* expr trees for expression entries, or NIL if none */
 	List	   *ii_Expressions; /* list of Expr */
 	/* exec state for expressions, or NIL if none */
diff --git a/src/test/regress/expected/alter_table.out b/src/test/regress/expected/alter_table.out
index ac1a7345d0f..7e530357345 100644
--- a/src/test/regress/expected/alter_table.out
+++ b/src/test/regress/expected/alter_table.out
@@ -119,6 +119,26 @@ HINT:  Alter statistics on table column instead.
 ALTER INDEX attmp_idx ALTER COLUMN 4 SET STATISTICS 1000;
 ERROR:  column number 4 of relation "attmp_idx" does not exist
 ALTER INDEX attmp_idx ALTER COLUMN 2 SET STATISTICS -1;
+ALTER TABLE attmp
+    ADD COLUMN col1 int GENERATED ALWAYS AS (a),
+    ADD COLUMN col2 int GENERATED ALWAYS AS (a + 1);
+CREATE INDEX attmp_idx1 ON attmp (a, col1, col2);
+ALTER INDEX attmp_idx1 ALTER COLUMN 1 SET STATISTICS 1000;
+ERROR:  cannot alter statistics on non-expression column "a" of index "attmp_idx1"
+HINT:  Alter statistics on table column instead.
+ALTER INDEX attmp_idx1 ALTER COLUMN 2 SET STATISTICS 1000;
+ERROR:  cannot alter statistics on non-expression column "col1" of index "attmp_idx1"
+HINT:  Alter statistics on table column instead.
+ALTER INDEX attmp_idx1 ALTER COLUMN 3 SET STATISTICS 1000;
+\d+ attmp_idx1
+                   Index "public.attmp_idx1"
+ Column |  Type   | Key? | Definition | Storage | Stats target 
+--------+---------+------+------------+---------+--------------
+ a      | integer | yes  | a          | plain   | 
+ col1   | integer | yes  | col1       | plain   | 
+ col2   | integer | yes  | col2       | plain   | 1000
+btree, for table "public.attmp"
+
 DROP TABLE attmp;
 --
 -- rename - check on both non-temp and temp tables
diff --git a/src/test/regress/expected/collate.icu.utf8.out b/src/test/regress/expected/collate.icu.utf8.out
index 1325e123877..c1ad91b23e5 100644
--- a/src/test/regress/expected/collate.icu.utf8.out
+++ b/src/test/regress/expected/collate.icu.utf8.out
@@ -2703,6 +2703,19 @@ SELECT * FROM t5 ORDER BY c ASC, a ASC;
  3 | d1 | d1
 (3 rows)
 
+CREATE INDEX t5_idx1 ON t5 USING btree((b COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((b));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated,
+        indcollation[0]::regcollation
+FROM    pg_index
+WHERE   indrelid = 't5'::regclass
+ORDER BY indexrelid;
+ indexrelid | indrelid | indnatts | indattrgenerated | indcollation 
+------------+----------+----------+------------------+--------------
+ t5_idx1    | t5       |        1 | 0                | "POSIX"
+ t5_idx2    | t5       |        1 | 0                | "C"
+(2 rows)
+
 -- Check that DEFAULT expressions in SQL/JSON functions use the same collation
 -- as the RETURNING type.  Mismatched collations should raise an error.
 CREATE DOMAIN d1 AS text COLLATE case_insensitive;
diff --git a/src/test/regress/expected/fast_default.out b/src/test/regress/expected/fast_default.out
index ccbcdf8403f..ef19f667cc1 100644
--- a/src/test/regress/expected/fast_default.out
+++ b/src/test/regress/expected/fast_default.out
@@ -70,6 +70,14 @@ NOTICE:  rewriting table has_volatile for reason 4
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 NOTICE:  rewriting table has_volatile for reason 2
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+NOTICE:  rewriting table has_volatile for reason 2
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
+NOTICE:  rewriting table has_volatile for reason 4
 -- Test a large sample of different datatypes
 CREATE TABLE T(pk INT NOT NULL PRIMARY KEY, c_int INT DEFAULT 1);
 SELECT set('t');
diff --git a/src/test/regress/expected/generated_virtual.out b/src/test/regress/expected/generated_virtual.out
index 249e68be654..147c6980540 100644
--- a/src/test/regress/expected/generated_virtual.out
+++ b/src/test/regress/expected/generated_virtual.out
@@ -745,30 +745,322 @@ ERROR:  primary keys on virtual generated columns are not supported
 --INSERT INTO gtest22b VALUES (2);
 --INSERT INTO gtest22b VALUES (2);
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer, a integer GENERATED ALWAYS AS (c+1)) PARTITION BY RANGE (b);
+CREATE TABLE gtestpart3 (a integer GENERATED ALWAYS AS (c), b integer, c integer);
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 FOR VALUES FROM (1) to (10);
+-- error: An index cannot be created when the partitioned table and its
+-- partitions have different generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a);
+ERROR:  cannot create index on partitioned table "gtestparted"
+DETAIL:  The virtual generated column expression of partitioned table "gtestparted" does not match that of table "gtestpart3"
+ALTER TABLE gtestpart3 ALTER COLUMN a SET EXPRESSION AS (c + 1);
+CREATE TABLE gtestpart1 (c integer, a integer GENERATED ALWAYS AS (c), b integer);
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+-- error: An index cannot be created when the partitioned table and its
+-- partitions have different generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 FOR VALUES FROM (10) TO (20);
+ERROR:  cannot attach table "gtestpart1" as partition of partitioned table "gtestparted"
+DETAIL:  The virtual generated column expression of partitioned table "gtestparted" does not match that of table "gtestpart1"
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 FOR VALUES FROM (10) TO (20); --ok
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+       relid       |    parentrelid    | isleaf | level 
+-------------------+-------------------+--------+-------
+ gtestparted_a_idx |                   | f      |     0
+ gtestpart2_a_idx  | gtestparted_a_idx | t      |     1
+ gtestpart3_a_idx  | gtestparted_a_idx | t      |     1
+(3 rows)
+
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+ERROR:  cannot attach index "gtestpart2_a_idx_copy" as a partition of index "gtestparted_a_idx"
+DETAIL:  Another index "gtestpart2_a_idx" is already attached for partition "gtestpart2".
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+         relid         |     parentrelid     | isleaf | level 
+-----------------------+---------------------+--------+-------
+ gtestparted_a_idx_1   |                     | f      |     0
+ gtestpart2_a_idx_copy | gtestparted_a_idx_1 | t      |     1
+ gtestpart3_a_idx1     | gtestparted_a_idx_1 | t      |     1
+(3 rows)
+
+INSERT INTO gtestparted(b, c) SELECT g, g + 1 FROM generate_series(16, 1, -1) g;
+CLUSTER gtestparted USING gtestparted_a_idx_1;
+\d gtestpart2
+              Table "generated_virtual_tests.gtestpart2"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ b      | integer |           |          | 
+ a      | integer |           |          | generated always as (c + 1)
+ c      | integer |           |          | 
+Partition of: gtestparted FOR VALUES FROM (10) TO (20)
+Indexes:
+    "gtestpart2_a_idx" btree (a)
+    "gtestpart2_a_idx_copy" btree (a) CLUSTER
+
+\d gtestpart3
+              Table "generated_virtual_tests.gtestpart3"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ a      | integer |           |          | generated always as (c + 1)
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+Partition of: gtestparted FOR VALUES FROM (1) TO (10)
+Indexes:
+    "gtestpart3_a_idx" btree (a)
+    "gtestpart3_a_idx1" btree (a) CLUSTER
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted INCLUDING ALL);
+\d gtestparted_like
+           Table "generated_virtual_tests.gtestparted_like"
+ Column |  Type   | Collation | Nullable |           Default           
+--------+---------+-----------+----------+-----------------------------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+ a      | integer |           |          | generated always as (c + 1)
+Indexes:
+    "gtestparted_like_a_idx" btree (a)
+    "gtestparted_like_a_idx1" btree (a)
+
+ALTER TABLE gtestparted_like DROP COLUMN a;
+\d gtestparted_like
+ Table "generated_virtual_tests.gtestparted_like"
+ Column |  Type   | Collation | Nullable | Default 
+--------+---------+-----------+----------+---------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+
+CREATE TABLE gtest22c (
+    a int,
+    b int GENERATED ALWAYS AS (a * 2),
+    c int GENERATED ALWAYS AS (11),
+    d int GENERATED ALWAYS AS (a * 3),
+    e int4range GENERATED ALWAYS AS (int4range(a, a + 10)),
+    e1 int8range GENERATED ALWAYS AS (int8range(a, a + 10)),
+    f int GENERATED ALWAYS AS (a),
+    f1 oid GENERATED ALWAYS AS (tableoid)
+) WITH (autovacuum_enabled = false);
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+ERROR:  index creation on system columns is not supported
+LINE 1: CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+                                                    ^
+CREATE INDEX gtest22c_error ON gtest22c ((f1));
+ERROR:  index creation on system columns is not supported
+LINE 1: CREATE INDEX gtest22c_error ON gtest22c ((f1));
+                                                 ^
+ALTER TABLE gtest22c DROP COLUMN f1;
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e      | int4range |           |          | generated always as (int4range(a, a + 10))
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c)
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+    "gtest22c_e_e1_idx" gist (e, e1)
+
+INSERT INTO gtest22c(a) SELECT g FROM generate_series(1, 1_000) g;
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 AND c = 11;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 2) = 4)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 4 AND c = 11;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_d_idx on gtest22c
+   Index Cond: ((a * 3) = 6)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE d = 6;
+ a | b | c  | d |   e    |   e1   | f 
+---+---+----+---+--------+--------+---
+ 2 | 4 | 11 | 6 | [2,12) | [2,12) | 2
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 AND e @> 16 AND e1 @> 12::bigint;
+                                                                        QUERY PLAN                                                                        
+----------------------------------------------------------------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e_e1_idx on gtest22c
+         Index Cond: ((int4range(a, (a + 10)) @> 12) AND (int4range(a, (a + 10)) @> 16) AND (int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint))
+(3 rows)
+
+SELECT count(*) FROM gtest22c WHERE e @> 12 AND e @> 16 AND e1 @> 12::bigint;
+ count 
+-------
+     6
+(1 row)
+
+SELECT * FROM gtest22c WHERE e @> 12 AND e @> 16 AND e1 @> 12::bigint;
+ a  | b  | c  | d  |    e    |   e1    | f  
+----+----+----+----+---------+---------+----
+  7 | 14 | 11 | 21 | [7,17)  | [7,17)  |  7
+  8 | 16 | 11 | 24 | [8,18)  | [8,18)  |  8
+  9 | 18 | 11 | 27 | [9,19)  | [9,19)  |  9
+ 10 | 20 | 11 | 30 | [10,20) | [10,20) | 10
+ 11 | 22 | 11 | 33 | [11,21) | [11,21) | 11
+ 12 | 24 | 11 | 36 | [12,22) | [12,22) | 12
+(6 rows)
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint AND e1 @> 16::bigint;
+                                                                     QUERY PLAN                                                                      
+-----------------------------------------------------------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using gtest22c_e1_idx on gtest22c
+         Index Cond: ((int8range((a)::bigint, ((a + 10))::bigint) @> '12'::bigint) AND (int8range((a)::bigint, ((a + 10))::bigint) @> '16'::bigint))
+(3 rows)
+
+SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint AND e1 @> 16::bigint;
+ count 
+-------
+     6
+(1 row)
+
+SELECT * FROM gtest22c WHERE e1 @> 12::bigint AND e1 @> 16::bigint;
+ a  | b  | c  | d  |    e    |   e1    | f  
+----+----+----+----+---------+---------+----
+ 12 | 24 | 11 | 36 | [12,22) | [12,22) | 12
+ 11 | 22 | 11 | 33 | [11,21) | [11,21) | 11
+ 10 | 20 | 11 | 30 | [10,20) | [10,20) | 10
+  9 | 18 | 11 | 27 | [9,19)  | [9,19)  |  9
+  8 | 16 | 11 | 24 | [8,18)  | [8,18)  |  8
+  7 | 14 | 11 | 21 | [7,17)  | [7,17)  |  7
+(6 rows)
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+CLUSTER gtest22c USING gtest22c_b_idx;
+\d gtest22c
+                                 Table "generated_virtual_tests.gtest22c"
+ Column |   Type    | Collation | Nullable |                           Default                            
+--------+-----------+-----------+----------+--------------------------------------------------------------
+ a      | integer   |           |          | 
+ b      | integer   |           |          | generated always as (a * 2)
+ c      | integer   |           |          | generated always as (11)
+ d      | integer   |           |          | generated always as (a * 3)
+ e1     | int8range |           |          | generated always as (int8range(a::bigint, (a + 10)::bigint))
+ f      | integer   |           |          | generated always as (a)
+Indexes:
+    "gtest22c_b_idx" btree (b, c) CLUSTER
+    "gtest22c_d_idx" hash (d)
+    "gtest22c_e1_idx" spgist (e1)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+                 QUERY PLAN                  
+---------------------------------------------
+ Index Scan using gtest22c_b_idx on gtest22c
+   Index Cond: ((a * 4) = 8)
+(2 rows)
+
+SELECT * FROM gtest22c WHERE b = 8;
+ a | b | c  | d |   e1   | f 
+---+---+----+---+--------+---
+ 2 | 8 | 11 | 6 | [2,12) | 2
+(1 row)
+
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(
+  j   jsonb,
+  j1  jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+  f1  interval,
+  f2  interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1) SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX t2_f1_f2_brin_idx ON t2 USING BRIN (
+      f1 interval_minmax_multi_ops,
+      f2 interval_minmax_multi_ops) WITH (pages_per_range = 1);
+CREATE INDEX t2_j1_gin_idx ON t2 USING GIN (j1);
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+                                           QUERY PLAN                                            
+-------------------------------------------------------------------------------------------------
+ Aggregate
+   ->  Bitmap Heap Scan on t2
+         Recheck Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+         ->  Bitmap Index Scan on t2_j1_gin_idx
+               Index Cond: ((j || '{"hello": "world"}'::jsonb) @> '[{"hello": "world"}]'::jsonb)
+(5 rows)
+
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+ count 
+-------
+   141
+(1 row)
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+                                                  QUERY PLAN                                                   
+---------------------------------------------------------------------------------------------------------------
+ Bitmap Heap Scan on t2
+   Recheck Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+   ->  Bitmap Index Scan on t2_f1_f2_brin_idx
+         Index Cond: ((f1 > '@ 30 years'::interval) AND ((f1 + '@ 1 day'::interval) > '@ 30 years'::interval))
+(4 rows)
+
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+ j | j1 |    f1    |    f2    
+---+----+----------+----------
+   |    | infinity | infinity
+(1 row)
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
 --INSERT INTO gtest23a VALUES (1, 11), (2, 22), (3, 33);
@@ -1313,6 +1605,7 @@ ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello2');
 DROP STATISTICS gtest31_2_stat;
 CREATE INDEX gtest31_2_y_idx ON gtest31_2(((y).b));
 ALTER TABLE gtest31_1 ALTER COLUMN b SET EXPRESSION AS ('hello3');
+ERROR:  cannot alter table "gtest31_1" because column "gtest31_2.y" uses its row type
 DROP TABLE gtest31_1, gtest31_2;
 -- Check it for a partitioned table, too
 CREATE TABLE gtest31_1 (a int, b text GENERATED ALWAYS AS ('hello') VIRTUAL, c text) PARTITION BY LIST (a);
@@ -1685,3 +1978,16 @@ select * from gtest33 where b is null;
 
 reset constraint_exclusion;
 drop table gtest33;
+-- system catalog sanity check. If the index is based on a virtual generated
+-- column, then the corresponding attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
+ indrelid | attnum | attname | attgenerated 
+----------+--------+---------+--------------
+(0 rows)
+
diff --git a/src/test/regress/expected/indexing.out b/src/test/regress/expected/indexing.out
index 4d29fb85293..df4b700a798 100644
--- a/src/test/regress/expected/indexing.out
+++ b/src/test/regress/expected/indexing.out
@@ -702,6 +702,51 @@ select relname as child, inhparent::regclass as parent, pg_get_indexdef as child
  idxpart_a_idx   |               | CREATE INDEX idxpart_a_idx ON ONLY public.idxpart USING btree (a COLLATE "C")
 (7 rows)
 
+drop table idxpart;
+---test collation with virtual generated column
+drop table if exists idxpart, idxpart1, idxpart2;
+NOTICE:  table "idxpart" does not exist, skipping
+NOTICE:  table "idxpart1" does not exist, skipping
+NOTICE:  table "idxpart2" does not exist, skipping
+create table idxpart (b text, a text generated always as (b), c text) partition by range (c);
+create table idxpart1 (b text, a text generated always as (b || 'h'), c text);
+create table idxpart2 (like idxpart including generated);
+create index idxpart2_a_idx on idxpart2 (a collate "POSIX");
+create index idxpart2_a_idx1 on idxpart2 (a);
+create index idxpart2_a_idx2 on idxpart2 (a collate "C");
+alter table idxpart attach partition idxpart1 for values from ('aaa') to ('bbb');
+alter table idxpart attach partition idxpart2 for values from ('bbb') to ('ccc');
+-- error: An index cannot be created when the partitioned table and its
+-- partitions have different generation expressions.
+create index idxpart_a on idxpart (a collate "C");
+ERROR:  cannot create index on partitioned table "idxpart"
+DETAIL:  The virtual generated column expression of partitioned table "idxpart" does not match that of table "idxpart1"
+alter table idxpart1 alter column a set expression as (b collate "C");
+create index idxpart_a on idxpart (a collate "C"); --error
+ERROR:  cannot create index on partitioned table "idxpart"
+DETAIL:  The virtual generated column expression of partitioned table "idxpart" does not match that of table "idxpart1"
+alter table idxpart1 alter column a set expression as (b);
+create index idxpart_a on idxpart (a collate "C"); ---ok
+create table idxpart4 partition of idxpart for values from ('ddd') to ('eee');
+select relname as child, inhparent::regclass as parent,
+        pi.indkey, pi.indattrgenerated,
+        (pi.indcollation[0])::regcollation,
+        pg_get_indexdef as childdef
+from pg_class join pg_index pi on pi.indexrelid = pg_class.oid
+left join pg_inherits on inhrelid = oid,
+lateral pg_get_indexdef(pg_class.oid)
+where relkind in ('i', 'I') and relname like 'idxpart%'
+order by relname;
+      child      |  parent   | indkey | indattrgenerated | indcollation |                                    childdef                                    
+-----------------+-----------+--------+------------------+--------------+--------------------------------------------------------------------------------
+ idxpart1_a_idx  | idxpart_a | 1      | 2                | "C"          | CREATE INDEX idxpart1_a_idx ON public.idxpart1 USING btree (a COLLATE "C")
+ idxpart2_a_idx  |           | 1      | 2                | "POSIX"      | CREATE INDEX idxpart2_a_idx ON public.idxpart2 USING btree (a COLLATE "POSIX")
+ idxpart2_a_idx1 |           | 1      | 2                | "default"    | CREATE INDEX idxpart2_a_idx1 ON public.idxpart2 USING btree (a)
+ idxpart2_a_idx2 | idxpart_a | 1      | 2                | "C"          | CREATE INDEX idxpart2_a_idx2 ON public.idxpart2 USING btree (a COLLATE "C")
+ idxpart4_a_idx  | idxpart_a | 1      | 2                | "C"          | CREATE INDEX idxpart4_a_idx ON public.idxpart4 USING btree (a COLLATE "C")
+ idxpart_a       |           | 1      | 2                | "C"          | CREATE INDEX idxpart_a ON ONLY public.idxpart USING btree (a COLLATE "C")
+(6 rows)
+
 drop table idxpart;
 -- Verify behavior for opclass (mis)matches
 create table idxpart (a text) partition by range (a);
diff --git a/src/test/regress/sql/alter_table.sql b/src/test/regress/sql/alter_table.sql
index 417202430a5..0b215d4daf6 100644
--- a/src/test/regress/sql/alter_table.sql
+++ b/src/test/regress/sql/alter_table.sql
@@ -156,6 +156,15 @@ ALTER INDEX attmp_idx ALTER COLUMN 4 SET STATISTICS 1000;
 
 ALTER INDEX attmp_idx ALTER COLUMN 2 SET STATISTICS -1;
 
+ALTER TABLE attmp
+    ADD COLUMN col1 int GENERATED ALWAYS AS (a),
+    ADD COLUMN col2 int GENERATED ALWAYS AS (a + 1);
+
+CREATE INDEX attmp_idx1 ON attmp (a, col1, col2);
+ALTER INDEX attmp_idx1 ALTER COLUMN 1 SET STATISTICS 1000;
+ALTER INDEX attmp_idx1 ALTER COLUMN 2 SET STATISTICS 1000;
+ALTER INDEX attmp_idx1 ALTER COLUMN 3 SET STATISTICS 1000;
+\d+ attmp_idx1
 DROP TABLE attmp;
 
 
diff --git a/src/test/regress/sql/collate.icu.utf8.sql b/src/test/regress/sql/collate.icu.utf8.sql
index b6c54503d21..ab70aaed7e2 100644
--- a/src/test/regress/sql/collate.icu.utf8.sql
+++ b/src/test/regress/sql/collate.icu.utf8.sql
@@ -1000,6 +1000,14 @@ INSERT INTO t5 (a, b) values (1, 'D1'), (2, 'D2'), (3, 'd1');
 -- rewriting.)
 SELECT * FROM t5 ORDER BY c ASC, a ASC;
 
+CREATE INDEX t5_idx1 ON t5 USING btree((b COLLATE "POSIX"));
+CREATE INDEX t5_idx2 ON t5 USING btree((b));
+SELECT  indexrelid::regclass, indrelid::regclass, indnatts, indattrgenerated,
+        indcollation[0]::regcollation
+FROM    pg_index
+WHERE   indrelid = 't5'::regclass
+ORDER BY indexrelid;
+
 -- Check that DEFAULT expressions in SQL/JSON functions use the same collation
 -- as the RETURNING type.  Mismatched collations should raise an error.
 CREATE DOMAIN d1 AS text COLLATE case_insensitive;
diff --git a/src/test/regress/sql/fast_default.sql b/src/test/regress/sql/fast_default.sql
index 068dd0bc8aa..b39e76bcfc3 100644
--- a/src/test/regress/sql/fast_default.sql
+++ b/src/test/regress/sql/fast_default.sql
@@ -77,6 +77,12 @@ ALTER TABLE has_volatile ALTER COLUMN col1 SET DATA TYPE float8,
 -- stored generated columns need a rewrite
 ALTER TABLE has_volatile ADD col7 int GENERATED ALWAYS AS (55) stored;
 
+-- if there is any index over virtual generated columns,
+-- change generation expression need rewrite
+CREATE INDEX on has_volatile(col6);
+ALTER TABLE has_volatile ALTER COLUMN col6 SET EXPRESSION AS (col1 * 3);
+-- table rewrite again.
+ALTER TABLE has_volatile ALTER COLUMN col6 SET DATA TYPE INT8;
 
 
 -- Test a large sample of different datatypes
diff --git a/src/test/regress/sql/generated_virtual.sql b/src/test/regress/sql/generated_virtual.sql
index 81152b39a79..c8e933c8300 100644
--- a/src/test/regress/sql/generated_virtual.sql
+++ b/src/test/regress/sql/generated_virtual.sql
@@ -1,6 +1,4 @@
 -- keep these tests aligned with generated_stored.sql
-
-
 CREATE SCHEMA generated_virtual_tests;
 GRANT USAGE ON SCHEMA generated_virtual_tests TO PUBLIC;
 SET search_path = generated_virtual_tests;
@@ -396,32 +394,138 @@ CREATE TABLE gtest22b (a int, b int GENERATED ALWAYS AS (a / 2) VIRTUAL, PRIMARY
 --INSERT INTO gtest22b VALUES (2);
 
 -- indexes
-CREATE TABLE gtest22c (a int, b int GENERATED ALWAYS AS (a * 2) VIRTUAL);
---CREATE INDEX gtest22c_b_idx ON gtest22c (b);
+CREATE TABLE gtestparted (b integer, c integer, a integer GENERATED ALWAYS AS (c+1)) PARTITION BY RANGE (b);
+CREATE TABLE gtestpart3 (a integer GENERATED ALWAYS AS (c), b integer, c integer);
+
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart3 FOR VALUES FROM (1) to (10);
+-- error: An index cannot be created when the partitioned table and its
+-- partitions have different generation expressions.
+CREATE INDEX gtestparted_a_idx_error on gtestparted(a);
+ALTER TABLE gtestpart3 ALTER COLUMN a SET EXPRESSION AS (c + 1);
+
+CREATE TABLE gtestpart1 (c integer, a integer GENERATED ALWAYS AS (c), b integer);
+CREATE TABLE gtestpart2 (b integer, a integer GENERATED ALWAYS AS (c+1), c integer);
+CREATE INDEX gtestpart1_a_idx on gtestpart1(a);
+CREATE INDEX gtestpart2_a_idx on gtestpart2(a);
+CREATE INDEX gtestpart2_a_idx_copy on gtestpart2(a);
+CREATE INDEX gtestparted_a_idx on gtestparted(a);
+
+-- error: An index cannot be created when the partitioned table and its
+-- partitions have different generation expressions.
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart1 FOR VALUES FROM (10) TO (20);
+
+ALTER TABLE gtestparted ATTACH PARTITION gtestpart2 FOR VALUES FROM (10) TO (20); --ok
+SELECT * FROM pg_partition_tree('gtestparted_a_idx'::regclass);
+
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx_copy; --error
+ALTER INDEX gtestparted_a_idx ATTACH PARTITION gtestpart2_a_idx; --ok
+
+CREATE INDEX gtestparted_a_idx_1 on gtestparted(a);
+--now index gtestpart2_a_idx_copy should attach to the partition tree
+SELECT * FROM pg_partition_tree('gtestparted_a_idx_1'::regclass);
+
+INSERT INTO gtestparted(b, c) SELECT g, g + 1 FROM generate_series(16, 1, -1) g;
+CLUSTER gtestparted USING gtestparted_a_idx_1;
+\d gtestpart2
+\d gtestpart3
+
+--test create table like copy indexes
+CREATE TABLE gtestparted_like (LIKE gtestparted INCLUDING ALL);
+\d gtestparted_like
+ALTER TABLE gtestparted_like DROP COLUMN a;
+\d gtestparted_like
+
+CREATE TABLE gtest22c (
+    a int,
+    b int GENERATED ALWAYS AS (a * 2),
+    c int GENERATED ALWAYS AS (11),
+    d int GENERATED ALWAYS AS (a * 3),
+    e int4range GENERATED ALWAYS AS (int4range(a, a + 10)),
+    e1 int8range GENERATED ALWAYS AS (int8range(a, a + 10)),
+    f int GENERATED ALWAYS AS (a),
+    f1 oid GENERATED ALWAYS AS (tableoid)
+) WITH (autovacuum_enabled = false);
+
+--index can not based on tableoid column
+CREATE INDEX gtest22c_error ON gtest22c (b, f1);
+CREATE INDEX gtest22c_error ON gtest22c ((f1));
+ALTER TABLE gtest22c DROP COLUMN f1;
+
+--index include columns are not supported
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (b,c);
+-- CREATE INDEX gtest22c_idx1_inc ON gtest22c USING btree(a) include (f);
+
+--Other index access methods are supported
+CREATE INDEX gtest22c_b_idx ON gtest22c USING btree(b, c);
+CREATE INDEX gtest22c_d_idx ON gtest22c USING hash(d);
+CREATE INDEX gtest22c_e_e1_idx ON gtest22c USING gist(e, e1);
+CREATE INDEX gtest22c_e1_idx ON gtest22c USING spgist(e1);
+
 --CREATE INDEX gtest22c_expr_idx ON gtest22c ((b * 3));
 --CREATE INDEX gtest22c_pred_idx ON gtest22c (a) WHERE b > 0;
---\d gtest22c
+\d gtest22c
+
+INSERT INTO gtest22c(a) SELECT g FROM generate_series(1, 1_000) g;
+SET enable_seqscan TO off;
+SET enable_bitmapscan TO off;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
+SELECT * FROM gtest22c WHERE b = 4;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4 AND c = 11;
+SELECT * FROM gtest22c WHERE b = 4 AND c = 11;
+
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE d = 6;
+SELECT * FROM gtest22c WHERE d = 6;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e @> 12 AND e @> 16 AND e1 @> 12::bigint;
+SELECT count(*) FROM gtest22c WHERE e @> 12 AND e @> 16 AND e1 @> 12::bigint;
+SELECT * FROM gtest22c WHERE e @> 12 AND e @> 16 AND e1 @> 12::bigint;
+
+EXPLAIN (COSTS OFF) SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint AND e1 @> 16::bigint;
+SELECT count(*) FROM gtest22c WHERE e1 @> 12::bigint AND e1 @> 16::bigint;
+SELECT * FROM gtest22c WHERE e1 @> 12::bigint AND e1 @> 16::bigint;
+
+--column drop then the index over that column should also being dropped
+ALTER TABLE gtest22c DROP COLUMN e;
+CLUSTER gtest22c USING gtest22c_b_idx;
+\d gtest22c
 
---INSERT INTO gtest22c VALUES (1), (2), (3);
---SET enable_seqscan TO off;
---SET enable_bitmapscan TO off;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 4;
---SELECT * FROM gtest22c WHERE b = 4;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 6;
 --SELECT * FROM gtest22c WHERE b * 3 = 6;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 
---ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
---ANALYZE gtest22c;
---EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
---SELECT * FROM gtest22c WHERE b = 8;
+ALTER TABLE gtest22c ALTER COLUMN b SET EXPRESSION AS (a * 4);
+ANALYZE gtest22c;
+EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b = 8;
+SELECT * FROM gtest22c WHERE b = 8;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE b * 3 = 12;
 --SELECT * FROM gtest22c WHERE b * 3 = 12;
 --EXPLAIN (COSTS OFF) SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
 --SELECT * FROM gtest22c WHERE a = 1 AND b > 0;
---RESET enable_seqscan;
---RESET enable_bitmapscan;
+
+--test index over gin and brin index
+RESET enable_bitmapscan;
+CREATE TABLE t2(
+  j   jsonb,
+  j1  jsonb GENERATED ALWAYS AS (j || '{"hello": "world"}'),
+  f1  interval,
+  f2  interval GENERATED ALWAYS AS ( f1 + interval '1 day'));
+INSERT INTO t2(j, f1) SELECT i::text::jsonb, (i || ' days')::interval FROM generate_series(100, 240) s(i);
+INSERT INTO t2(f1) VALUES ('-infinity'), ('infinity');
+CREATE INDEX t2_f1_f2_brin_idx ON t2 USING BRIN (
+      f1 interval_minmax_multi_ops,
+      f2 interval_minmax_multi_ops) WITH (pages_per_range = 1);
+CREATE INDEX t2_j1_gin_idx ON t2 USING GIN (j1);
+
+EXPLAIN(COSTS OFF) SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+SELECT count(*) FROM t2 WHERE j1 @> '[{"hello":"world"}]';
+
+EXPLAIN(COSTS OFF) SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+SELECT * FROM t2 WHERE f1 > '30 years'::interval AND f2 > '30 years'::interval;
+
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 
 -- foreign keys
 CREATE TABLE gtest23a (x int PRIMARY KEY, y int);
@@ -891,3 +995,13 @@ select * from gtest33 where b is null;
 
 reset constraint_exclusion;
 drop table gtest33;
+
+-- system catalog sanity check. If the index is based on a virtual generated
+-- column, then the corresponding attribute's attgenerated should be 'v'.
+select pi.indrelid::regclass, pa.attnum,
+       pa.attname,
+       pa.attgenerated
+from pg_index pi, unnest(indattrgenerated) sub(a), pg_attribute pa
+where 0 <> a
+and pa.attrelid = pi.indrelid and pa.attnum = sub.a
+and (pa.attgenerated <> 'v' or pi.indnatts <> pi.indnkeyatts);
diff --git a/src/test/regress/sql/indexing.sql b/src/test/regress/sql/indexing.sql
index b5cb01c2d70..192d67be1ec 100644
--- a/src/test/regress/sql/indexing.sql
+++ b/src/test/regress/sql/indexing.sql
@@ -328,6 +328,36 @@ select relname as child, inhparent::regclass as parent, pg_get_indexdef as child
   where relkind in ('i', 'I') and relname like 'idxpart%' order by relname;
 drop table idxpart;
 
+---test collation with virtual generated column
+drop table if exists idxpart, idxpart1, idxpart2;
+create table idxpart (b text, a text generated always as (b), c text) partition by range (c);
+create table idxpart1 (b text, a text generated always as (b || 'h'), c text);
+create table idxpart2 (like idxpart including generated);
+create index idxpart2_a_idx on idxpart2 (a collate "POSIX");
+create index idxpart2_a_idx1 on idxpart2 (a);
+create index idxpart2_a_idx2 on idxpart2 (a collate "C");
+alter table idxpart attach partition idxpart1 for values from ('aaa') to ('bbb');
+alter table idxpart attach partition idxpart2 for values from ('bbb') to ('ccc');
+-- error: An index cannot be created when the partitioned table and its
+-- partitions have different generation expressions.
+create index idxpart_a on idxpart (a collate "C");
+alter table idxpart1 alter column a set expression as (b collate "C");
+create index idxpart_a on idxpart (a collate "C"); --error
+alter table idxpart1 alter column a set expression as (b);
+create index idxpart_a on idxpart (a collate "C"); ---ok
+create table idxpart4 partition of idxpart for values from ('ddd') to ('eee');
+select relname as child, inhparent::regclass as parent,
+        pi.indkey, pi.indattrgenerated,
+        (pi.indcollation[0])::regcollation,
+        pg_get_indexdef as childdef
+from pg_class join pg_index pi on pi.indexrelid = pg_class.oid
+left join pg_inherits on inhrelid = oid,
+lateral pg_get_indexdef(pg_class.oid)
+where relkind in ('i', 'I') and relname like 'idxpart%'
+order by relname;
+
+drop table idxpart;
+
 -- Verify behavior for opclass (mis)matches
 create table idxpart (a text) partition by range (a);
 create table idxpart1 (like idxpart);
-- 
2.34.1