This issue tracks implementing virtual computed columns (using VIRTUAL instead of STORED). This is closely related to #9682 - the expression-based index columns will be implemented as virtual columns internally. It is also related to hash shared indexes where we would like the bucket column to be virtual.

Running checklist:

• parser support
• test catalog support
• descriptors and catalog support
• support querying tables with virtual columns
• mutations of tables with virtual columns (with or without indexes on virtual columns)
  • INSERT
  • DELETE
  • UPDATE
  • UPSERT
    • Add rules for lookup joins with projections to fix plans for UPSERT
• disallow PK on virtual columns
• disallow indexes STORING virtual columns
• disallow FKs on virtual columns
• disallow computed/virtual columns depending on other virtual columns (already disallowed for all computed columns)
• support virtual columns in partial index predicates
• support adding / removing virtual columns
• support adding / removing indexes on virtual columns
• disallow or support virtual columns in check constraints
• support or disallow inverted indexes on virtual columns
• support unique (and partial unique) indexes on virtual columns
• support virtual column as leading column on a multi-column inverted index
• support partial indexes on virtual columns
• support virtual columns in unique constraints without index
• teach SQLsmith about virtual columns
• inline virtual column projections into filters (allowing use of indexes on virtual columns more cases)
• add backup/restore test with table with virtual columns

Non-critical items:

• figure out how to prove implication for cases like:

CREATE TABLE t (
  k INT PRIMARY KEY,
  a INT,
  b INT,
  c INT AS (b + 10) VIRTUAL,
  INDEX (a) WHERE c IN (10, 20, 30)
)

SELECT k FROM t WHERE c = 20

(filed separate issue #61565).

• handle numeric references case where we specify a virtual column but not a dependent one (applies to stored computed columns as well); filed separate issue opt: better validation of column numeric references #61563.
• teach indexConstraintCtx.simplifyFilter to remove the redundant filters like the b:2 = 3 below:

exec-ddl
CREATE TABLE tmp (
  a INT,
  b INT,
  v INT AS (b + 10) VIRTUAL,
  INDEX idx (v)
)
----

opt
SELECT * FROM tmp WHERE v = 13
----
  project
   ├── columns: a:1 b:2!null v:3!null
   ├── immutable
   ├── fd: ()-->(2,3)
   ├── select
   │    ├── columns: a:1 b:2!null
   │    ├── fd: ()-->(2)
   │    ├── index-join tmp
   │    │    ├── columns: a:1 b:2
   │    │    └── scan tmp@idx
   │    │         ├── columns: rowid:4!null
   │    │         ├── constraint: /3/4: [/13 - /13]
   │    │         └── key: (4)
   │    └── filters
   │         └── b:2 = 3 [outer=(2), constraints=(/2: [/3 - /3]; tight), fd=()-->(2)]
   └── projections
        └── b:2 + 10 [as=v:3, outer=(2), immutable]

(filed separate issue #61566).

21.2 items:

• use virtual column for hash shared indexes (filed separate issue sql: use virtual column for hash shared indexes #61564).