Hierarchical and recursive queries in SQL explained

A hierarchical query is a type of SQL query that handles hierarchical model data. They are special cases of more general recursive fixpoint queries, which compute transitive closures.

In standard hierarchical queries are implemented by way of recursive common table expressions (CTEs). Unlike Oracle's earlier connect-by clause, recursive CTEs were designed with fixpoint semantics from the beginning.^[1] Recursive CTEs from the standard were relatively close to the existing implementation in IBM DB2 version 2.^[1] Recursive CTEs are also supported by Microsoft SQL Server (since SQL Server 2008 R2),^[2] Firebird 2.1,^[3] PostgreSQL 8.4+,^[4] SQLite 3.8.3+,^[5] IBM Informix version 11.50+, CUBRID, MariaDB 10.2+ and MySQL 8.0.1+.^[6] Tableau has documentation describing how CTEs can be used. TIBCO Spotfire does not support CTEs, while Oracle 11g Release 2's implementation lacks fixpoint semantics.

Without common table expressions or connected-by clauses it is possible to achieve hierarchical queries with user-defined recursive functions.^[7]

Common table expression

A common table expression, or CTE, (in SQL) is a temporary named result set, derived from a simple query and defined within the execution scope of a SELECT, INSERT, UPDATE, or DELETE statement.

CTEs can be thought of as alternatives to derived tables (subquery), views, and inline user-defined functions.

Common table expressions are supported by Teradata (starting with version 14), IBM Db2, Informix (starting with version 14.1), Firebird (starting with version 2.1),^[8] Microsoft SQL Server (starting with version 2005), Oracle (with recursion since 11g release 2), PostgreSQL (since 8.4), MariaDB (since 10.2), MySQL (since 8.0), SQLite (since 3.8.3), HyperSQL, Informix (since 14.10),^[9] Google BigQuery, Sybase (starting with version 9), Vertica, H2 (experimental),^[10] and many others. Oracle calls CTEs "subquery factoring".^[11]

The syntax for a CTE (which may or may not be recursive) is as follows:

WITH [RECURSIVE] with_query [, ...]SELECT ...

where with_query's syntax is:

query_name [(column_name [,...]) ] AS (SELECT ...)

Recursive CTEs can be used to traverse relations (as graphs or trees) although the syntax is much more involved because there are no automatic pseudo-columns created (like LEVEL below); if these are desired, they have to be created in the code. See MSDN documentation^[2] or IBM documentation^{[12] [13]} for tutorial examples.

The RECURSIVE keyword is not usually needed after WITH in systems other than PostgreSQL.^[14]

In SQL:1999 a recursive (CTE) query may appear anywhere a query is allowed. It's possible, for example, to name the result using CREATE [<code>RECURSIVE</code>] VIEW.^[15] Using a CTE inside an INSERT INTO, one can populate a table with data generated from a recursive query; random data generation is possible using this technique without using any procedural statements.^[16]

Some Databases, like PostgreSQL, support a shorter CREATE RECURSIVE VIEW format which is internally translated into WITH RECURSIVE coding.^[17]

An example of a recursive query computing the factorial of numbers from 0 to 9 is the following:WITH recursive temp (n, fact) AS (SELECT 0, 1 -- Initial Subquery UNION ALL SELECT n+1, (n+1)*fact FROM temp WHERE n < 9 -- Recursive Subquery)SELECT * FROM temp;

CONNECT BY

An alternative syntax is the non-standard CONNECT BY construct; it was introduced by Oracle in the 1980s.^[18] Prior to Oracle 10g, the construct was only useful for traversing acyclic graphs because it returned an error on detecting any cycles; in version 10g Oracle introduced the NOCYCLE feature (and keyword), making the traversal work in the presence of cycles as well.^[19]

CONNECT BY is supported by Snowflake, EnterpriseDB,^[20] Oracle database,^[21] CUBRID,^[22] IBM Informix^[23] and IBM Db2 although only if it is enabled as a compatibility mode.^[24] The syntax is as follows:

SELECT select_listFROM table_expression[WHERE ... ][START WITH start_expression ]CONNECT BY [NOCYCLE] [ORDER SIBLINGS BY column1 [ ASC | DESC ] [, column2 [ ASC | DESC ] ] ... ][GROUP BY ... ][HAVING ... ]...

For example,

SELECT LEVEL, LPAD (' ', 2 * (LEVEL - 1)) || ename "employee", empno, mgr "manager"FROM emp START WITH mgr IS NULLCONNECT BY PRIOR empno = mgr;

The output from the above query would look like:

level | employee | empno | manager -------+-------------+-------+--------- 1 | KING | 7839 | 2 | JONES | 7566 | 7839 3 | SCOTT | 7788 | 7566 4 | ADAMS | 7876 | 7788 3 | FORD | 7902 | 7566 4 | SMITH | 7369 | 7902 2 | BLAKE | 7698 | 7839 3 | ALLEN | 7499 | 7698 3 | WARD | 7521 | 7698 3 | MARTIN | 7654 | 7698 3 | TURNER | 7844 | 7698 3 | JAMES | 7900 | 7698 2 | CLARK | 7782 | 7839 3 | MILLER | 7934 | 7782 (14 rows)

Unary operators

The following example returns the last name of each employee in department 10, each manager above that employee in the hierarchy, the number of levels between manager and employee, and the path between the two:

SELECT ename "Employee", CONNECT_BY_ROOT ename "Manager", LEVEL-1 "Pathlen", SYS_CONNECT_BY_PATH(ename, '/') "Path"FROM empWHERE LEVEL > 1 AND deptno = 10CONNECT BY PRIOR empno = mgrORDER BY "Employee", "Manager", "Pathlen", "Path";

Functions

• SYS_CONNECT_BY_PATH

See also

• Datalog also implements fixpoint queries
• Regular path queries are a specific kind of recursive query in graph databases
• Deductive databases
• Hierarchical model
• Reachability
• Transitive closure
• Tree structure

Further reading

• Book: C. J. Date. C. J. Date. SQL and Relational Theory: How to Write Accurate SQL Code. 2011. O'Reilly Media. 978-1-4493-1640-2. 2nd. 159–163.

Academic textbooks. Note that these cover only the SQL:1999 standard (and Datalog), but not the Oracle extension.

• Book: Abraham Silberschatz. Henry Korth. S. Sudarshan. Database System Concepts. 2010. 6th. McGraw-Hill. 978-0-07-352332-3. 187–192.
• Book: Raghu Ramakrishnan. Johannes Gehrke. Database management systems. 2003. McGraw-Hill. 978-0-07-246563-1. 3rd. Chapter 24.
• Book: Hector Garcia-Molina. Jeffrey D. Ullman. Jennifer Widom. Database systems: the complete book. 2009. Pearson Prentice Hall. 978-0-13-187325-4. 2nd. 437–445.

External links

• https://stackoverflow.com/questions/1731889/cycle-detection-with-recursive-subquery-factoring
• http://explainextended.com/2009/11/18/sql-server-are-the-recursive-ctes-really-set-based/
• https://web.archive.org/web/20131114094211/http://gennick.com/with.html
• http://www.cs.duke.edu/courses/fall04/cps116/lectures/11-recursion.pdf
• http://www.blacktdn.com.br/2015/06/blacktdn-mssql-usando-consulta-cte.html

Notes and References

1. Book: Jim Melton. Alan R. Simon. SQL:1999: Understanding Relational Language Components. 2002. Morgan Kaufmann. 978-1-55860-456-8.
2. Web site: Recursive Queries Using Common Table Expressions . Microsoft . 2009-12-23.
3. Web site: Firebird 2.1 Release Notes . Helen Borrie . 2008-07-15 . 2015-11-24.
4. Web site: WITH Queries. 10 February 2022. PostgreSQL
5. Web site: WITH Clause. SQLite
6. Web site: MySQL 8.0 Labs: [Recursive] Common Table Expressions in MySQL (CTEs) ]. 2017-12-20 . 2019-08-16 . https://web.archive.org/web/20190816150345/https://mysqlserverteam.com/mysql-8-0-labs-recursive-common-table-expressions-in-mysql-ctes/ . dead . mysqlserverteam.com
7. http://www.paragoncorporation.com/ArticleDetail.aspx?ArticleID=24 Paragon corporation: Using PostgreSQL User-Defined Functions to solve the Tree Problem
8. https://firebirdsql.org/file/documentation/reference_manuals/reference_material/Firebird-2.5-LangRef-Update.pdf
9. possible before 14.10 with temp tables https://stackoverflow.com/questions/42579298/why-does-a-with-clause-give-a-syntax-error-on-informix
10. Web site: Advanced.
11. Book: Karen Morton. Robyn Sands. Jared Still. Riyaj Shamsudeen . Kerry Osborne. Pro Oracle SQL. 2010. Apress. 978-1-4302-3228-5. 283.
12. Web site: IBM Docs.
13. Web site: IBM Docs.
14. Book: Regina Obe. Leo Hsu. PostgreSQL: Up and Running. 2012. O'Reilly Media. 978-1-4493-2633-3. 94.
15. Book: Jim Melton. Alan R. Simon. SQL:1999: Understanding Relational Language Components. 2002. Morgan Kaufmann. 978-1-55860-456-8. 352.
16. Book: Don Chamberlin. A Complete Guide to DB2 Universal Database. 1998. Morgan Kaufmann. 978-1-55860-482-7. 253–254.
17. Web site: Create View. 10 February 2022.
18. Book: Benedikt . M. . Senellart . P. . 10.1007/978-1-4614-1168-0_10 . Databases . Computer Science. The Hardware, Software and Heart of It. 189. 2011 . 978-1-4614-1167-3. Blum. Edward K.. Aho. Alfred V. .
19. Book: Sanjay Mishra. Alan Beaulieu. Mastering Oracle SQL. 2004. O'Reilly Media, Inc.. 978-0-596-00632-7. 227.
20. http://www.enterprisedb.com/documentation/hierarchical-queries.html Hierarchical Queries
21. http://download.oracle.com/docs/cd/B19306_01/server.102/b14200/queries003.htm Hierarchical Queries
22. Web site: CUBRID Hierarchical Query. 11 February 2013. 14 February 2013. https://web.archive.org/web/20130214060900/http://www.cubrid.org/manual/841/en/Hierarchical%20Query. dead.
23. https://www-01.ibm.com/support/knowledgecenter/SSGU8G_12.1.0/com.ibm.sqls.doc/ids_sqs_2033.htm Hierarchical Clause
24. Book: Jonathan Gennick. SQL Pocket Guide. 2010. O'Reilly Media, Inc.. 978-1-4493-9409-7. 8. 3rd.