WITH Queries (Common Table Expressions)

`WITH` Queries (Common Table Expressions)

SELECT in WITH
Recursive Queries
Common Table Expression Materialization
Data-Modifying Statements in WITH

WITH provides a way to write auxiliary statements for use in a larger query. These statements, which are often referred to as Common Table Expressions or CTEs, can be thought of as defining temporary tables that exist just for one query. Each auxiliary statement in a WITH clause can be a SELECT, INSERT, UPDATE, or DELETE; and the WITH clause itself is attached to a primary statement that can also be a SELECT, INSERT, UPDATE, or DELETE.

`SELECT` in `WITH`

The basic value of SELECT in WITH is to break down complicated queries into simpler parts. An example is:

WITH regional_sales AS (
    SELECT region, SUM(amount) AS total_sales
    FROM orders
    GROUP BY region
), top_regions AS (
    SELECT region
    FROM regional_sales
    WHERE total_sales > (SELECT SUM(total_sales)/10 FROM regional_sales)
)
SELECT region,
       product,
       SUM(quantity) AS product_units,
       SUM(amount) AS product_sales
FROM orders
WHERE region IN (SELECT region FROM top_regions)
GROUP BY region, product;

which displays per-product sales totals in only the top sales regions. The WITH clause defines two auxiliary statements named regional_sales and top_regions, where the output of regional_sales is used in top_regions and the output of top_regions is used in the primary SELECT query. This example could have been written without WITH, but we'd have needed two levels of nested sub-SELECTs. It's a bit easier to follow this way.

Recursive Queries

The optional RECURSIVE modifier changes WITH from a mere syntactic convenience into a feature that accomplishes things not otherwise possible in standard SQL. Using RECURSIVE, a WITH query can refer to its own output. A very simple example is this query to sum the integers from 1 through 100:

WITH RECURSIVE t(n) AS (
    VALUES (1)
  UNION ALL
    SELECT n+1 FROM t WHERE n < 100
)
SELECT sum(n) FROM t;

The general form of a recursive WITH query is always a non-recursive term, then UNION (or UNION ALL), then a recursive term, where only the recursive term can contain a reference to the query's own output. Such a query is executed as follows:

Recursive Query Evaluation

Evaluate the non-recursive term. For UNION (but not UNION ALL), discard duplicate rows. Include all remaining rows in the result of the recursive query, and also place them in a temporary working table.

So long as the working table is not empty, repeat these steps:

Evaluate the recursive term, substituting the current contents of the working table for the recursive self-reference. For UNION (but not UNION ALL), discard duplicate rows and rows that duplicate any previous result row. Include all remaining rows in the result of the recursive query, and also place them in a temporary intermediate table.

Replace the contents of the working table with the contents of the intermediate table, then empty the intermediate table.

Strictly speaking, this process is iteration not recursion, but RECURSIVE is the terminology chosen by the SQL standards committee.

In the example above, the working table has just a single row in each step, and it takes on the values from 1 through 100 in successive steps. In the 100th step, there is no output because of the WHERE clause, and so the query terminates.

Recursive queries are typically used to deal with hierarchical or tree-structured data. A useful example is this query to find all the direct and indirect sub-parts of a product, given only a table that shows immediate inclusions:

WITH RECURSIVE included_parts(sub_part, part, quantity) AS (
    SELECT sub_part, part, quantity FROM parts WHERE part = 'our_product'
  UNION ALL
    SELECT p.sub_part, p.part, p.quantity
    FROM included_parts pr, parts p
    WHERE p.part = pr.sub_part
)
SELECT sub_part, SUM(quantity) as total_quantity
FROM included_parts
GROUP BY sub_part

Search Order

When computing a tree traversal using a recursive query, you might want to order the results in either depth-first or breadth-first order. This can be done by computing an ordering column alongside the other data columns and using that to sort the results at the end. Note that this does not actually control in which order the query evaluation visits the rows; that is as always in SQL implementation-dependent. This approach merely provides a convenient way to order the results afterwards.

To create a depth-first order, we compute for each result row an array of rows that we have visited so far. For example, consider the following query that searches a table tree using a link field:

WITH RECURSIVE search_tree(id, link, data) AS (
    SELECT t.id, t.link, t.data
    FROM tree t
  UNION ALL
    SELECT t.id, t.link, t.data
    FROM tree t, search_tree st
    WHERE t.id = st.link
)
SELECT * FROM search_tree;

To add depth-first ordering information, you can write this:

WITH RECURSIVE search_tree(id, link, data, path) AS (
    SELECT t.id, t.link, t.data, ARRAY[t.id]
    FROM tree t
  UNION ALL
    SELECT t.id, t.link, t.data, path || t.id
    FROM tree t, search_tree st
    WHERE t.id = st.link
)
SELECT * FROM search_tree ORDER BY path;

In the general case where more than one field needs to be used to identify a row, use an array of rows. For example, if we needed to track fields f1 and f2:

WITH RECURSIVE search_tree(id, link, data, path) AS (
    SELECT t.id, t.link, t.data, ARRAY[ROW(t.f1, t.f2)]
    FROM tree t
  UNION ALL
    SELECT t.id, t.link, t.data, path || ROW(t.f1, t.f2)
    FROM tree t, search_tree st
    WHERE t.id = st.link
)
SELECT * FROM search_tree ORDER BY path;

Omit the ROW() syntax in the common case where only one field needs to be tracked. This allows a simple array rather than a composite-type array to be used, gaining efficiency.

To create a breadth-first order, you can add a column that tracks the depth of the search, for example:

WITH RECURSIVE search_tree(id, link, data, depth) AS (
    SELECT t.id, t.link, t.data, 0
    FROM tree t
  UNION ALL
    SELECT t.id, t.link, t.data, depth + 1
    FROM tree t, search_tree st
    WHERE t.id = st.link
)
SELECT * FROM search_tree ORDER BY depth;

To get a stable sort, add data columns as secondary sorting columns.

The recursive query evaluation algorithm produces its output in breadth-first search order. However, this is an implementation detail and it is perhaps unsound to rely on it. The order of the rows within each level is certainly undefined, so some explicit ordering might be desired in any case.

There is built-in syntax to compute a depth- or breadth-first sort column. For example:

WITH RECURSIVE search_tree(id, link, data) AS (
    SELECT t.id, t.link, t.data
    FROM tree t
  UNION ALL
    SELECT t.id, t.link, t.data
    FROM tree t, search_tree st
    WHERE t.id = st.link
) SEARCH DEPTH FIRST BY id SET ordercol
SELECT * FROM search_tree ORDER BY ordercol;
 
WITH RECURSIVE search_tree(id, link, data) AS (
    SELECT t.id, t.link, t.data
    FROM tree t
  UNION ALL
    SELECT t.id, t.link, t.data
    FROM tree t, search_tree st
    WHERE t.id = st.link
) SEARCH BREADTH FIRST BY id SET ordercol
SELECT * FROM search_tree ORDER BY ordercol;

This syntax is internally expanded to something similar to the above hand-written forms. The SEARCH clause specifies whether depth- or breadth first search is wanted, the list of columns to track for sorting, and a column name that will contain the result data that can be used for sorting. That column will implicitly be added to the output rows of the CTE.

Cycle Detection

When working with recursive queries it is important to be sure that the recursive part of the query will eventually return no tuples, or else the query will loop indefinitely. Sometimes, using UNION instead of UNION ALL can accomplish this by discarding rows that duplicate previous output rows. However, often a cycle does not involve output rows that are completely duplicate: it may be necessary to check just one or a few fields to see if the same point has been reached before. The standard method for handling such situations is to compute an array of the already-visited values. For example, consider again the following query that searches a table graph using a link field:

WITH RECURSIVE search_graph(id, link, data, depth) AS (
    SELECT g.id, g.link, g.data, 0
    FROM graph g
  UNION ALL
    SELECT g.id, g.link, g.data, sg.depth + 1
    FROM graph g, search_graph sg
    WHERE g.id = sg.link
)
SELECT * FROM search_graph;

This query will loop if the link relationships contain cycles. Because we require a “depth” output, just changing UNION ALL to UNION would not eliminate the looping. Instead we need to recognize whether we have reached the same row again while following a particular path of links. We add two columns is_cycle and path to the loop-prone query:

WITH RECURSIVE search_graph(id, link, data, depth, is_cycle, path) AS (
    SELECT g.id, g.link, g.data, 0,
      false,
      ARRAY[g.id]
    FROM graph g
  UNION ALL
    SELECT g.id, g.link, g.data, sg.depth + 1,
      g.id = ANY(path),
      path || g.id
    FROM graph g, search_graph sg
    WHERE g.id = sg.link AND NOT is_cycle
)
SELECT * FROM search_graph;

Aside from preventing cycles, the array value is often useful in its own right as representing the “path” taken to reach any particular row.

In the general case where more than one field needs to be checked to recognize a cycle, use an array of rows. For example, if we needed to compare fields f1 and f2:

WITH RECURSIVE search_graph(id, link, data, depth, is_cycle, path) AS (
    SELECT g.id, g.link, g.data, 0,
      false,
      ARRAY[ROW(g.f1, g.f2)]
    FROM graph g
  UNION ALL
    SELECT g.id, g.link, g.data, sg.depth + 1,
      ROW(g.f1, g.f2) = ANY(path),
      path || ROW(g.f1, g.f2)
    FROM graph g, search_graph sg
    WHERE g.id = sg.link AND NOT is_cycle
)
SELECT * FROM search_graph;

Omit the ROW() syntax in the common case where only one field needs to be checked to recognize a cycle. This allows a simple array rather than a composite-type array to be used, gaining efficiency.

There is built-in syntax to simplify cycle detection. The above query can also be written like this:

WITH RECURSIVE search_graph(id, link, data, depth) AS (
    SELECT g.id, g.link, g.data, 1
    FROM graph g
  UNION ALL
    SELECT g.id, g.link, g.data, sg.depth + 1
    FROM graph g, search_graph sg
    WHERE g.id = sg.link
) CYCLE id SET is_cycle USING path
SELECT * FROM search_graph;

and it will be internally rewritten to the above form. The CYCLE clause specifies first the list of columns to track for cycle detection, then a column name that will show whether a cycle has been detected, and finally the name of another column that will track the path. The cycle and path columns will implicitly be added to the output rows of the CTE.

The cycle path column is computed in the same way as the depth-first ordering column show in the previous section. A query can have both a SEARCH and a CYCLE clause, but a depth-first search specification and a cycle detection specification would create redundant computations, so it's more efficient to just use the CYCLE clause and order by the path column. If breadth-first ordering is wanted, then specifying both SEARCH and CYCLE can be useful.

A helpful trick for testing queries when you are not certain if they might loop is to place a LIMIT in the parent query. For example, this query would loop forever without the LIMIT:

WITH RECURSIVE t(n) AS (
    SELECT 1
  UNION ALL
    SELECT n+1 FROM t
)
SELECT n FROM t LIMIT 100;

This works because Tacnode's implementation evaluates only as many rows of a WITH query as are actually fetched by the parent query. Using this trick in production is not recommended, because other systems might work differently. Also, it usually won't work if you make the outer query sort the recursive query's results or join them to some other table, because in such cases the outer query will usually try to fetch all of the WITH query's output anyway.

Common Table Expression Materialization

A useful property of WITH queries is that they are normally evaluated only once per execution of the parent query, even if they are referred to more than once by the parent query or sibling WITH queries. Thus, expensive calculations that are needed in multiple places can be placed within a WITH query to avoid redundant work. Another possible application is to prevent unwanted multiple evaluations of functions with side-effects. However, the other side of this coin is that the optimizer is not able to push restrictions from the parent query down into a multiply-referenced WITH query, since that might affect all uses of the WITH query's output when it should affect only one. The multiply-referenced WITH query will be evaluated as written, without suppression of rows that the parent query might discard afterwards. (But, as mentioned above, evaluation might stop early if the reference(s) to the query demand only a limited number of rows.)

However, if a WITH query is non-recursive and side-effect-free (that is, it is a SELECT containing no volatile functions) then it can be folded into the parent query, allowing joint optimization of the two query levels. By default, this happens if the parent query references the WITH query just once, but not if it references the WITH query more than once. You can override that decision by specifying MATERIALIZED to force separate calculation of the WITH query, or by specifying NOT MATERIALIZED to force it to be merged into the parent query. The latter choice risks duplicate computation of the WITH query, but it can still give a net savings if each usage of the WITH query needs only a small part of the WITH query's full output.

A simple example of these rules is

WITH w AS (
    SELECT * FROM big_table
)
SELECT * FROM w WHERE key = 123;

This WITH query will be folded, producing the same execution plan as

SELECT * FROM big_table WHERE key = 123;

In particular, if there's an index on key, it will probably be used to fetch just the rows having key = 123. On the other hand, in

WITH w AS (
    SELECT * FROM big_table
)
SELECT * FROM w AS w1 JOIN w AS w2 ON w1.key = w2.ref
WHERE w2.key = 123;

the WITH query will be materialized, producing a temporary copy of big_table that is then joined with itself — without benefit of any index. This query will be executed much more efficiently if written as

WITH w AS NOT MATERIALIZED (
    SELECT * FROM big_table
)
SELECT * FROM w AS w1 JOIN w AS w2 ON w1.key = w2.ref
WHERE w2.key = 123;

so that the parent query's restrictions can be applied directly to scans of big_table.

An example where NOT MATERIALIZED could be undesirable is

WITH w AS (
    SELECT key, very_expensive_function(val) as f FROM some_table
)
SELECT * FROM w AS w1 JOIN w AS w2 ON w1.f = w2.f;

Here, materialization of the WITH query ensures that very_expensive_function is evaluated only once per table row, not twice.

The examples above only show WITH being used with SELECT, but it can be attached in the same way to INSERT, UPDATE, or DELETE. In each case it effectively provides temporary table(s) that can be referred to in the main command.

Data-Modifying Statements in `WITH`

You can use data-modifying statements (INSERT, UPDATE, or DELETE) in WITH. This allows you to perform several different operations in the same query. An example is:

WITH moved_rows AS (
    DELETE FROM products
    WHERE
        "date" >= '2010-10-01' AND
        "date" < '2010-11-01'
    RETURNING *
)
INSERT INTO products_log
SELECT * FROM moved_rows;

This query effectively moves rows from products to products_log. The DELETE in WITH deletes the specified rows from products, returning their contents by means of its RETURNING clause; and then the primary query reads that output and inserts it into products_log.

A fine point of the above example is that the WITH clause is attached to the INSERT, not the sub-SELECT within the INSERT. This is necessary because data-modifying statements are only allowed in WITH clauses that are attached to the top-level statement. However, normal WITH visibility rules apply, so it is possible to refer to the WITH statement's output from the sub-SELECT.

Data-modifying statements in WITH usually have RETURNING clauses (see Section 5.4), as shown in the example above. It is the output of the RETURNING clause, not the target table of the data-modifying statement, that forms the temporary table that can be referred to by the rest of the query. If a data-modifying statement in WITH lacks a RETURNING clause, then it forms no temporary table and cannot be referred to in the rest of the query. Such a statement will be executed nonetheless. A not-particularly-useful example is:

WITH t AS (
    DELETE FROM foo
)
DELETE FROM bar;

This example would remove all rows from tables foo and bar. The number of affected rows reported to the client would only include rows removed from bar.

Recursive self-references in data-modifying statements are not allowed. In some cases it is possible to work around this limitation by referring to the output of a recursive WITH, for example:

WITH RECURSIVE included_parts(sub_part, part) AS (
    SELECT sub_part, part FROM parts WHERE part = 'our_product'
  UNION ALL
    SELECT p.sub_part, p.part
    FROM included_parts pr, parts p
    WHERE p.part = pr.sub_part
)
DELETE FROM parts
  WHERE part IN (SELECT part FROM included_parts);

This query would remove all direct and indirect subparts of a product.

Data-modifying statements in WITH are executed exactly once, and always to completion, independently of whether the primary query reads all (or indeed any) of their output. Notice that this is different from the rule for SELECT in WITH: as stated in the previous section, execution of a SELECT is carried only as far as the primary query demands its output.

The sub-statements in WITH are executed concurrently with each other and with the main query. Therefore, when using data-modifying statements in WITH, the order in which the specified updates actually happen is unpredictable. All the statements are executed with the same snapshot , so they cannot “see” one another's effects on the target tables. This alleviates the effects of the unpredictability of the actual order of row updates, and means that RETURNING data is the only way to communicate changes between different WITH sub-statements and the main query. An example of this is that in

WITH t AS (
    UPDATE products SET price = price * 1.05
    RETURNING *
)
SELECT * FROM products;

the outer SELECT would return the original prices before the action of the UPDATE, while in

WITH t AS (
    UPDATE products SET price = price * 1.05
    RETURNING *
)
SELECT * FROM t;

the outer SELECT would return the updated data.

Trying to update the same row twice in a single statement is not supported. Only one of the modifications takes place, but it is not easy (and sometimes not possible) to reliably predict which one. This also applies to deleting a row that was already updated in the same statement: only the update is performed. Therefore you should generally avoid trying to modify a single row twice in a single statement. In particular avoid writing WITH sub-statements that could affect the same rows changed by the main statement or a sibling sub-statement. The effects of such a statement will not be predictable.

At present, any table used as the target of a data-modifying statement in WITH must not have a conditional rule, nor an ALSO rule, nor an INSTEAD rule that expands to multiple statements.

WITH Queries (Common Table Expressions)