The PartiQL GROUP BY clause expands SQL’s grouping. Unlike SQL, the PartiQL GROUP BY can be thought of as a standalone operator that inputs a collection of binding tuples and outputs a collection of binding tuples.

As is typical in many clauses, the semantics proceed in two steps:

  • Core GROUP BY explains the core PartiQL GROUP BY structure.

  • SQL GROUP BY shows that SQL’s can be explained over the core GROUP BY.


The GROUP BY clause

GROUP BY e1 AS x1, ..., em AS xm GROUP AS g

creates a group. Each \$e_i\$ is a grouping expression, each \$x_i\$ is a grouping variable [1] and \$g\$ is the group variable.

As in SQL, the bag of input binding tuples \$B_"GROUP"^"in"\$ is partitioned into the minimal number of equivalence groups \$B_1,...,B_n\$, such that any two binding tuples \$b, b' in B_"GROUP"^"in"\$ are in the same equivalence group if and only if every grouping expression \$e_i\$ evaluates to equivalent values \$v_i\$ (when evaluated on \$b\$) and \$ v_i' \$ (when evaluated on \$b'\$). More precisely, as in SQL, there is an equivalence function \$"eqg"\$, used by the GROUP BY to determine if two values \$v_i\$ and \$ v_i' \$ are equivalent for grouping purposes. The equivalence function \$"eqg"(v_i, v_i' )\$ returns only true or false; true meaning that the values are equivalent for grouping purposes. See Equivalence in Grouping for specifics of eqg. If a grouping expression evaluates to MISSING, it is first coerced into NULL, thus bringing MISSING and NULL in the same group.

Unlike SQL, for each group \$B_j (1 <= j <= n)\$, the GROUP BY clause outputs a binding tuple \$b_j = (: x_1 : v_1,...,x_m : v_m, g : B_j:)\$ that has the full group \$B_j\$. Notice:

  1. the binding tuples that appear in the \$g\$ collection have one attribute for each of the variables defined in the FROM clause, since these binding tuples come as-is from \$B_"GROUP"^"in"\$.

  2. even if the bag \$B_"GROUP"^"in"\$ is flat binding tuples, the output bag \$B_"GROUP"^"out"\$ is not just flat binding tuples, since \$g\$ has nested binding tuples. Note, we have been explicitly denoting binding attributes with MISSING values in the binding tuples. However, once these binding tuples become the tuples of the PartiQL data model, any binding attribute with MISSING value will not appear.

Example 1.  

Consider the data logs and assume that we want to group the co readings by sensor. The following query solves the problem using only core features.

  sensors: [
  logs: [
    {'sensor':1, 'co':0.4},
    {'sensor':1, 'co':0.2},
    {'sensor':2, 'co':0.3}

  'sensor': sensor,
  'readings': (SELECT VALUE FROM g AS v)
FROM logs AS l
GROUP BY l.sensor AS sensor GROUP AS g

The GROUP BY outputs the collection of binding tuples

\$ B_"GROUP"^"out" = B_"SELECT"^"in" = \$ \$<<<<\$
\$ (: "sensor":1, g: <<<<\ (: l:{"'sensor'":1, "'co'":0.4} :), (: l:{"'sensor'":1, "'co'":0.2} :) >>>> :) \$
\$ (: "sensor":2, g: <<<<\ (: l:{"'sensor'":2, "'co'":0.3} :)\ >>>> :) \$

Notice that the collection \$g\$ has tuples with a single attribute \$l\$, since this is the single variable of the FROM clause in this example.

Consequently the SELECT clause outputs

\$" " {"'sensor'":1, "'readings'": <<<< 0.4, 0.2 >>>> }, \$
\$" " {"'sensor'":2, "'readings'": <<<< 0.3 >>>> } \$

Notice that the query of the nested SELECT example and the query of the present example do not always produce the same result. For example, if there were no readings for a sensor, the query of the nested SELECT example would still have this sensor in the result (and its readings would be empty). In contrast, the query of the present example will not have this sensor in the result.

Here is a shorter equivalent query that uses PartiQL collection paths and SQL’s aliases.

  'sensor': sensor,
  'readings': g[*]
FROM logs AS l
GROUP BY l.sensor AS sensor GROUP AS g

Notice, the output binding tuple provides the partitioned input binding tuples in the group variable \$g\$, which can be explicitly utilized in subsequent HAVING, ORDER BY, and SELECT clauses. Thus, an PartiQL query can perform complex computations on the groups, leading to results of any type (e.g. collections nested within collections). The explicit presence of groups in PartiQL, while more general than SQL, also leads to simpler semantics than those of SQL, since the GROUP BY clause semantics are independent of the presence of subsequent functions in HAVING, ORDER BY, and SELECT.

Example 2. GROUP BY with Collection Aggregates

The following PartiQL query counts and averages the readings of each sensor. It also refers to the logs value from the previous example. The COLL_COUNT function is simply given the group variable and counts how many elements are in that collection.

  'sensor': sensor,
  'count': COLL_COUNT(g)
GROUP BY l.sensor AS sensor GROUP AS g

Notice, the aggregate functions COLL_AVG and COLL_COUNT (and for that matter, by convention, any function starting with COLL) can be thought of as general-purpose functions. Generally, they do not have to be fed by the result of a grouping operation - unlike SQL’s COUNT and AVG that are being fed exclusively from the results of grouping operations. (Furthermore, the SQL COUNT and AVG make use of SQL’s syntactic sugar, where there is no explicit use of group variable, as explained in SQL’s Implicit Group Variable.)

Example 3.  

This is a legitimate PartiQL expression:

COLL_COUNT([5, {a:2, b:3}])

The result is 2, since the input to COLL_COUNT is an array with two elements.

Similarly, it is fine to include in any clause an aggregate function fed by the result of a (sub)query.

Example 4.  

In the following expression COLL_COUNT inputs the result of a query

An efficient implementation will often avoid materializing the group variable. In many cases, like the ones of the above examples, the group can be streamed into the aggregate function.

The semantics of the SELECT and HAVING clauses do not need to be aware of the presence of GROUP BY and treat differently (as SQL would do) these classes of functions:

  • scalar functions (e.g. +) that input scalars and output scalars

  • SQL aggregation functions (e.g. SUM) that input bags and output scalars

Indeed, HAVING behaves identical to a WHERE, once groups are already formulated earlier.

The PartiQL approach provides two benefits: First, it leads to shorter, modular semantics. Second, it enables GROUP BY to address use cases that would otherwise need knowledge and non-trivial SQL programming of window functions. See Windows by Grouping.

Equivalence in Grouping

The equivalence function \$eqg\$ extends SQL’s respective function. In particular, it behaves as follows:

  • \$eqg("NULL", "NULL")\$ is true, despite \$"NULL"="NULL"\$ not being true.

  • for any two non-null values \$x\$ and \$y\$, \$\gl{eqg}(x,y)\$ returns the same with \$x=y\$. As is the case generally for \$=\$, while SQL’s \$=\$ will error when given incompatible types, while the PartiQL \$=\$ will return false.

Notice that PartiQL will group together the NULL and the MISSING grouping expressions, since any grouping expression resulting to MISSING has been coerced into NULL before eqg does comparisons for grouping. Example 5 shows the repercussions of coercing NULL into MISSING and also shows how to discriminate between NULL and MISSING, if so desired.

Example 5.  

The query of   will group together any log readings where the sensor attribute is either NULL or is altogether MISSING. For example, if logs is

logs: [
  {'sensor':  1, 'co':0.4},
  {'sensor':  2, 'co':0.3},
  {'sensor':  null, 'co':0.1},
  {'sensor':  1, 'co':0.2},

then the GROUP BY will output the collection of binding tuples

\$ B_"GROUP"^"out" = B_"SELECT"^"in" = \$ \$<<<<\$
\$" " (: "sensor":1, g: <<<< (: l:{"'sensor'":1, "'co'":0.4} :) (: l:{"'sensor'":1, "'co'":0.2} :) >>>> :) \$
\$" " (: "sensor":2, g: <<<< (: l:{"'sensor'":2, "'co'":0.3} :) >>>> :) \$
\$" " (: "sensor":"null", g: <<<< (: l:{"'sensor'":"null", "'co'":0.1} :) (: l:{"'co'":0.5} :) > > :) \$

Notice that both the 3rd and 5th tuples logs of were grouped under the \$"sensor":"null"\$ group, despite the sensor of the 3rd being NULL while the sensor of the 5th being MISSING. The query result is

  {'sensor':1, 'readings':<0.4, 0.2>},
  {'sensor':2, 'readings':<0.3>},
  {'sensor':null, 'readings':<0.1, 0.5>}

If we wanted to discriminate the NULL from the MISSING we could write the following query

  'sensor': CASE WHEN missingFlag THEN MISSING ELSE sensor END,
  'readings': (SELECT VALUE FROM g AS v)
FROM logs AS l
GROUP BY l.sensor IS MISSING AS missingFlag, l.sensor AS sensor GROUP AS g

In this case the would output the collection of binding tuples

\$ B_"GROUP"^"out" = B_"SELECT"^"in" = \$ \$<<<<\$
\$ (: "missingFlag":"false", "sensor":1, g: <<<< (: l:{"'sensor'":1, "'co'":0.4} :) (: l:{"'sensor'":1, "'co'":0.2} :) >>>> :) \$
\$ (: "missingFlag":"false", "sensor":2, g: <<<< (: l:{"'sensor'":2, "'co'":0.3} :) >>>> :) \$
\$ (: "missingFlag":"false", "sensor":"null", g: <<<< (: l:{"'sensor'":"null", "'co'":0.1} :) >>>> :) \$
\$ (: "missingFlag":"true", "sensor":"null", g: <<<< (: l:{"'co'":0.5} :) >>>> :) \$

and the query result would be

  {'sensor':1, 'readings':<0.4, 0.2>},
  {'sensor':2, 'readings':<0.3>},
  {'sensor':null, 'readings':<0.1>},


The group-by and aggregation of PartiQL is backwards compatible to SQL.

Grouping Attributes and Direct Use of Grouping Expressions

For SQL compatibility PartiQL allows GROUP BY …​,e,…​ i.e., a grouping expression \$e\$ that is not associated with a grouping variable \$x\$. (In core PartiQL, one would write GROUP BY …​,e AS x,…​.)

For SQL compatibility, PartiQL supports using the grouping expression e in HAVING, ORDER BY, and SELECT clauses.

The SQL form:

FROM ...
GROUP BY e, ...
HAVING f(e, ...)
ORDER BY f2(e, ...)
SELECT f3(e, ...)

is syntactic sugar for the core PartiQL:

FROM ...
GROUP BY e AS x, ...
HAVING f(x, ...)
ORDER BY f2(x, ...)
SELECT f3(x, ...)
Example 6. SQL vs Core

The SQL-compatible query

SELECT v.a+1 AS bar
FROM foo AS v
GROUP BY v.a+1

is written in core PartiQL as

SELECT VALUE {'bar':  x}
FROM foo AS v
GROUP BY v.a+1 AS x GROUP AS dontcare
What is the "same expression"?

An open question in the equivalence of the two queries in SQL vs Core is the exact meaning of “same expression \$e\$ in GROUP BY and SELECT (or HAVING, ORDER BY)”. Is v.a + 1 the same with 1 + v.a? Is v.a+1 the same with a+1 in the presence of a schema that dictates that the variable v is a tuple with an attribute a? Both SQL and PartiQL answer “no" and “yes" respectively to the two questions. In particular:

An expression \$e\$ that appears in the GROUP BY clause and an expression \$e'\$ that appears in the SELECT or HAVING or ORDER BY are considered the same expression if they are syntactically identical after performing the schema-based rewritings.

SQL’s Implicit Group Variable

SQL does not have explicit group variables. For SQL compatibility, PartiQL allows the SQL aggregation functions to be fed by expressions that do not explicitly say that there is iteration over the group variable. Suppose that a query

  1. is a SELECT query,

  2. lacks a GROUP AS clause, and

  3. any of the SELECT, HAVING, and/or ORDER BY clauses contains a function call \$f(e)\$, where \$f\$ is a SQL aggregation function such as SUM and AVG. (See Designation of SQL aggregate functions)

Then, the query is rewritten as follows:

  • if the query has a GROUP BY clause, add to it

    GROUP AS g

    where g is a fresh variable, i.e., a variable that is not a database name nor a variable of the query or a variable of the queries within which it is nested.

  • if the query has no GROUP BY clause, add to it


    where g is a fresh variable.

  • if the aggregation function call is COUNT(*), then rewrite into COUNT(g)

  • otherwise, rewrite \$f(e)\$ into

    f(SELECT VALUE e1 FROM g AS p)

    where \$e1\$ is produced from \$e\$ as follows: Consider the variables \$v_1, ..., v_n\$ that appear in \$B_"GROUP"^"in"\$ (i.e., the variables defined by the query’s FROM and LET clauses) and are not grouping attributes. Substitute each identifier \$v_i\$ (that does not stand for attribute name) in \$e\$ with \$p.v_i\$.

Example 7. SQL GROUP BY

Consider again the query of GROUP BY with Collection Aggregates. It can be written in an SQL compatible way as

SELECT l.sensor AS sensor,
       AVG( AS avg,
       COUNT(*) AS count
FROM logs AS l
GROUP BY l.sensor
Example 8. SQL GROUP BY Nothing

The query of GROUP ALL Core can be written in standard SQL syntax as

SELECT COUNT(g) AS largeco
FROM logs AS l
WHERE > 1.5

Notice that SQL does not allow nested aggregate functions. Respectively, PartiQL does not allow one to write queries that lack a GROUP AS or GROUP ALL clause and have nested aggregate SQL functions.

Designation of SQL aggregate functions

Each implementation will have a list of SQL aggregate functions, which are not necessarily just the ones prescribed by the standard (COUNT, SUM, AVG, etc). (Recall from SQL’s Implicit Group Variable that SQL aggregate functions do not use an explicit group variable.)

Furthermore, it is required that for each SQL aggregate function f, if an implementation offers a corresponding core PartiQL aggregate function, the PartiQL function is named COLL_f. For example, the core PartiQL aggregate COLL_AVG corresponds to the SQL AVG aggregate . Nevertheless, it is possible that an implementation offers only COLL_AVG or offers only AVG. The semantic relationship between the SQL aggregate function and the corresponding core PartiQL aggregate function is the one explained in SQL’s Implicit Group Variable: The SQL aggregate functions do not input explicit group variables and, thus, their semantics are explained by the reduction to the corresponding core PartiQL aggregate.

Aliases from the SELECT Clause

In SQL, a grouping expression may be an alias that is defined by the SELECT clause. For compatibility purposes, PartiQL adopts the same behavior.

The query, which uses the SELECT-defined alias feature:

SELECT ...,e AS a,...
FROM ...
GROUP BY ...,a,...

is syntactic sugar for the query:

SELECT ...e AS a,...
FROM ...
GROUP BY ...,e,...

Notice that the grouping expression a is simply a shorthand for e.

In the case that the grouping expression is a constant positive integer literal \$n\$, then it stands for the \$n\$th attribute of the SELECT clause. However, this requires that the tuples produced by the SELECT have schema and they are ordered tuples. The relevant examples will be provided in the schema section.

Example 9. SELECT Aliases in GROUP BY

Consider the database

people: <<
  {'name': 'zoe', 'age': 10, 'tag': 'child'},
  {'name': 'zoe', 'age': 20, 'tag': 'adult'},
  {'name': 'bill', 'age': 30, 'tag': 'adult'}

The query

SELECT p.tag || ':' || AS tagname, AVG(p.age) AS average
FROM people AS p
GROUP BY tagname

is equivalent to the query

SELECT p.tag || ':' || AS tagname, AVG(p.age) AS average
FROM people AS p
GROUP BY p.tag || ':' ||

Either query results into

people: <<
  {'tagname': 'child:zoe', 'average': 10},
  {'tagname': 'adult:zoe', 'average': 20},
  {'tagname': 'adult:bill', 'average': 30}
Example 10. Windows by Grouping

Consider again a collection of sensor readings, this time with a timestamp.

logs:  [
  {'sensor':1, 'co':0.4, 'timestamp':04:05:06},
  {'sensor':1, 'co':0.2, 'timestamp':04:05:07},
  {'sensor':1, 'co':0.5, 'timestamp':04:05:10},
  {'sensor':2, 'co':0.3}

We look for the “jump" readings that are more than 2x the previous reading at the same sensor. The following query solves the problem using GROUP BY.

SELECT sensor AS sensor,
      (WITH orderedReadings
               AS (SELECT v FROM oneSensorsReadings v ORDER BY v.timestamp)
       SELECT, r.timestamp
       FROM orderedReadings r AT p
       WHERE > 2*orderedReadings[p-1].co
       ORDER BY p
      ) AS jumpReadings
FROM logs l
GROUP BY l.sensor AS sensor GROUP AS oneSensorsReadings

The result is

  {'sensor':1, 'jumpReadings':[{'co':0.4, 'timestamp':04:05:06}]},
  {'sensor':2, 'jumpReadings':[]}


The GROUP ALL variant of GROUP BY outputs a single binding tuple, regardless of whether the FROM/WHERE produced any tuples, i.e., regardless of whether its input \$B_"GROUP"^"in"\$ is empty or not.

The GROUP ALL is not increasing the expressiveness of PartiQL. GROUP ALL Core shows how to achieve without GROUP ALL, what the GROUP ALL can do. However, we include GROUP ALL for facilitating the reduction of SQL’s aggregation into the core PartiQL (see SQL’s Implicit Group Variable).

Example 11. GROUP ALL Core

Consider again the logs data and assume that we want to count the total number of readings that are above 1.5 with a core PartiQL query. (SQL GROUP BY Nothing does the same with SQL.)

SELECT VALUE {'largeco':  COLL_COUNT(g)}
FROM logs AS l
WHERE > 1.5

Notice, there are no readings above 1.5 in the example data. Since there is no tuple that satisfies the WHERE clause

\$B_"WHERE"^"out" = B_"GROUP"^"in" = <<<<\ >>>>\$
\$B_"GROUP"^"out" = B_"SELECT"^"in" = <<<<\ (: g: <<<<\ >>>>\ :)\ >>>>\$

Since COLL_COUNT(<<>>) is 0, the query result is the collection

<< {'largeco': 0} >>

Therefore the PartiQL query is equivalent to the plain SQL query

SELECT COUNT(*) AS largeco
FROM logs AS l
WHERE > 1.5

The following core PartiQL also accomplishes the same computation, without using GROUP ALL.

{ 'largeco':  COLL_COUNT(SELECT VALUE l FROM logs AS l WHERE > 1.5) }

1. Grouping variables is an extension of SQL by PartiQL, which interestingly simplifies dramatically the explanation of SQL semantics, as it enables the GROUP BY to be seen as a standalone function.