Relational algebra is at the heart of Calcite. Every query is represented as a tree of relational operators. You can translate from SQL to relational algebra, or you can build the tree directly.

Planner rules transform expression trees using mathematical identities that preserve semantics. For example, it is valid to push a filter into an input of an inner join if the filter does not reference columns from the other input.

Calcite optimizes queries by repeatedly applying planner rules to a relational expression. A cost model guides the process, and the planner engine generates an alternative expression that has the same semantics as the original but a lower cost.

The planning process is extensible. You can add your own relational operators, planner rules, cost model, and statistics.

Algebra builder

The simplest way to build a relational expression is to use the algebra builder, RelBuilder. Here is an example:


final FrameworkConfig config;
final RelBuilder builder = RelBuilder.create(config);
final RelNode node = builder

(You can find the full code for this and other examples in

The code prints

LogicalTableScan(table=[[scott, EMP]])

It has created a scan of the EMP table; equivalent to the SQL

FROM scott.EMP;

Adding a Project

Now, let’s add a Project, the equivalent of

SELECT ename, deptno
FROM scott.EMP;

We just add a call to the project method before calling build:

final RelNode node = builder
  .project(builder.field("DEPTNO"), builder.field("ENAME"))

and the output is

LogicalProject(DEPTNO=[$7], ENAME=[$1])
  LogicalTableScan(table=[[scott, EMP]])

The two calls to builder.field create simple expressions that return the fields from the input relational expression, namely the TableScan created by the scan call.

Calcite has converted them to field references by ordinal, $7 and $1.

Adding a Filter and Aggregate

A query with an Aggregate, and a Filter:

final RelNode node = builder
      builder.count(false, "C"),
      builder.sum(false, "S", builder.field("SAL")))

is equivalent to SQL

SELECT deptno, count(*) AS c, sum(sal) AS s
FROM emp
GROUP BY deptno
HAVING count(*) > 10

and produces

LogicalFilter(condition=[>($1, 10)])
  LogicalAggregate(group=[{7}], C=[COUNT()], S=[SUM($5)])
    LogicalTableScan(table=[[scott, EMP]])

Push and pop

The builder uses a stack to store the relational expression produced by one step and pass it as an input to the next step. This allows the methods that produce relational expressions to produce a builder.

Most of the time, the only stack method you will use is build(), to get the last relational expression, namely the root of the tree.

Sometimes the stack becomes so deeply nested it gets confusing. To keep things straight, you can remove expressions from the stack. For example, here we are building a bushy join:

             /      \
        join          join
      /      \      /      \

We build it in three stages. Store the intermediate results in variables left and right, and use push() to put them back on the stack when it is time to create the final Join:

final RelNode left = builder
  .join(JoinRelType.INNER, "ORDER_ID")

final RelNode right = builder
  .join(JoinRelType.INNER, "PRODUCT_ID")

final RelNode result = builder
  .join(JoinRelType.INNER, "ORDER_ID")

Field names and ordinals

You can reference a field by name or ordinal.

Ordinals are zero-based. Each operator guarantees the order in which its output fields occur. For example, Project returns the fields in the generated by each of the scalar expressions.

The field names of an operator are guaranteed to be unique, but sometimes that means that the names are not exactly what you expect. For example, when you join EMP to DEPT, one of the output fields will be called DEPTNO and another will be called something like DEPTNO_1.

Some relational expression methods give you more control over field names:

  • project lets you wrap expressions using alias(expr, fieldName). It removes the wrapper but keeps the suggested name (as long as it is unique).
  • values(String[] fieldNames, Object... values) accepts an array of field names. If any element of the array is null, the builder will generate a unique name.

If an expression projects an input field, or a cast of an input field, it will use the name of that input field.

Once the unique field names have been assigned, the names are immutable. If you have a particular RelNode instance, you can rely on the field names not changing. In fact, the whole relational expression is immutable.

But if a relational expression has passed through several rewrite rules (see RelOptRule), the field names of the resulting expression might not look much like the originals. At that point it is better to reference fields by ordinal.

When you are building a relational expression that accepts multiple inputs, you need to build field references that take that into account. This occurs most often when building join conditions.

Suppose you are building a join on EMP, which has 8 fields [EMPNO, ENAME, JOB, MGR, HIREDATE, SAL, COMM, DEPTNO] and DEPT, which has 3 fields [DEPTNO, DNAME, LOC]. Internally, Calcite represents those fields as offsets into a combined input row with 11 fields: the first field of the left input is field #0 (0-based, remember), and the first field of the right input is field #8.

But through the builder API, you specify which field of which input. To reference “SAL”, internal field #5, write builder.field(2, 0, "SAL"), builder.field(2, "EMP", "SAL"), or builder.field(2, 0, 5). This means “the field #5 of input #0 of two inputs”. (Why does it need to know that there are two inputs? Because they are stored on the stack; input #1 is at the top of the stack, and input #0 is below it. If we did not tell the builder that were two inputs, it would not know how deep to go for input #0.)

Similarly, to reference “DNAME”, internal field #9 (8 + 1), write builder.field(2, 1, "DNAME"), builder.field(2, "DEPT", "DNAME"), or builder.field(2, 1, 1).

API summary

Relational operators

The following methods create a relational expression (RelNode), push it onto the stack, and return the RelBuilder.

Method Description
scan(tableName) Creates a TableScan.
values(fieldNames, value...)
values(rowType, tupleList)
Creates a Values.
Creates a Filter over the AND of the given predicates.
project(exprList [, fieldNames])
Creates a Project. To override the default name, wrap expressions using alias, or specify the fieldNames argument.
Variant of project that keeps original fields and appends the given expressions.
permute(mapping) Creates a Project that permutes the fields using mapping.
convert(rowType [, rename]) Creates a Project that converts the fields to the given types, optionally also renaming them.
aggregate(groupKey, aggCall...)
aggregate(groupKey, aggCallList)
Creates an Aggregate.
distinct() Creates an Aggregate that eliminates duplicate records.
Creates a Sort.

In the first form, field ordinals are 0-based, and a negative ordinal indicates descending; for example, -2 means field 1 descending.

In the other forms, you can wrap expressions in as, nullsFirst or nullsLast.
sortLimit(offset, fetch, expr...)
sortLimit(offset, fetch, exprList)
Creates a Sort with offset and limit.
limit(offset, fetch) Creates a Sort that does not sort, only applies with offset and limit.
exchange(distribution) Creates an Exchange.
sortExchange(distribution, collation) Creates a SortExchange.
join(joinType, expr...)
join(joinType, exprList)
join(joinType, fieldName...)
Creates a Join of the two most recent relational expressions.

The first form joins on a boolean expression (multiple conditions are combined using AND).

The last form joins on named fields; each side must have a field of each name.
semiJoin(expr) Creates a SemiJoin of the two most recent relational expressions.
union(all [, n]) Creates a Union of the n (default two) most recent relational expressions.
intersect(all [, n]) Creates an Intersect of the n (default two) most recent relational expressions.
minus(all) Creates a Minus of the two most recent relational expressions.
match(pattern, strictStart, strictEnd, patterns, measures, after, subsets, allRows, partitionKeys, orderKeys, interval) Creates a Match.

Argument types:

  • expr, interval RexNode
  • expr... Array of RexNode
  • exprList, measureList, partitionKeys, orderKeys Iterable of RexNode
  • fieldOrdinal Ordinal of a field within its row (starting from 0)
  • fieldName Name of a field, unique within its row
  • fieldName... Array of String
  • fieldNames Iterable of String
  • rowType RelDataType
  • groupKey RelBuilder.GroupKey
  • aggCall... Array of RelBuilder.AggCall
  • aggCallList Iterable of RelBuilder.AggCall
  • value... Array of Object
  • value Object
  • tupleList Iterable of List of RexLiteral
  • all, distinct, strictStart, strictEnd, allRows boolean
  • alias String
  • varHolder Holder of RexCorrelVariable
  • patterns Map whose key is String, value is RexNode
  • subsets Map whose key is String, value is a sorted set of String
  • distribution RelDistribution
  • collation RelCollation

The builder methods perform various optimizations, including:

  • project returns its input if asked to project all columns in order
  • filter flattens the condition (so an AND and OR may have more than 2 children), simplifies (converting say x = 1 AND TRUE to x = 1)
  • If you apply sort then limit, the effect is as if you had called sortLimit

There are annotation methods that add information to the top relational expression on the stack:

Method Description
as(alias) Assigns a table alias to the top relational expression on the stack
variable(varHolder) Creates a correlation variable referencing the top relational expression

Stack methods

Method Description
build() Pops the most recently created relational expression off the stack
push(rel) Pushes a relational expression onto the stack. Relational methods such as scan, above, call this method, but user code generally does not
pushAll(collection) Pushes a collection of relational expressions onto the stack
peek() Returns the relational expression most recently put onto the stack, but does not remove it

Scalar expression methods

The following methods return a scalar expression (RexNode).

Many of them use the contents of the stack. For example, field("DEPTNO") returns a reference to the “DEPTNO” field of the relational expression just added to the stack.

Method Description
literal(value) Constant
field(fieldName) Reference, by name, to a field of the top-most relational expression
field(fieldOrdinal) Reference, by ordinal, to a field of the top-most relational expression
field(inputCount, inputOrdinal, fieldName) Reference, by name, to a field of the (inputCount - inputOrdinal)th relational expression
field(inputCount, inputOrdinal, fieldOrdinal) Reference, by ordinal, to a field of the (inputCount - inputOrdinal)th relational expression
field(inputCount, alias, fieldName) Reference, by table alias and field name, to a field at most inputCount - 1 elements from the top of the stack
field(alias, fieldName) Reference, by table alias and field name, to a field of the top-most relational expressions
field(expr, fieldName) Reference, by name, to a field of a record-valued expression
field(expr, fieldOrdinal) Reference, by ordinal, to a field of a record-valued expression
fields(fieldOrdinalList) List of expressions referencing input fields by ordinal
fields(mapping) List of expressions referencing input fields by a given mapping
fields(collation) List of expressions, exprList, such that sort(exprList) would replicate collation
call(op, expr...)
call(op, exprList)
Call to a function or operator
Logical AND. Flattens nested ANDs, and optimizes cases involving TRUE and FALSE.
Logical OR. Flattens nested ORs, and optimizes cases involving TRUE and FALSE.
not(expr) Logical NOT
equals(expr, expr) Equals
isNull(expr) Checks whether an expression is null
isNotNull(expr) Checks whether an expression is not null
alias(expr, fieldName) Renames an expression (only valid as an argument to project)
cast(expr, typeName)
cast(expr, typeName, precision)
cast(expr, typeName, precision, scale)
Converts an expression to a given type
desc(expr) Changes sort direction to descending (only valid as an argument to sort or sortLimit)
nullsFirst(expr) Changes sort order to nulls first (only valid as an argument to sort or sortLimit)
nullsLast(expr) Changes sort order to nulls last (only valid as an argument to sort or sortLimit)

Pattern methods

The following methods return patterns for use in match.

Method Description
patternConcat(pattern...) Concatenates patterns
patternAlter(pattern...) Alternates patterns
patternQuantify(pattern, min, max) Quantifies a pattern
patternPermute(pattern...) Permutes a pattern
patternExclude(pattern) Excludes a pattern

Group key methods

The following methods return a RelBuilder.GroupKey.

Method Description
Creates a group key of the given expressions
groupKey(exprList, exprListList) Creates a group key of the given expressions with grouping sets
groupKey(bitSet [, bitSets]) Creates a group key of the given input columns, with multiple grouping sets if bitSets is specified

Aggregate call methods

The following methods return an RelBuilder.AggCall.

Method Description
aggregateCall(op, expr...)
aggregateCall(op, exprList)
Creates a call to a given aggregate function
count([ distinct, alias, ] expr...)
count([ distinct, alias, ] exprList)
Creates a call to the COUNT aggregate function
countStar(alias) Creates a call to the COUNT(*) aggregate function
sum([ distinct, alias, ] expr) Creates a call to the SUM aggregate function
min([ alias, ] expr) Creates a call to the MIN aggregate function
max([ alias, ] expr) Creates a call to the MAX aggregate function

To further modify the AggCall, call its methods:

Method Description
approximate(approximate) Allows approximate value for the aggregate of approximate
as(alias) Assigns a column alias to this expression (see SQL AS)
distinct() Eliminates duplicate values before aggregating (see SQL DISTINCT)
distinct(distinct) Eliminates duplicate values before aggregating if distinct
filter(expr) Filters rows before aggregating (see SQL FILTER (WHERE ...))
Sorts rows before aggregating (see SQL WITHIN GROUP)