• Start date: 2021/09/13
• Tracking issues: https://github.com/databendlabs/databend/issues/1217

Summary

In order to support more complicated SQL queries, for example the queries contain JOIN and correlated subquery, we need to redesign the SQL planner component.

The main problems of current implementation we are going to discussed in this RFC are as follows:

• Doesn't support JOIN and correlated subquery
• Doesn't have ability to do strict semantic checking, e.g. type check and name resolution, which brings unnecessary complexity of correctness ensurance during SQL optimization and execution
• Doesn't have a universal SQL optimization framework

Let's start with a simple example.

In SQL, it allows duplicated names of fields in a tuple. In PostgreSQL, a result set can contain different columns with same name:

postgres=# create table t(a INT);
CREATE TABLE
postgres=# insert into t values(1),(2);
INSERT 0 2
postgres=# SELECT * from t t1 cross join t t2;
 a | a
---+---
 1 | 1
 1 | 2
 2 | 1
 2 | 2
(4 rows)

We can see that there are two fields named with a, one of them comes from derived table t1 and the other one comes from derived table t2.

If you try to reference the column with duplicated name a, it will return an error:

postgres=# SELECT a from t t1, t t2;
ERROR:  column reference "a" is ambiguous
LINE 1: SELECT a from t t1, t t2;

While you can reference the column with a canonical name like t.a since the table name is required to be unique in a query context.

Currently, databend uses DataSchema to represent input and output relation schema, which can not provide enough information to handle the case shown above. In a DataSchema, each column is represented with DataField, which has following definition:

pub struct DataField {
    name: String,
    data_type: DataType,
    nullable: bool,
}

Each DataField inside a DataSchema is identified with a unique name string. For now, the name just represent column name, thus it's difficult to implement JOIN with this abstraction. We will talk about the detailed solution of this in later sections.

The second problem is about semantic check.

Take type check as an example, each variable(e.g. column reference, constant value) inside an expression has it's own data type. And each scalar expression has requirement of data type for its arguments, for instance, a + expression requires its arguments to be numeric.

To make sure that the query is valid and correct, we need to do type checking before executing the query.

Since both optimizer and executor has requirement on type checking, it's better to resolve this with a single component, which can make it more maintainable.

The last problem is about the query optimization framework.

Many of modern optimizers are implemented in Volcano/Cascades style, which is a highly modular approach.

A typical Cascades optimizer consists of independent modules:

• Transformation rules
• Implementation rules
• Exploration engine
• Cost model

What's interesting is that, the rule system(transformation and implementation) is decoupled with exploration engine and cost model, which means it's easy to build a heuristic optimizer without CBO(cost based optimization). And as soon as we're going to implement CBO, the rule system can be reused.

Actually, this is the practical way. In some industrial Cascades implementation(e.g. SQL Server and CockroachDB), there is always a heuristic optimization phase, for example pre-exploration in SQL Server and normalization in CockroachDB, which generally shares a same rule system with exploration engine.

In summary, this RFC will:

• Introduce a new framework to support planning JOIN and correlated subquery
• Introduce a rule system that allows developer to write transformation rules easily

Design Details

Architecture

In current implementation, a SQL query will be processed as follows:

1. PlanParser will parse the SQL text into AST(Abstract Syntax Tree)
2. PlanParser will also build a canonical plan tree represented with PlanNode from the AST
3. After building plan tree, Optimizer will do some canonical optimization to the plan, and produce the final PlanNode
4. Interpreter will take the PlanNode as input and interpret it as an executable Pipeline consists of Processors
5. Executor will execute the Pipeline with specific runtime

In our new framework, PlanParser will be refactored into two components:

• Parser: parsing SQL text into uniform AST representation, which has been introduced in this PR
• Binder: bind variables appeared in the AST with objects(e.g. tables, columns, etc) in database and perform semantic check(name resolution, type checking). Will produce logical representation of plan tree

Besides, a new optimizer will be introduced with a rule system tod replace the current optimizer.

Binder

Since there maybe many syntactic contexts in a SQL query, we need a way to track the dependency relationship between them and the visibility of names in different contexts.

Here we propose the abstraction Metadata, which stores all the metadata we need for query optimization, including base tables from catalog, derived tables(subquery and join) and columns. Each table and column will be assigned with a unique identifier.

pub struct Metadata {
    pub tables: Vec<TableEntry>,
}

pub struct TableEntry {
    pub index: IndexType, // Index of the table in `Metadata`
    pub columns: Vec<ColumnEntry>,
    // And metadata about the table, e.g. name, database name and etc.
}

pub struct ColumnEntry {
    pub index: ColumnIndex,
    // And metadata about the column, e.g. name, data type and etc.
}

pub type IndexType = usize;

pub struct ColumnIndex {
    pub table_index: IndexType, // Index of the table this column belongs to
    pub column_index: IndexType, // Index of the column inside its `TableEntry`
}

Therefore, after name resolution each variable will be bound with a unique ColumnIndex but not a string, so we don't need to worry about the issues like duplicated name.

During the binding procedure, we need to track the state of binding. The state may contain the following information:

• Visible columns in current context, used when processing wildcard result set(SELECT * FROM t)
• If a column in a context is group by key or not
• If a column is derived column(i.e. projection like a+1 AS a) or not
• If a variable is from current subquery or not, to identify correlated column reference

To maintain the state, we propose a data structure BindContext(this name is inspired by BinderContext from CMU Peloton, which is a very appropriate name in my mind).

BindContext is a stack-like structure, each BindContext node in the stack records state of corresponding syntactic context. SQL binding is a bottom-up procedure, which means it will process AST recursively, add columns produced by data source(e.g. table scan, join, subquery) into

Briefly, BindContext is a set of column references. To be clear, we will use diagram to explain how this mechanism works.

Take this example:

create table t (a int);

SELECT * from t -- table: context 1 [t.a]
cross join t t1 -- table: context 2 [t1.a]
-- join: context 3 [t.a, t1.a]
where t.a = 1

According to semantic of SQL, we can describe the binding procedure as follows:

1. Create an empty BindContext context 1 for table t, and fill it with columns from t
2. Create an empty BindContext context 2 for table t, fill it with columns from t, and rename the table to t1
3. Create an empty BindContext context 3 for t cross join t1, and fill it with columns from t and t1
4. Perform name resolution for predicate t.a = 1
5. Lookup context 3, and find the corresponding ColumnEntry for variable t.a

Let's take a look at how BindContext handles correlated subquery.

A correlated subquery indicates that the subquery depends on a column from outer context.

There is a canonical Apply operator to execute correlated subquery, which will evaluate the subquery expression for each tuple(like a cross join). While most of the correlated subqueries can be decorrelated into join(e.g. semi-join, anti-semi-join and etc.).

Take this query as example:

create table t (a int);

SELECT * from t -- table: context 1 [t.a]
where exists (
    SELECT * from t t1 -- table: context 2 with parent 1 [t1.a]
    where t1.a = t.a -- t.a is a correlated column since it comes from t that appears in outer query
);

Before binding the exists subquery, we will create a new BindContext for it, and pass the outer BindContext as its parent context.

When we bind the correlated column reference t.a inside the subquery, we will first lookup current BindContext to see if it exists an appropriate column, if not, then we will keep trying to do the lookup in parent context until we find the corresponding column or we exhaust all the parents.

If we find the column in parent context, then we can confirm that this subquery is a correlated subquery, and the column reference bound with parent context is the correlated column.

The procedure can be summarized as follows:

1. Create an empty BindContext context 1 for table t, and fill it with columns from t
2. Create an empty BindContext context 2 for table t with context 1 as its parent context, fill it with columns from t, and rename the table to t1
3. Perform name resolution for predicate t1.a = t.a
4. Lookup context 2, and find the corresponding ColumnEntry for variable t1.a, but can not find t.a. So we will keep going through step 5
5. Lookup parent of context 2(context 1), and find the corresponding ColumnEntry for variable t.a. Since the variable is found in outer context, it will be marked as correlated column reference, and the subquery will be marked as correlated

Optimizer

A brief introduction to Cascades optimizer

SQL optimization is based on the equivalence of relational algebra. There are a bunch of different theorems and lemmas can help us identify if two relational algebra trees are logically equivalent. With a set of equivalent relational expressions, we can evaluate them with a cost model and find the optimal expression.

Cascades optimizer is a framework of query optimization introduced by Goetz Graefe in his paper.

In Cascades query optimizer, a SQL query will be translated into a tree-like structure Expression, with relational operators(Operator) as its nodes.

There are three kinds of Operator:

• Logical operator: represents a relational algebra, e.g. Select, Get, Inner Join
• Physical operator: represents a relational algebra with implementation, e.g. Hash Join
• Scalar operator: represents a scalar expression, e.g. predicate expressions(AND, OR, +) inside Select operator

Transformation rules are used to perform the algebra transformation on an Expression.

Each transformation rule has description about the relational operator it can be applied to, which we call it a rule pattern. The optimizer will provide a scheme to walk through an Expression, check if any rule can be applied to a sub-Expression, and then apply transformation for the matched rules.

The alternations of an Expression are generated during the transformation process. For example:

SELECT * FROM t INNER JOIN t1 ON t.a = t1.a;

With JoinCommutativity rule, the above SQL can be transformed into a equivalent SQL:

SELECT * FROM t1 INNER JOIN t ON t.a = t1.a;

To reduce the duplicated Expressions generated by transformations, Cascades use a top-down approach to enumerate the alternations.

A structure Memo is introduced to store the alternations. Each Memo consists of Groups, and each Group is a set of equivalent Expression.

Different from the Expression we mentioned above, the Expression inside Group take Groups as its children instead of Expressions, so that equivalent Expressions can share the children candidates.

Take the JoinCommutativity example, the Memo of original SQL can be represented as:

Group 1: [Get(t)]

Group 2: [Get(t1)]

Group 3: [Join(1, 2, "t.a = t1.a")]

After applying JoinCommutativity transformation, the Memo will become:

Group 1: [Get(t)]

Group 2: [Get(t1)]

Group 3: [Join(1, 2, "t.a = t1.a"), Join(2, 1, "t.a = t1.a")]

Now you have basic knowledge about Cascades optimizer framework. Although there are many other important concepts of Cascades, this brief introduction is enough for you to understand the RFC.

New optimizer of Databend

In new optimizer framework, there are several core structures.

Plan, enum of logical operators and physical operators. Different from canonical Cascades, we don't make scalar operators a part of Plan.

enum Plan {
    // ...
}

SExpr, abbreviation for single expression, represents a tree of Plan.

struct SExpr {
    pub plan: Plan,
    pub children: Vec<Plan>,
}

Memo, collection of Groups, as Memo in Cascades.

struct Memo {
    pub groups: Vec<Group>,
}

Group, collection of MExprs, as Group in Cascades.

struct Group {
    pub expressions: Vec<MExpr>,
}

MExpr, the representation of Expression inside Memo.

struct MExpr {
    pub plan: Plan,
    pub children: Vec<GroupIndex>,
}

Rule, trait of transformation rules. The Rules can be categorized as exploration rules(generate equivalent logical expressions) and implementation rules(generate physical expressions).

trait Rule {
    fn pattern(&self) -> &SExpr;

    fn apply(&self, expr: &SExpr, state: &mut TransformState) -> Result<()>;
}

HeuristicOptimizer, the optimizer applies transformations to a SExpr and does not generate alternations.

CascadesOptimizer, the optimizer applies transformations to a SExpr, generates Memo, and finally extract the optimal SExpr from the Memo.

Let's take a look at the whole procedure of translating a SQL query into Processor:

1. SQL query text is parsed into AST
2. Binder translates AST into canonical logical SExpr with Catalog
3. HeuristicOptimizer optimizes the canonical logical SExpr
4. CascadesOptimizer takes the output of HeuristicOptimizer, builds a Memo, applies rules, and returns the optimal SExpr
5. Executor takes the physical SExpr produced by CascadesOptimizer, and builds a executable Processor

Milestone

After this refactoring, we want:

• Provide naive implementation(hash join for equi-join and nested-loop join for cross join) for JOIN, including planning and execution
• Support running most of the queries from TPCH benchmark(contains different types of joins and correlated subquery) with databend
• Implement several simple optimization rules, e.g. outer join elimination, decorrelation, predicate pushdown and etc.
• Migrate to the new planner framework

And at the same time, we won't:

• Take performance serious, related work should be done in next stage
• Implement cost based optimization, this work depends on design of statistics system