Implement a Rule-Based Query Optimizer

The goal of this challenge is to build a fundamental query optimizer in Python. Query optimizers are crucial components of database systems, as they analyze and transform a user's query into an efficient execution plan. This problem focuses on a rule-based approach, where we apply a set of predefined transformation rules to simplify and improve a query representation.

Problem Description

You need to implement a query optimizer that takes a query expressed as an Abstract Syntax Tree (AST) and applies a series of transformation rules to produce an optimized query AST. The optimizer should be extensible, allowing for new rules to be added easily.

What needs to be achieved:

• Represent a query using a structured data format (e.g., Python classes or dictionaries) that can be traversed and manipulated like an AST.
• Define a set of transformation rules that can be applied to the query AST.
• Implement a mechanism to iterate through the AST and apply applicable rules until no further transformations can be made.

Key requirements:

• AST Representation: The query should be representable in a tree-like structure. You can define your own AST node classes (e.g., SelectNode, FilterNode, JoinNode, TableNode, ColumnNode, LiteralNode, OperatorNode).
• Rule Definition: Each rule should encapsulate a specific optimization pattern (e.g., pushing down filters, eliminating redundant joins). A rule should define a pattern to match within the AST and a transformation to apply when the pattern is found.
• Optimization Engine: A core engine that traverses the AST, identifies matching rules, and applies transformations. The traversal should be comprehensive, ensuring all parts of the tree are considered.
• Idempotency: The optimization process should be idempotent, meaning applying the optimizer multiple times to an already optimized query should not change it.
• Extensibility: It should be straightforward to add new optimization rules without modifying the core optimization engine.

Expected behavior:

The optimizer should take an initial query AST and return a new, optimized query AST. The optimization process should terminate when no more rules can be applied to the AST.

Important edge cases to consider:

• Empty queries or queries with no operations.
• Queries with deeply nested structures.
• Rules that might have side effects if not applied in the correct order or multiple times.

Examples

Example 1: Pushing Down Filters

Input AST:
SelectNode(
    columns=[ColumnNode(name='name')],
    from_table=TableNode(name='users'),
    filters=[
        FilterNode(
            operator='AND',
            operands=[
                OperatorNode(
                    operator='=',
                    operands=[ColumnNode(name='age'), LiteralNode(value=30)]
                ),
                OperatorNode(
                    operator='>',
                    operands=[ColumnNode(name='income'), LiteralNode(value=50000)]
                )
            ]
        )
    ]
)

Transformation Rule (Push Down Filter):
If a FilterNode is directly above a TableNode, and the filter only references columns from that table, move the FilterNode to be a child of the TableNode.

Output AST:
SelectNode(
    columns=[ColumnNode(name='name')],
    from_table=FilterNode(
        operator='AND',
        operands=[
            OperatorNode(
                operator='=',
                operands=[ColumnNode(name='age'), LiteralNode(value=30)]
            ),
            OperatorNode(
                operator='>',
                operands=[ColumnNode(name='income'), LiteralNode(value=50000)]
            )
        ],
        child=TableNode(name='users') # The filter is now attached to the table
    )
)

Explanation: The filter conditions were moved from the SELECT clause directly to the FROM clause, associated with the 'users' table. This allows filtering to happen earlier, potentially reducing the number of rows processed by subsequent operations.

Example 2: Eliminating Redundant Filters

Input AST:
SelectNode(
    columns=[ColumnNode(name='id')],
    from_table=TableNode(name='products'),
    filters=[
        FilterNode(
            operator='AND',
            operands=[
                OperatorNode(
                    operator='=',
                    operands=[ColumnNode(name='category'), LiteralNode(value='electronics')]
                ),
                OperatorNode(
                    operator='<',
                    operands=[ColumnNode(name='price'), LiteralNode(value=100)]
                ),
                OperatorNode(
                    operator='=',
                    operands=[ColumnNode(name='category'), LiteralNode(value='electronics')]
                ) # Duplicate filter
            ]
        )
    ]
)

Transformation Rule (Remove Duplicate Filters):
If a FilterNode contains multiple identical child filter conditions (e.g., two 'category = electronics' filters), remove the duplicates.

Output AST:
SelectNode(
    columns=[ColumnNode(name='id')],
    from_table=TableNode(name='products'),
    filters=[
        FilterNode(
            operator='AND',
            operands=[
                OperatorNode(
                    operator='=',
                    operands=[ColumnNode(name='category'), LiteralNode(value='electronics')]
                ),
                OperatorNode(
                    operator='<',
                    operands=[ColumnNode(name='price'), LiteralNode(value=100)]
                )
            ]
        )
    ]
)

Explanation: The duplicate 'category = electronics' filter was removed because it provides no additional information and can be safely eliminated.

Example 3: Combining AND conditions

Input AST:
SelectNode(
    columns=[ColumnNode(name='id')],
    from_table=TableNode(name='orders'),
    filters=[
        FilterNode(
            operator='AND',
            operands=[
                OperatorNode(
                    operator='>',
                    operands=[ColumnNode(name='order_date'), LiteralNode(value='2023-01-01')]
                ),
                FilterNode( # Nested FilterNode
                    operator='AND',
                    operands=[
                        OperatorNode(
                            operator='<',
                            operands=[ColumnNode(name='order_date'), LiteralNode(value='2023-12-31')]
                        ),
                        OperatorNode(
                            operator='=',
                            operands=[ColumnNode(name='status'), LiteralNode(value='shipped')]
                        )
                    ]
                )
            ]
        )
    ]
)

Transformation Rule (Flatten AND):
If an AND filter node has another AND filter node as one of its operands, promote the operands of the inner AND filter to the outer one.

Output AST:
SelectNode(
    columns=[ColumnNode(name='id')],
    from_table=TableNode(name='orders'),
    filters=[
        FilterNode(
            operator='AND',
            operands=[
                OperatorNode(
                    operator='>',
                    operands=[ColumnNode(name='order_date'), LiteralNode(value='2023-01-01')]
                ),
                OperatorNode(
                    operator='<',
                    operands=[ColumnNode(name='order_date'), LiteralNode(value='2023-12-31')]
                ),
                OperatorNode(
                    operator='=',
                    operands=[ColumnNode(name='status'), LiteralNode(value='shipped')]
                )
            ]
        )
    ]
)

Explanation: The nested AND filter was merged into the top-level AND filter, creating a single list of conditions for better readability and potentially for other optimization rules to apply.

Constraints

• The query AST will be represented using Python objects. You are free to define your own AST node structure.
• You should implement at least three distinct optimization rules.
• The optimization process must complete within a reasonable time for moderately complex query ASTs (e.g., up to 100 nodes).
• The AST traversal should be depth-first or breadth-first, but it must be thorough.

Notes

• Consider how to represent your AST nodes. Classes offer strong typing and encapsulation. Dictionaries can be simpler but might be harder to manage for complex structures.
• Your rules should be designed to be order-independent as much as possible, or you need a strategy to determine the correct application order. A common approach is to repeatedly scan the AST and apply rules until a fixed point is reached.
• Think about how to detect patterns in the AST. Recursive functions are a natural fit for traversing and matching tree structures.
• When applying a transformation, ensure you create a new AST rather than modifying the original AST in place to avoid unintended side effects.