Toasty: Expression Simplification Rules For Query Engine
This article tracks the expression simplification rules implemented in Toasty's query engine, a project under the Tokio-rs umbrella. Expression simplification is a crucial optimization technique that enhances query performance by reducing the complexity of expressions before execution. This process involves applying logical and arithmetic identities to rewrite expressions into simpler, equivalent forms. Let's delve into the specifics of these rules and their implementation status within Toasty.
Understanding Expression Simplification
In the realm of query engines, expression simplification serves as a linchpin for optimizing query execution. By meticulously applying a suite of logical and arithmetic identities, this technique aims to transmute complex expressions into their more streamlined equivalents, thereby paving the way for swifter and more efficient query processing. The significance of this process lies in its ability to preemptively reduce computational overhead, ensuring that the query engine operates with peak performance. Through the strategic reduction of complexity, expression simplification not only accelerates query speeds but also minimizes resource consumption, marking it as an indispensable component of modern database systems. Its integration into the query processing pipeline is a testament to its role in fostering responsiveness and scalability, enabling systems to handle increasingly intricate queries with grace and agility. In essence, expression simplification is the cornerstone of query optimization, ensuring that the pathway from query submission to result retrieval is as efficient and economical as possible.
Why is Expression Simplification Important?
Expression simplification is paramount for several reasons. First and foremost, it reduces the computational cost of query execution. Simpler expressions require fewer operations, leading to faster processing times. This is especially crucial for large datasets and complex queries where even minor optimizations can yield significant performance gains. Furthermore, simplified expressions are easier to understand and maintain, contributing to better code quality and reduced debugging efforts. By minimizing the complexity of query logic, expression simplification also enhances the overall scalability and efficiency of the system, making it a critical component of any high-performance query engine.
The Role of Simplification Rules
Simplification rules are the heart of expression simplification. These rules are based on mathematical and logical identities that allow for the rewriting of expressions without changing their meaning. For instance, the rule x and true simplifies to x because the logical AND of any value with true is the value itself. Similarly, arithmetic rules like x + 0 simplifying to x leverage the identity property of addition. By systematically applying these rules, a query engine can transform complex expressions into simpler forms that are more efficient to evaluate.
Expression Simplification Rules in Toasty
Toasty's query engine incorporates a variety of expression simplification rules, drawing inspiration from projects like DataFusion, to enhance its performance. These rules cover a range of logical and arithmetic simplifications. The implementation status of each rule is tracked to provide a clear overview of the ongoing development efforts.
Legend
- ✅ Implemented
- 🔲 Not yet implemented
Implemented Rules ✅
Several key expression simplification rules have already been successfully implemented in Toasty. These rules cover a wide range of logical and arithmetic simplifications, significantly enhancing the query engine's performance. Let's explore some of these implemented rules in detail.
Double Negation Elimination: not(not(x)) → x
The double negation elimination rule is a fundamental logical simplification. In essence, it states that negating a negation returns the original value. This rule is represented as not(not(x)) simplifies to x. This simplification is particularly useful in complex boolean expressions where multiple negations can obscure the underlying logic. By eliminating these double negations, the expression becomes clearer and more efficient to evaluate. For instance, consider a query that filters out records that are not not active. The double negation can be confusing and adds unnecessary complexity. Applying this rule simplifies the condition to active, making the query easier to understand and faster to process.
This rule, sourced from DataFusion, is a foundational optimization technique that streamlines boolean logic within queries. By removing unnecessary negations, the query engine can evaluate conditions more directly, reducing computational overhead and improving overall performance. This seemingly small change can have a significant impact, especially in scenarios involving deeply nested boolean expressions or large datasets where even minor inefficiencies can compound.
Constant Folding for not: not(true) → false, not(false) → true
Constant folding is a technique where expressions involving constants are evaluated at compile time rather than runtime. For the not operator, this means that not(true) is immediately replaced with false, and not(false) is replaced with true. This simplification avoids the need to evaluate these expressions during query execution, saving valuable processing time. Imagine a scenario where a query includes a condition like WHERE NOT TRUE. Without constant folding, the engine would need to evaluate this condition for each row. With constant folding, the engine immediately recognizes that NOT TRUE is FALSE and can optimize the query accordingly, potentially skipping entire sections of the data.
Also sourced from DataFusion, constant folding for the not operator is a straightforward yet impactful optimization. It exemplifies how pre-evaluation of constant expressions can significantly reduce the workload of the query engine, leading to faster response times and more efficient resource utilization. This rule is particularly beneficial in scenarios where queries contain complex boolean logic that includes constant values, as it allows the engine to simplify these expressions before execution, thereby streamlining the query processing pipeline.
Negation of Comparisons: not(x = y) → x != y
This rule transforms negated comparisons into their equivalent non-negated forms. For example, not(x = y) becomes x != y. This simplification makes the query logic more direct and easier to process. Instead of evaluating a comparison and then negating the result, the engine can directly evaluate the inequality. This is particularly useful because many query engines have optimized routines for handling comparison operators directly. Consider a query that filters out records where name is not equal to John. The original expression NOT (name = 'John') can be directly translated to name != 'John', which the engine can often process more efficiently.
Another rule inspired by DataFusion, the negation of comparisons is a vital optimization technique for improving the readability and efficiency of query logic. By converting negated comparisons into their direct counterparts, this rule not only simplifies the expression but also leverages the optimized comparison operations within the query engine. This results in quicker evaluation times and a more streamlined query execution process, making it an indispensable part of Toasty's optimization strategy. The rule applies to all six comparison operators (=, !=, <, >, <=, >=), ensuring comprehensive coverage of comparison simplifications.
Self-Comparison: x = x → true (non-nullable), x != x → false (non-nullable)
Self-comparison rules simplify expressions where a value is compared to itself. If a value is compared to itself for equality (x = x), the result is always true, assuming the value is non-nullable. Conversely, if a value is compared to itself for inequality (x != x), the result is always false (again, assuming non-nullable values). These simplifications are powerful because they can eliminate entire branches of query logic. For instance, a condition like WHERE id = id can be immediately replaced with WHERE TRUE, which might then lead to further simplifications such as removing the entire WHERE clause. However, it's crucial to check for nullability because if x is NULL, then NULL = NULL evaluates to NULL, not TRUE.
These self-comparison rules, drawing from DataFusion, are essential for optimizing queries by recognizing and simplifying redundant comparisons. The engine must carefully consider the nullability of the values being compared to ensure the correctness of the simplification. By addressing self-comparisons effectively, Toasty can significantly reduce the complexity of query logic and enhance the speed of query execution. This careful handling of nullability underscores the importance of precision in expression simplification to maintain the integrity of query results.
Constant Comparison Folding: 5 = 5 → true, 5 < 10 → true
This rule involves evaluating comparisons between constant values at compile time. If the values are known constants, the comparison can be performed immediately, and the result (true or false) can replace the expression. This avoids runtime evaluation, saving processing time. For example, the expression 5 < 10 can be immediately evaluated as true. This is a straightforward but effective optimization, especially in queries with complex conditions involving multiple constant comparisons. Consider a query that checks if a constant value falls within a certain range, like WHERE 10 BETWEEN 5 AND 15. Constant comparison folding allows the engine to determine the result of this condition immediately.
Inspired by DataFusion, constant comparison folding is a cornerstone of query optimization. By pre-evaluating comparisons between constants, Toasty can streamline query execution and minimize computational overhead. This rule is particularly beneficial in scenarios where queries contain complex filtering logic involving constant values, as it enables the engine to simplify these conditions before runtime, thereby enhancing overall performance.
OR Dominance and Identity Laws: x or true → true, x or false → x
The OR dominance law states that if any operand in an OR expression is true, the entire expression is true. The OR identity law states that if one operand in an OR expression is false, the expression simplifies to the other operand. These rules are powerful for simplifying complex boolean expressions. For example, if a query has a condition like WHERE age > 18 OR TRUE, the entire condition can be simplified to WHERE TRUE. Similarly, WHERE city = 'New York' OR FALSE simplifies to WHERE city = 'New York'. These simplifications can drastically reduce the complexity of the query logic.
These OR simplification rules, originating from DataFusion, are fundamental for enhancing the efficiency of boolean expression evaluation within Toasty. By leveraging the dominance and identity laws of the OR operator, the engine can effectively reduce the complexity of query conditions, leading to faster processing times. These simplifications are particularly valuable in scenarios where queries involve multiple OR conditions, as they enable the engine to quickly identify and eliminate redundant or unnecessary comparisons.
AND Dominance and Identity Laws: x and false → false, x and true → x
Similar to the OR laws, AND dominance law dictates that if any operand in an AND expression is false, the entire expression is false. The AND identity law specifies that if one operand is true, the expression simplifies to the other operand. For instance, WHERE age > 18 AND FALSE simplifies to WHERE FALSE, and WHERE city = 'New York' AND TRUE simplifies to WHERE city = 'New York'. These rules are complementary to the OR laws and equally crucial for boolean expression simplification.
The AND simplification rules play a critical role in optimizing boolean expressions within Toasty. By applying the dominance and identity laws of the AND operator, the engine can efficiently reduce the complexity of query conditions, thereby enhancing performance. These rules are especially effective in scenarios where queries involve multiple AND conditions, allowing the engine to quickly identify and eliminate irrelevant or redundant comparisons.
AND and OR Flattening: and(and(a, b), c) → and(a, b, c), or(or(a, b), c) → or(a, b, c)
Flattening involves removing nested AND or OR expressions and combining them into a single expression with multiple operands. This simplifies the structure of the expression and can make it easier to evaluate. For example, AND(AND(a, b), c) becomes AND(a, b, c). Similarly, OR(OR(a, b), c) becomes OR(a, b, c). This restructuring can help the query engine better optimize the expression evaluation order.
Flattening AND and OR expressions is a crucial step in simplifying complex boolean logic within Toasty. By removing nested structures, the engine can more easily analyze and optimize the expression as a whole. This simplification not only enhances readability but also enables the engine to apply other simplification rules more effectively. The result is a more streamlined query processing pipeline and improved overall performance.
Rules Not Yet Implemented 🔲
While significant progress has been made, several expression simplification rules are yet to be implemented in Toasty. These rules represent opportunities for further optimization and are part of the ongoing development roadmap. Let's take a look at some of these rules and their potential impact.
De Morgan's Laws: not(a and b) → not(a) or not(b), not(a or b) → not(a) and not(b)
De Morgan's Laws are fundamental rules in boolean algebra that provide a way to distribute negation over AND and OR operations. The first law states that the negation of an AND expression is equivalent to the OR of the negations. The second law states that the negation of an OR expression is equivalent to the AND of the negations. These rules are invaluable for transforming complex boolean expressions into equivalent forms that may be easier to simplify or evaluate. For instance, NOT (a AND b) can be rewritten as NOT a OR NOT b. Similarly, NOT (a OR b) becomes NOT a AND NOT b. These transformations can help in scenarios where direct evaluation of the original expression is difficult or inefficient.
Drawing inspiration from DataFusion, implementing De Morgan's Laws in Toasty will significantly enhance the engine's ability to simplify complex boolean expressions. These rules enable the transformation of expressions into more manageable forms, which can lead to improved query performance and more efficient evaluation strategies. The application of De Morgan's Laws is particularly beneficial in scenarios involving nested boolean logic and negated conditions, as it provides a systematic approach to expression simplification.
Idempotent Law: x and x → x, x or x → x
The idempotent law states that performing the same operation multiple times has the same effect as performing it once. In boolean logic, this means that x AND x is equivalent to x, and x OR x is equivalent to x. This simplification is straightforward yet effective in reducing redundancy in boolean expressions. Consider a condition like WHERE age > 18 AND age > 18. The idempotent law allows this to be simplified to WHERE age > 18, eliminating the redundant comparison. However, implementing this rule requires Expr: Eq + Hash, meaning the expression type must implement the Eq and Hash traits for efficient comparison and deduplication.
Also sourced from DataFusion, the idempotent law is a valuable addition to Toasty's expression simplification toolkit. By removing redundant boolean operations, this rule contributes to cleaner and more efficient query logic. The requirement for Expr: Eq + Hash highlights the importance of efficient data structures and algorithms in implementing simplification rules effectively. Once implemented, this rule will further enhance Toasty's ability to optimize query execution and improve overall performance.
Absorption Law: x or (x and y) → x, x and (x or y) → x
The absorption law is another key principle in boolean algebra that helps simplify complex expressions. The first absorption law states that x OR (x AND y) is equivalent to x. The second absorption law states that x AND (x OR y) is also equivalent to x. These rules are less intuitive than some other simplification laws but can be very effective in reducing the complexity of certain types of expressions. For example, consider a condition like WHERE age > 18 OR (age > 18 AND city = 'New York'). The absorption law allows this to be simplified to WHERE age > 18, eliminating the need to evaluate the second part of the condition.
Inspired by DataFusion, implementing the absorption law in Toasty will provide further capabilities for simplifying intricate boolean expressions. These rules offer a powerful mechanism for identifying and eliminating redundant conditions, leading to more efficient query execution. The absorption law is particularly useful in scenarios where queries involve complex interactions between AND and OR operations, enabling the engine to reduce these expressions to their simplest forms.
Filter Elimination: WHERE true → remove filter, WHERE false → empty result
Filter elimination rules target WHERE clauses that contain constant boolean values. If a WHERE clause evaluates to true, the filter can be removed entirely because it does not affect the result set. Conversely, if a WHERE clause evaluates to false, the result set will be empty, so the query can be optimized to return no results without further processing. These rules are crucial for optimizing query execution paths. For example, a query with WHERE TRUE is equivalent to selecting all rows, so the WHERE clause can be dropped. A query with WHERE FALSE will never return any rows, so the engine can avoid scanning the table altogether.
Filter elimination is a fundamental optimization technique that can significantly improve query performance in Toasty. By recognizing and acting upon constant boolean conditions in WHERE clauses, the engine can avoid unnecessary processing and streamline query execution. This rule is particularly effective in scenarios where queries are generated dynamically or where conditions are based on configuration settings that may resolve to constant values. Implementing filter elimination will enhance Toasty's ability to handle a wide range of query patterns efficiently.
Arithmetic Constant Folding: 2 + 3 → 5
Similar to constant folding for boolean expressions, arithmetic constant folding involves evaluating arithmetic expressions with constant operands at compile time. For example, 2 + 3 is immediately replaced with 5. This avoids runtime calculation, saving processing time. This rule is applicable to various arithmetic operations, including addition, subtraction, multiplication, and division. Consider a query that calculates a value based on constants, like SELECT price * 0.1 AS discount FROM products. Arithmetic constant folding allows the engine to pre-calculate 0.1, potentially simplifying the overall query execution.
Arithmetic constant folding is a key optimization technique for improving the performance of numerical computations within Toasty. By pre-evaluating constant arithmetic expressions, the engine can reduce the workload during query execution and achieve faster results. This rule is particularly beneficial in scenarios where queries involve complex calculations or data transformations, as it enables the engine to simplify these operations before runtime.
Arithmetic Identity and Annihilator: x + 0 → x, x * 1 → x, x * 0 → 0
These rules leverage the identity and annihilator properties of arithmetic operations. The additive identity states that adding 0 to any number does not change the number (x + 0 → x). The multiplicative identity states that multiplying any number by 1 does not change the number (x * 1 → x). The multiplicative annihilator states that multiplying any number by 0 results in 0 (x * 0 → 0). These rules are fundamental for simplifying arithmetic expressions. For example, a calculation like price + 0 can be simplified to price, and quantity * 1 can be simplified to quantity. Similarly, amount * 0 will always result in 0.
These arithmetic simplification rules are essential for optimizing numerical calculations within Toasty. By applying the identity and annihilator properties, the engine can eliminate redundant operations and streamline query execution. These rules are particularly valuable in scenarios where queries involve complex mathematical expressions or data transformations, as they enable the engine to reduce these operations to their simplest forms.
OR-to-IN Conversion: a=1 or a=2 → a in (1,2)
This rule transforms a series of OR-connected equality comparisons into an IN predicate. The IN predicate checks if a value exists within a set of values, which can often be evaluated more efficiently than multiple OR conditions. For example, WHERE a = 1 OR a = 2 OR a = 3 can be rewritten as WHERE a IN (1, 2, 3). This transformation is particularly useful when the number of OR conditions is large, as the IN predicate can leverage optimized data structures and algorithms for membership testing.
The OR-to-IN conversion is a powerful optimization technique for improving the performance of queries with multiple OR conditions. By transforming these conditions into a single IN predicate, Toasty can leverage optimized evaluation strategies and reduce the complexity of the query. This rule is particularly beneficial in scenarios where queries involve filtering data based on a large set of possible values, as it enables the engine to process these conditions more efficiently.
Constant Propagation: a=b and b=5 → infer a=5
Constant propagation involves inferring and substituting constant values based on equality conditions. If two variables are equal and one of them is a constant, the other variable can be replaced with the constant value. For example, if a query contains the conditions a = b and b = 5, the engine can infer that a is also 5. This can lead to further simplifications and optimizations. Constant propagation is a complex optimization that can significantly improve query performance but also requires careful handling to ensure correctness.
Constant propagation is an advanced optimization technique that can significantly enhance query performance in Toasty. By inferring and substituting constant values, the engine can simplify expressions and potentially eliminate entire branches of query logic. This rule is particularly effective in scenarios where queries involve complex relationships between variables and constants, as it enables the engine to deduce and apply constant values throughout the query. However, the high complexity of this optimization requires careful implementation to ensure accuracy and avoid unintended side effects.
Conclusion
Expression simplification is a critical aspect of query engine optimization. By implementing these rules, Toasty aims to enhance its query processing capabilities, delivering faster and more efficient data retrieval. The implemented rules already provide a solid foundation, and the planned rules promise further improvements. This ongoing effort ensures that Toasty remains a high-performance query engine capable of handling complex queries with ease. You can learn more about expression simplification and query optimization techniques on websites like Database Performance Blog.
