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Abstract Syntax Tree (AST)

In systems that parse expressions, SQL, or domain-specific languages (DSLs), the Abstract Syntax Tree (AST) is a core representation that bridges parsing and execution.

Parsing and Execution Pipeline​

The processing typically follows this pipeline:


Raw Input → Lexer → Parser → AST → IR / Optimizer → Execution Plan → Execution Engine

Step-by-Step Explanation​

  1. Lexer (Tokenization)

    • Converts raw input text into tokens: keywords, identifiers, operators, literals.
    • Example: 
      SELECT a, b FROM tbla WHERE a > 10;
      → 
      ["SELECT", "a", ",", "b", "FROM", "tbla", "WHERE", "a", ">", "10"]

  2. Parser

    • Consumes tokens and produces a Parse Tree, capturing the exact syntactic structure.
    • Handles grammar rules, operator precedence, and parentheses.
    • Parse trees are often verbose and include every syntactic element.

  3. AST (Abstract Syntax Tree)

    • Converts the parse tree into a semantic representation.
    • Abstracts away syntax details like commas or parentheses.
    • Organizes the program into nodes such as expressions, constants, identifiers, and statements.

    Example AST​

    For the query:

    SELECT a, b FROM tbla WHERE a > 10;

The AST could look like:

SelectStmt
├─ Columns
│  ├─ Identifier(a)
│  └─ Identifier(b)
├─ Table(tbla)
└─ Where
   └─ Comparison
      ├─ Identifier(a)
      ├─ Operator(>)
      └─ Constant(10)
  • Identifier(a) and Identifier(b) are nodes representing column references.
  • Constant(10) is a literal node.
  • The AST captures semantics rather than raw syntax, making it suitable for optimization and code generation.
  1. IR / Optimizer
  • AST is transformed into an Intermediate Representation (IR) for optimization or execution planning.
  • Typical optimizations: constant folding, predicate pushdown, operator reordering.
  • IR represents execution-ready structures abstracted from language-specific syntax.
  1. Execution Plan
  • IR is converted into a plan for the execution engine.
  • Includes operator ordering, index selection, memory allocation, and scheduling.
  1. Execution Engine
  • Executes the plan to produce results.
  • May involve multi-threading, I/O scheduling, caching, or parallelism depending on the environment.

Role of AST​

  • AST sits at the core of the pipeline, connecting parsing with optimization and execution.

  • Its design influences:

  • Ease of traversal and transformation

  • Cross-language compatibility

  • Performance and memory usage

  • ASTs are defined differently across languages, but the concept remains: a tree representing the structure and semantics of the input.

Performance Considerations​

  • Complexity of AST construction depends heavily on the grammar and expression depth.
  • Backtracking grammars or deeply nested expressions can increase parsing and AST generation cost.
  • AST design should balance semantic clarity with traversal efficiency.

Use Cases​

  • Expression Evaluation: For inline computations or user-defined functions.
  • SQL Parsing: Forms the semantic layer for query optimization and execution.
  • DSL Processing: AST abstracts domain-specific semantics for interpreters or compilers.

Note: For typical business applications, users rarely interact directly with ASTs; they are mainly relevant for database engines, compilers, or expression evaluation systems.

This AST module provides the foundation for IR generation, optimizations, and execution planning. Different languages and ecosystems may implement ASTs differently, but the core role remains the same: translating syntax into a semantically meaningful, manipulable structure.