Operator Precedence Parsing: A Simple Parsing Technique

Learn about operator precedence parsing, a simple yet effective parsing technique for specific grammars. This guide explains its underlying principles, the use of precedence relations and tables, and the step-by-step parsing process.

Operator Precedence Parsing

Understanding Operator Precedence Parsing

Operator precedence parsing is a type of shift-reduce parsing used for specific grammars (grammars that describe the structure of a programming language). It's a relatively simple parsing technique suitable for grammars with these properties:

  • No production rule's right-hand side contains the empty string (ε).
  • No two non-terminal symbols are adjacent in any production rule.
  • Precedence is defined only between terminal symbols (like operators and identifiers), ignoring non-terminals.

Operator Precedence Relations

Operator precedence parsing uses these three relations to compare terminal symbols:

  • a ⋗ b: Terminal a has higher precedence than terminal b.
  • a ⋖ b: Terminal a has lower precedence than terminal b.
  • a ≐ b: Terminals a and b have equal precedence.

The Precedence Table and Parsing Process

A precedence table defines the precedence relationships between all terminal symbols. The parsing process follows these steps:

  1. Add $ symbols to both ends of the input string.
  2. Scan from left to right until you find a ⋗ relationship.
  3. Scan leftward from that point until you find a ⋖ relationship, including all symbols with equal precedence (≐).
  4. The portion between the leftmost ⋖ and rightmost ⋗ is the handle (the next part of the parse tree to be reduced).
  5. Repeat until the string ends with $, indicating successful parsing.

Example: Parsing an Expression

Let's consider this grammar:

Grammar

E → E + T | T
T → T * F | F
F → id

And this input string: w = id + id * id

A parse tree would visually represent the expression's structure based on the grammar's rules. An operator precedence table, derived from the grammar, would guide the parsing process, defining which operations to perform first based on precedence.