Shift-Reduce Parsing: A Bottom-Up Parsing Technique Explained

Learn about shift-reduce parsing, a bottom-up parsing method used to check if a string conforms to a context-free grammar. This guide explains the "shift" and "reduce" actions, the parsing process, and how a stack is used to manage symbols during parsing.

Understanding Shift-Reduce Parsing

What is Shift-Reduce Parsing?

Shift-reduce parsing is a method used to check if a given string can be generated by a specific context-free grammar. It uses a stack to store the symbols being processed and an input string (the string to parse). The process involves repeatedly applying "shift" and "reduce" actions until the entire string is processed. If the string can be reduced to the grammar's start symbol, then the parse was successful.

Shift and Reduce Actions

The two fundamental actions are:

• Shift: The current input symbol is pushed onto the stack.
• Reduce: A sequence of symbols on the top of the stack is replaced with a non-terminal symbol. This replacement is based on a production rule from the grammar. If the right-hand side of a production rule matches the top of the stack, the symbols on the right-hand side are replaced by the corresponding left-hand side non-terminal.

Example: Shift-Reduce Parsing

Let's consider this grammar:

S → S + S
S → S - S
S → (S)
S → a

And this input string: a1 - (a2 + a3)

A shift-reduce parsing table would guide the parsing process, dictating whether to perform a shift or reduce action based on the current input symbol and the top symbol on the stack.

Categories of Shift-Reduce Parsing

There are two primary categories of shift-reduce parsers:

• Operator-Precedence Parsing: A simpler parsing technique that leverages operator precedence to guide reductions. It's suitable for a limited class of grammars.
• LR Parser: A more powerful and versatile parsing technique that can handle a broader range of grammars. It uses a more sophisticated parsing table and stack operations.