Q3Compiler Design
Question
Explain the concept of operator precedence parsing.
Answer
Operator Precedence Parsing is a shift-reduce parsing method for operator grammars that uses precedence relations (⋖, ≐, ⋗) between terminal symbols to identify handles without building the full LR automaton.
Operator Precedence Parsing is a simple, efficient bottom-up parsing technique for a class of grammars called operator grammars (no production has two adjacent non-terminals or ε on the RHS). It uses three precedence relations between pairs of terminals:
- a ⋖ b (a 'yields precedence' to b): b has higher precedence — a will be shifted before any reduction involving b.
- a ≐ b (a 'has equal precedence' to b): a and b are at the same level (e.g., operators with the same associativity).
- a ⋗ b (a 'takes precedence over' b): a has higher precedence — reduce a before considering b.
The precedence relations are stored in a precedence table. During parsing, the parser compares the terminal on top of the stack with the incoming terminal to decide shift or reduce. A handle is found between ⋖ and ⋗ in the stack. The method is simple and efficient but limited — it can only handle operator grammars and cannot handle all ambiguity. It is used in calculators and simple expression parsers.