Operator Precedence Parsing in Compiler Design
In this blog post, we will delve into the concept of operator precedence parsing in compiler design, understand how it works, and explore its implementation with practical example.
Let's illustrate this process with the expression 3 + 4 * 2:
1. Read '3': Shift it onto the stack.
2. Read '+': Shift it onto the stack.
3. Read '4': Shift it onto the stack.
4. Read '*': Since '*' has higher precedence than '+', reduce the stack. Apply the '*' operator to the top two elements of the stack, i.e., 4 * 2. Replace the top three elements on the stack with the result of the reduction.
For example, with the expression 2 + 3 * 4, the parser will first shift 2 onto the stack, then +. When it encounters 3, it compares the precedence of '*' (higher) with '+' (lower) in the table. Since '*' has higher precedence, it reduces the stack by applying the '*' operation first before proceeding with '+', resulting in the correct parse tree.
Example: Mixed Arithmetic Expression
Result: The parse tree represents the expression (5 * 3) + (6 / 2), and the final result is 18.
Operator Precedence Parsing
Operator Precedence Parsing is a parsing technique used to parse expressions and resolve ambiguities in programming languages. It relies on the precedence levels assigned to operators to guide the parsing process and construct a parse tree. By analyzing the tokens in an expression based on their precedence, the parser can make informed decisions on how to combine and group them correctly.To understand operator precedence parsing better, let's consider the expression: 3 + 4 * 2. The operators here are + and *, and they have different precedence levels. In this case, the * operator has higher precedence than the + operator. So, the parsing process will give preference to the * operator and construct the parse tree accordingly.
How Does Operator Precedence Parsing Work?
1. Shifting and Reducing Operations
In operator precedence parsing, the parser examines the input expression one token at a time, moving from left to right. It uses a stack data structure to keep track of the tokens and their precedence levels as it processes them.
The two primary actions performed by the parser are shifting and reducing:
- Shifting: As the parser reads each token from the input expression, it "shifts" or places it onto the top of the stack. The stack holds a sequence of tokens encountered so far, forming a partial expression.
- Reducing: After shifting a token onto the stack, the parser checks if the token's operator precedence is higher than that of the operator currently on top of the stack. If it is, the parser "reduces" or combines the operands using the higher precedence operator. It then replaces the operands and the operator on top of the stack with a new non-terminal symbol, representing the simplified sub-expression.
The parser repeats these steps until the entire expression is parsed and reduced to a single non-terminal symbol, which represents the fully simplified expression.
1. Read '3': Shift it onto the stack.
Stack: [3]
2. Read '+': Shift it onto the stack.
Stack: [3, +]
3. Read '4': Shift it onto the stack.
Stack: [3, +, 4]
4. Read '*': Since '*' has higher precedence than '+', reduce the stack. Apply the '*' operator to the top two elements of the stack, i.e., 4 * 2. Replace the top three elements on the stack with the result of the reduction.
Stack: [3, +, 8]
5. The expression is fully parsed, and the final result(8) is on the top of the stack.
Consider the operator precedence table for a simple arithmetic language:
2. Operator Precedence Table
The core of operator precedence parsing lies in the operator precedence table. This table contains all the operators in the language along with their precedence levels. The parser refers to this table to determine the order in which operators should be applied during reduction. Operators with higher precedence appear higher in the table. In case of equal precedence, associativity rules are used to decide the order of operations.Consider the operator precedence table for a simple arithmetic language:
| Operator | Precedence |
|---|---|
| * | High |
| / | High |
| + | Low |
| - | Low |
For example, with the expression 2 + 3 * 4, the parser will first shift 2 onto the stack, then +. When it encounters 3, it compares the precedence of '*' (higher) with '+' (lower) in the table. Since '*' has higher precedence, it reduces the stack by applying the '*' operation first before proceeding with '+', resulting in the correct parse tree.
Example: Mixed Arithmetic Expression
Expression: 5 * 3 + 6 / 2
| Stack | Input | Action |
|---|---|---|
| [5] | * 3 + 6 / 2 | Shift |
| [5, *] | 3 + 6 / 2 | Shift |
| [5, *, 3] | + 6 / 2 | Reduce (5 * 3 -> 15) |
| [15, +] | 6 / 2 | Shift |
| [15, +, 6] | / 2 | Reduce (6 / 2 -> 3) |
| [15, +, 3] | Reduce (15 + 3 -> 18) |
Result: The parse tree represents the expression (5 * 3) + (6 / 2), and the final result is 18.
Advantages of Operator Precedence Parsing
- Simplicity: Operator precedence parsing is relatively easy to implement compared to other parsing techniques like LR or LALR parsing.
- Efficiency: It requires only one pass through the input expression, making it more efficient for simple expressions.
- Deterministic Parsing: Operator precedence parsing eliminates the need for backtracking, resulting in deterministic parsing.
Disadvantages of Operator Precedence Parsing
- Limited Grammar Support: Operator precedence parsing may not handle all types of grammars, especially those with left-recursive or ambiguous rules.
- Lack of Context Sensitivity: The parser only considers the precedence of operators and may miss certain context-specific language constructs.
