Postfix translation in compiler design - The Logic Tutorial

Postfix Translation: Streamlining Code Generation

In compiler design, postfix translation is a technique used within syntax-directed translation (SDT) to generate code (often in postfix notation) during the parsing process. Here's a breakdown of the key concepts:

• Syntax-Directed Translation (SDT): A method that associates semantic actions with productions in a context-free grammar (CFG) to perform specific tasks while parsing the source code. These actions can involve building an abstract syntax tree (AST), generating intermediate code, or performing type checking.
• Postfix Notation: Also known as Reverse Polish Notation (RPN), postfix notation expresses an expression by placing the operator after its operands. For example, the infix expression x + y becomes xy + in postfix. This notation eliminates the need for parentheses in most cases, simplifying evaluation.

How Postfix Translation Works

In postfix translation, the semantic actions associated with grammar productions are placed at the end (rightmost part) of the production rule. This placement allows the actions to be executed immediately after the corresponding production is reduced during the parsing process. The actions typically involve:

• Evaluating the attributes (properties) associated with the non-terminals in the production rule.
• Generating code (often in postfix notation) based on the operator or construct being parsed.
• Updating the attributes of the newly formed symbol on the stack (usually the left-hand side non-terminal of the production).

Benefits of Postfix Translation

• Efficiency: Since actions are performed during reduction, the code generation process is tightly integrated with parsing, potentially leading to more efficient code generation.
• Simplicity: The semantics of the language can be directly expressed within the grammar, making the translation scheme easier to understand and maintain.
• Suitability for Bottom-Up Parsing: Postfix translation schemes are well-suited for use with bottom-up parsing techniques like LR(k) parsers, as the actions are executed as reductions occur during the bottom-up parse.

Example: Converting Infix to Postfix

Consider a simple grammar rule for an arithmetic expression:

Expr -> Expr + Term | Term

The corresponding postfix translation scheme might look like:

Expr.CODE = Expr1.CODE Term.CODE "+"
Term.CODE = Factor.CODE

Here, Expr.CODE and Term.CODE represent the code generated for the non-terminals Expr and Term, respectively. During parsing, when the Expr -> Expr + Term production is reduced, the + operator is appended to the concatenation of the codes generated for Expr1 and Term. This effectively builds the postfix representation of the expression.

In Conclusion

Postfix translation is a valuable technique in compiler design, offering a streamlined approach to code generation during the parsing phase. By placing semantic actions at the end of grammar productions, it allows for efficient and direct translation of source code constructs into their corresponding code representation.