GATE CS 2021 Set 1 — Question 36

MCQ+2 / -0.67MediumType CheckingSemantic AnalysisCompiler DesignSyntax-Directed Translation

Compiler Design → Semantic Analysis → Syntax-Directed Translation

Last updated 5 September 2026

Question

Consider the following grammar (that admits a series of declarations, followed by expressions) and the associated syntax directed translation (SDT) actions, given as pseudo-code: P -> D* E* D -> int ID {record that ID.lexeme is of type int} D -> bool ID {record that ID.lexeme is of type bool} E -> E1 + E2 {check that E1.type = E2.type = int; set E.type := int} E -> !E1 {check that E1.type = bool; set E.type := bool} E -> ID {set E.type := int} With respect to the above grammar, which one of the following choices is correct?

Correct answer (B) The actions can be used to type-check syntactically correct integer variable declarations and integer expressions. Solution Analyze the SDT actions: The rule E -> ID {set E.type := int} unconditionally sets the type of any identifier expression to int, regardless of how the identifier was declared (even though the declaration rules record the correct type). Integer expressions: If we have an expression like x + y, x and y are reduced to E with type int . The rule E -> E1 + E2 checks if operands are int, which they are. This works correctly for integers. Boolean expressions: If we have an expression like!b where b is a boolean variable, b is reduced to E via E -> ID, setting E.type to int . The rule E -> !E1 checks if E1.type is bool . Since it is int, the type check fails. Thus, the SDT works for integer expressions but fails for boolean expressions involving variables. Option (B) is correct. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

Review answer and solution without JavaScript

Interactive answer checking needs JavaScript. The published solution is available below.

Correct answer (B) The actions can be used to type-check syntactically correct integer variable declarations and integer expressions. Solution Analyze the SDT actions: The rule E -> ID {set E.type := int} unconditionally sets the type of any identifier expression to int, regardless of how the identifier was declared (even though the declaration rules record the correct type). Integer expressions: If we have an expression like x + y, x and y are reduced to E with type int . The rule E -> E1 + E2 checks if operands are int, which they are. This works correctly for integers. Boolean expressions: If we have an expression like!b where b is a boolean variable, b is reduced to E via E -> ID, setting E.type to int . The rule E -> !E1 checks if E1.type is bool . Since it is int, the type check fails. Thus, the SDT works for integer expressions but fails for boolean expressions involving variables. Option (B) is correct.

Continue learning with Success Tracker

Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans

PYQs with solutions: Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts: Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support: Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.