# GATE | GATE-CS-2005 | Question 85

• Last Updated : 12 Jul, 2021

Consider the following expression grammar. The seman­tic rules for expression calculation are stated next to each grammar production.

``` E → number 	 E.val = number. val
| E '+' E 	 E(1).val = E(2).val + E(3).val
| E '×' E	 E(1).val = E(2).val × E(3).val```

The above grammar and the semantic rules are fed to a yacc tool (which is an LALR (1) parser generator) for parsing and evaluating arithmetic expressions. Which one of the following is true about the action of yacc for the given grammar?
(A) It detects recursion and eliminates recursion
(B) It detects reduce-reduce conflict, and resolves
(C) It detects shift-reduce conflict, and resolves the conflict in favor of a shift over a reduce action
(D) It detects shift-reduce conflict, and resolves the conflict in favor of a reduce over a shift action

Explanation:

Background
yacc conflict resolution is done using following rules:
shift is preferred over reduce while shift/reduce conflict.
first reduce is preferred over others while reduce/reduce conflict.

You can answer to this question straightforward by constructing LALR(1) parse table, though its a time taking process. To answer it faster, one can see intuitively that this grammar will have a shift-reduce conflict for sure. In that case, given this is a single choice question, (C) option will be the right answer.

Fool-proof explanation would be to generate LALR(1) parse table, which is a lengthy process. Once we have the parse table with us, we can clearly see that
i. reduce/reduce conflict will not arise in the above given grammar
ii. shift/reduce conflict will be resolved by giving preference to shift, hence making the expression calculator right associative.

According to the above conclusions, only correct option seems to be (C).

Reference:

http://dinosaur.compilertools.net/yacc/

This solution is contributed by Vineet Purswani.

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