8) Consider the unambiguous expression grammar G' of Example 11.19. a) Trace the derivation of the string id+id*id*id in G'. b) Add exponentiation (**) and unary minus (-) to G', assigning the highest precedence to unary minus, followed by exponentiation, multiplication, and addition, in that order.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Example 11.19
An Unambiguous Expression Grammar
Consider again the language Expr, which we defined with the following context-free grammar G=({E, id, +, *, (, )},
{id, +, *, (, )}, R, E), where:
R={E→E+E
E EE
E→ (E)
Eid}.
G is ambiguous in two ways:
1.
2.
It fails to specify associativity. So, for example, there are two parses for the string id+id+ id, corresponding
to the bracketings (id+id) + id and id+(id+id).
It fails to define a precedence hierarchy for the operators + and *. So, for example, there are two parses for the
string id + id * id, corresponding to the bracketings (id+id) * id and id+(id * id).
Transcribed Image Text:Example 11.19 An Unambiguous Expression Grammar Consider again the language Expr, which we defined with the following context-free grammar G=({E, id, +, *, (, )}, {id, +, *, (, )}, R, E), where: R={E→E+E E EE E→ (E) Eid}. G is ambiguous in two ways: 1. 2. It fails to specify associativity. So, for example, there are two parses for the string id+id+ id, corresponding to the bracketings (id+id) + id and id+(id+id). It fails to define a precedence hierarchy for the operators + and *. So, for example, there are two parses for the string id + id * id, corresponding to the bracketings (id+id) * id and id+(id * id).
8) Consider the unambiguous expression grammar G' of Example 11.19.
a)
Trace the derivation of the string id+id*id*id in G'.
b) Add exponentiation (**) and unary minus (-) to Gʻ, assigning the highest precedence to unary minus, followed
by exponentiation, multiplication, and addition, in that order.
Transcribed Image Text:8) Consider the unambiguous expression grammar G' of Example 11.19. a) Trace the derivation of the string id+id*id*id in G'. b) Add exponentiation (**) and unary minus (-) to Gʻ, assigning the highest precedence to unary minus, followed by exponentiation, multiplication, and addition, in that order.
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