Homework 1 Provide a CFG that describes expressions with operators +,/, and ** s

Question

Homework 1 Provide a CFG that describes expressions with operators +,/, and ** such that the operators and / are left associative, the operator **is right associative and has higher precedence than the operator / which also has higher precedence the operator +. 2. Provide the CFG that describes expressions with operators +,, * and ** such that the operators +, -, *, and / are left associative, the operator **is right associative and has higher precedence than the operators * and /which also have higher precedence the operators with the same precedence, C to-right. 3. Questions 3 and 9 page 163 -164.

Explanation / Answer

1. CFG that describes expressions with operators +,/ and ** is :

E -> E + T | T

T -> T / F | H

F -> H ** F | H

H -> n

Rule with operator at lowest level has highest precendence and rule with operator nearest to start symbol has lowest precedence.

E -> E + T is left associative i.e. done from left to right

T -> T/F is also left associative i.e. done from left to right

F -> H**F is right associative i.e. done from right to left

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