Use any language for the question (Hand in source programs and test runs). Consider the following grammar for arithmetic expressions:

E -> T

E -> E + T

T -> F

T -> T * F

F -> int

F -> (E)

where int denotes an integer.

a) Modify the rules to remove left recursion (you may use EBNF).

b) Suppose that the value of an expression is given by its corresponding post-fix expression. Add the semantics rules computing the value of an expression.

c) Modify the program (given in the text and in the PPT) for parsing an arithmetic expression to produce a post-fix expression from an in-fix expression.

d) Do b) and c) for pre-fix expression.

e) Give grammar rules for post-fix expressions.

f) Write a program to compute the value of a post-fix expression