3. Consider the following grammar for infix arithmetic expressions.

E -> E + T

-> E - T

-> + T

-> - T

-> T

T -> T * F

-> T / F

-> F

F -> ( E )

-> i

a) Add semantic actions in appropriate positions in the rules to effect

a translation from infix to postfix code for the 8087 FPU. The

instructions corresponding to the various stack operations are given

in the following table.

load i on stack: fld i

negate: fchs

add: fadd

subtract: fsub

multiply: fmul

divide: fdiv

b) Construct a parse tree with actions to derive the output for the

expression -a + b*c - d/e.

c) Convert the translation grammar produced in (a) to a form that can be

parsed by a recursive descent parser.

d) Write procedures E, T, and F for a recursive descent parser for the

grammar in (c). Include any extra code needed for the translation.

4. Consider the following grammar G (with start symbol A).

A -> i B := e

B -> S B

B ->

S -> [ e C ]

S -> .i

C -> , e C

C ->

a) Construct the leftmost derivation and the associated parse tree

for the input i [ e ] := e.

b) Calculate the FIRST and FOLLOW sets for all non-terminals in the

grammar G.

c) Calculate the SELECT sets for each production.

d) Construct the LL( 1) parsing table for this grammar.

e) Show the sequence of configurations of an LL( 1) parser for the

input i [ e ] := e.