There are two kinds of implementation of LL top$-$down parsing: recursive descent and table driven.

$1.$ Recursive Descent Parser $($textbook $2\mathrm{.}3\mathrm{.}1)$

A recursive descent parser $($RDP$)$ is a parser that constructs a parse tree from the root down, predicting at

each step which production will be used to expand the current node, based on the next available token of

input. It also reports any syntactical errors if any. In RDP$,$ each subroutine corresponds, one to one, to a

nonterminal of the grammar. Example $2\mathrm{.}24$ on page $75$ illustrates how RDP parses a $$sum and average$$

program in simple calculator language.

Figure $2\mathrm{.}17$ shows the pseudo$-$code of RDP for calculator language. It verifies that a program is

syntactically correct $($i$.$e$.,$ that none of the $$otherwise parse$\_$error$$ clauses in the case statements are

executed and that match$()$ always sees what it expects to see$).$ The basic implementation of the parser for

the calculator language, called $$parser$.$c$,$ is given.

Corresponding to Figure $2\mathrm{.}17,$ there are ten functions in parser.c as follows:

void program$()$;

void stmt$\_$list$()$;

void stmt$()$;

void expr$()$;

void term$\_$tail$()$;

void term$()$;

void factor$\_$tail$()$;

void factor$()$;

void add$\_$op$()$;

void mult$\_$op$()$;

$2.$ Table Driven Parser $($textbook $2\mathrm{.}3\mathrm{.}3)$

In table driven top$-$down parser, it requires a stack and parse table to do the same job as RDP$.$ The parser

iterates around a loop in which it pops the top symbol off the stack and performs the following actions. If

the popped symbol is a terminal, the parser attempts to match it against an incoming token from the

scanner. If the match fails, the parser announces a syntax error. If the popped symbol is a nonterminal, the

parser uses that nonterminal together with the next available input token to index into the two$-$dimensional

table that tells it which production to predict $($or whether to announce a syntax error$).$

The $$scanner$.$c$$ is given and is partially working. First, it only checks whether the first token in an input

string of tokens is valid or not. Second, it does not check for comments. That is$,$ it should check if the

comments have the correct forms $($either $/*....*/$ or $//)$ following the regular expression we discussed in

class and in Project $1.$

$3.$ Task Description

Your task is to implement a parser using table$-$driven parsing, using C programming language, called

$$parser$.$c$,$ that works correctly with $$scanner$.$c$.$

When executing your programs, it can take a calculator language program $($with comments$)$ and find if it

has lexical errors and syntax errors or not.

Please compile both programs by typing

gcc parser.c scanner.c $-$o parser

To run the program, the user will type at command line:

$./$parser prog$1$

$,$ where prog$1$ is the name of the calculator program to be checked input by the user.

Next, your program should output error messages indicating any lexical or syntax error in the

calculator program; otherwise, output a $$No lexical and syntax error.$$ message.

For example, below calculator program below, called $$prog$1,$ is both lexically and syntactically

correct:

$/*$ prog$1*/$

read a

read b

area :$=$ a $*$ b

perimeter :$=2*($a $+$ b$)$

write area

write perimeter

Below program, called $$prog$2$ is lexically incorrect.

$/*$ prog$2$

read a

read b

area :$=$ a $*$ b

perimeter :$=2*($a $+$ b$)$

write area

write perimeter

The below program, called $$prog$3,$ is lexically correct but syntactically incorrect.

$/*$ prog$3*/*/$

read a

read b

area :$=$ a $*$ b

perimeter :$=2*($a $+$ b$)$

write area

write perimeter

The below programs, called $$prog$4$ and $$prog$5,$ respectively, are lexically correct but syntactically

incorrect.

$//$ prog$4$

read a b

area :$=$ a $*$ b

perimeter :$=2*($a $+$ b$)$

write area

write perimeter

and

$//$ prog$5$

read a

read b

area :$=$ a $*$ b

perimeter :$=2*($a $+$ b

write area

write perimeter

If you have more test programs, please name them $$prog$6,$prog$7,$ etc..

Please make sure that the error messages $($both lexical and syntactical$)$ are detailed and informative by showing which lines of the program has errors