Consider the following grammar for applied Lambda expressions:

::$=|"+"|"-"|"*"|"/"|"\%"//$ constants

$|//$ variable

$|"("*")"//$ application

$|"(""$L$"+"."+")"//$ abstraction

Implement the following:

Write a JJTree specification Prog$2.$jjt to generate the AST for any applied Lambda expression.

Implement the method String astToString$()$ to convert the AST of a Lambda expression into its concrete syntax form.

Implement the method Set FV$()$ to find the set of free variables of a Lambda expression AST.

Implement the method void dumpFV$()$ to dump a Lambda expression AST with free variables.

Implement the method SimpleNode substitute$($String var, SimpleNode expr$)$ for substituting all the free occurrences of the variable var with a copy of the Lambda expression AST expr in this Lambda expresson AST.

Implement the method SimpleNode normalOrderEvaluate$()$ for performing a normal order evaluation of this Lambda expression.

Create a tar file named Prog$2.$tar from your program files for this assignment and submit it by the due date through Canvas.

Here is a sample execution for the main part:

$[$hs$15$@zeus Prog$2]$$ java Prog$2$

$>>>$ Lambda Expression Evaluator $$

Enter an applied Lambda expression:

$(($L f x$1.$ f $($f x$1))($L n $.*2(-$ n $1))3)$

The abstract syntax tree:

appl

appl

lamb

f

lamb

x$1$

appl

f

appl

f

x$1$

lamb

n

appl

appl

mul

$2$

appl

appl

sub

n

$1$

$3$

The Lambda expression in the concrete syntax:

$((($L f $.($L x$1.($f $($f x$1))))($L n $.((*2)((-$ n$)1))))3)$

The abstract syntax tree with free variables:

appl $[]$

appl $[]$

lamb $[]$

f $[$f$]$

lamb $[$f$]$

x$1[$x$1]$

appl $[$f$,$ x$1]$

f $[$f$]$

appl $[$f$,$ x$1]$

f $[$f$]$

x$1[$x$1]$

lamb $[]$

n $[$n$]$

appl $[$n$]$

appl $[]$

mul $[]$

$2[]$

appl $[$n$]$

appl $[$n$]$

sub $[]$

n $[$n$]$

$1[]$

$3[]$

Enter an applied Lambda expression:

$($L x$1.$ f $($f x$1))$

The abstract syntax tree:

lamb

x$1$

appl

f

appl

f

x$1$

Enter the variable to be substituted:

f

Enter the substituting applied Lambda expression:

$($L n $.*2(-$ n $1))$

The abstract syntax tree:

lamb

n

appl

appl

mul

$2$

appl

appl

sub

n

$1$

The substitution result:

lamb

x$1$

appl

lamb

n

appl

appl

mul

$2$

appl

appl

sub

n

$1$

appl

lamb

n

appl

appl

mul

$2$

appl

appl

sub

n

$1$

x$1$

Enter an applied Lambda expression:

$(($L f x$1.$ f $($f x$1))($L n $.*2(-$ n $1))3)$

The normal order evaluation result:

$6$

give next code and files of classes i need to create and changes to be made to those files im doing project in eclipse soo kindly give accordingly and ive removed simplenode.java methods in prog$2.$jjt file as i got errors soo give me code for rest of evaluation methods and prog$2.$java $($main$)$code also im attaching screenshots of warnings and the files generated by $.$jjt thank you i have already done until jjtree but next part im getting error at parsing soo can u give code for rest of the project Java Compiler Compiler Version $7\mathrm{.}0\mathrm{.}12($Parser Generator$)$

$($type "javacc" with no arguments for help$)$

Reading from file Prog $2.jj...$

Warning: Choice conflict involving two expansions at

line $39,$ column $4$ and line $39,$ column $36$ respectively.

A common prefix is: $"(""("$

Consider using a lookahead of $3$ or more for earlier expansion.

Warning: Choice conflict involving two expansions at

line $39,$ column $20$ and line $39,$ column $36$ respectively.

A common prefix is: $"("$

Consider using a lookahead of $2$ for earlier expansion.

File "TokenMgrError.java" does not exist. Will create one.

File "ParseException.java" does not exist. Will create one.$|$

File "Token.java" does not exist. Will create one.

File "SimpleCharStream.java" does not exist. Will create one.

Parser generated with $0$ errors and $2$ warnings. Prog $9$