Check the Lisp program below and make sure it behaves as same as the given instruction and make the necessary adjusments if needed.

THE CODE:

$($defun simplify$-$arithmetic$-$expression $($expression$)$

$($let$*(($simplified $($remove$-$if #$\text{'}($lambda $($char$)($char$=$ char #$\backslash$space$))$ expression$))$

$($terms $($split$-$sequence:split$-$sequence #$\backslash +$ simplified$))$

$($simplified$-$terms $($mapcar #$\text{'}($lambda $($term$)$

$($string$-$trim $""$ term$))$

terms$))$

$($final$-$simplified $($format nil $"$~$\{$~a~$^+$ ~$\}"$ simplified$-$terms$)))$

final$-$simplified$))$

$($defun evaluate$-$arithmetic$-$expression $($expression values$)$

$($let$*(($tokens $($split$-$sequence:split$-$sequence #$\backslash +$ expression$))$

$($evaluated$-$tokens $($mapcar #$\text{'}($lambda $($token$)$

$($eval $($read$-$from$-$string token$)))$

tokens$))$

$($result $($apply #$\text{'}+$ evaluated$-$tokens$)))$

$($format t "Expression value: ~a~$\%"$ result$)))$

$($defun main $()$

$($loop

$($format t "Enter arithmetic expression: $")$

$($let $(($input $($read$-$line$)))$

$($cond $(($string$=$ input "quit"$)$

$($format t "Good Bye!~$\%")$

$($return$))$

$($t

$($let$*(($simplified $($simplify$-$arithmetic$-$expression input$)))$

$($if $($string$=$ simplified "INVALID"$)$

$($progn

$($format t "Invalid expression. Please enter a valid arithmetic expression.~$\%")$

$($return$))$

$($progn

$($format t "Simplification: ~a~$\%"$ simplified$)$

$($format t "Evaluate $($y$/$n$)?")$

$($let $(($decision $($read$-$line$)))$

$($cond $(($string$=$ decision $"$y$")$

$($format t "Provide variable values~$\%")$

$($let $(($values $($make$-$hash$-$table :test 'equal$)))$

$($loop for var across $($remove$-$duplicates $($remove$-$if$-$not #'alpha$-$char$-$p $($coerce simplified 'list$)))$

do $($progn $($format t $"$~a: $"$ var$)$

$($setf $($gethash var values$)($read$))))$

$($evaluate$-$arithmetic$-$expression simplified values$)))$

$(($string$=$ decision $"$n$")$

$($format t $"***$~$\%"))$

$($t $($format t "Invalid choice.~$\%"))))))))))))$

$($main$)$

THE INSTRUCTION :

Create a program for the simplification and evaluation of arithmetic expressions. The program, when executed, should prompt the user to enter an arithmetic expression:

$>$ exeval

Enter arithmetic expression: $2$x $+13+$ y $-$ x

The expression should be a linear combination of single letter variables. The program will then simplify the expression:

$>$ exeval

Enter arithmetic expression: $2$x $+13+$ y $-$ x

Simplification: x $+$ y $+13$

and then will ask whether to evaluate the expression. If the answer is $\text{'}$y$\text{'}$ then it will prompt for values for each of the variables and evaluate the expression:

$>$ exeval

Enter arithmetic expression: $2$x $+13+$ y $-$ x

Simplification: x $+$ y $+13$

Evaluate? y

Provide variable values

x : $1$

y : $3$

Expression value: $18$

$***$

Enter arithmetic expression:

then ask for a new expression to evaluate. If the answer is $\text{'}$n$\text{'},$ then it will simply ask for a new expression to evaluate:

$>$ exeval

Enter arithmetic expression: $2$x $+13+$ y $-$ x

Simplification: x $+$ y $+13$

Evaluate? n

$***$

Enter arithmetic expression:

The program will quit with command 'quit' enter at the expression prompt:

$>$ exeval

Enter arithmetic expression: $2$x $+13+$ y $-$ x

Simplification: x $+$ y $+13$

Evaluate? n

$***$

Enter arithmetic expression: quit

Good Bye!

$($PLZ include screenshots of the execution the program for assurance.$)$