$1)$ Below is the parser written in class for the grammar S$$ aA$|$; A $$ bS:

$($setf program $\text{'}())$

$($defun get$-$tk $()($car program$))$

$($defun accept$-$tk $()($setf program $($cdr program$)))$

$($defun S $()$

$($if $($null program$)$

$"$Parsing successful"$$

$($if $($eq $($get$-$tk$)\text{'}$a$)$

$($progn $($accept$-$tk$)($A$))$

$"$unexpected token"$$

$)$

$)$

$)$

$($defun A $()$

$($if $($null program$)$

$"$Program ended unexpectedly"$$

$($if $($eq $($get$-$tk$)\text{'}$b$)$

$($progn $($accept$-$tk$)($S$))$

$"$unexpected token"$$

$)$

$))$

Modify the above parser for the following grammar, and demonstrate using non$-$trivial strings that the$$ parser correctly parses valid and invalid strings allowed by the grammar:$$

S $$ bA $|$ c$$

A$$ cS $|$ d$$

Note #$1$: By correctly, it is meant as expected by flagging errors for invalid strings and displaying$$ "success" for valid strings.$$

Note #$2$: By non$-$trivial string, it is meant a string other than a trivial string, examples of trivial strings are $\text{'}($c$),\text{'}($b d$),\text{'}(),$ and $\text{'}($e$).$