Vfrdtyky

Long-time reader, first time poster. Working on a homework question asking to write a DFA-acceptor in Scheme. Alphabet: {0, 1} Start-state: {Q0} Final-state: {Q2}. String must have a 01 in the sequence to be accepted.
States:
Q0 on 1 transitions to Q1.
Q0 on 0 transitions to Q0.
Q1 on 1 transitions to Q2.
Q1 on 0 transitions to P.
Q2 on 0 and 1 transitions to Q1.
The teacher requested each state to be a function and to return a function that it transitions to. (Q0 1) returns Q1, etc. Code below is an attempt to get things running, before worrying about checking if 01 is in the string. Currently getting an error: "Q0: unbound identifier;" and am not sure why after doing some searching. Any pointers would be helpful. The question is for homework, so not looking for direct answers. Thank you!

#lang racket

(define DFA-trans '((Q0 x) (Q1 x) '((Q2 x)) (P x)))



(define x '(1 1 0 1 0))



(define P(null? 1))



(define Q2 (lambda(x)

         (if (null? (car x))

             #t

         (if (equal? (car x) 0)

             (Q2 (cdr x))

         (if (equal? (car x) 1)

             (Q2 (cdr x))

             #t

             )))))



(define Q1 (lambda(x)

         (if (null? (car x))

             #f

         (if (equal? (car x) 0)

             (P (cdr x))

         (if (equal? (car x) 1)

             (Q2 (cdr x))

             #f

             )))))



(define Q0 (lambda(x)

         (if (null? (car x))

             #f

         (if (equal? (car x) 0)

             (Q0 (cdr x))

         (if (equal? (car x) 1)

             (Q1 (cdr x))

             #f

             )))))



(define DFA(map eval DFA-trans))

(DFA)