Assignment 6 Solution


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Problem I { Scheme

Write Scheme programs that generate the following lists as output using only cons as the list building operator:

  1. ((c (e f (b))) g b)

  1. ((g) ((((h) i)) (a f)) d)

  1. A list l that contains three items: the atom ’g’, the division operator ’/’, and the atom ’6’ such that ((cadr l) 18 9) evaluates to 2.

Note that cadr is composed of car and cdr such that (cadr l) = (car (cdr l)).

Problem II { Scheme

Write the following functions on lists in Scheme. The semantics of the func-tions is described through examples.

1. Get nth digit of an integer

(define getnthdigit

(lambda (m n)


(getnthdigit 32145 1) –> 5

(getnthdigit 32145 2) –> 4

Note: You can use Scheme build-in function “modulo” and ” oor”.


  1. (define rev (lambda (l)


(rev ‘(e((b)(c d)(((f)))))) –> ‘(((((f)))(d c)(b))e)

Note: Do not use the Scheme build-in function “reverse”.

3. Position of rst occurrence of k in list

(define positionof

(lambda (k lst)


(positionof ‘c ‘(c b d c e f)) –> 1

Note: You may want to de ne a helper function


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