Solutions to the Exercises due October 29, 2004

2. Solution to Exercise 2:

   > (first (rest '(1 2 (3 4) 5 6)))
   2
   > (first (rest (rest '(1 2 (3 4) 5 6))))
   (3 4)
   > (first (rest (rest (rest '(1 2 (3 4) 5 6)))))
   5
   > (first (rest (first (rest (rest '(1 2 (3 4) 5 6))))))
   4


3. A solution to Exercise 3 with in-line comments:

   (define (special-list-type? arg)
     (and ;; is it a list
          (list? arg)
          ;; is there at least one element in the list
          (not (null? arg))
          ;; is the first element a number
          (number? (first arg))
          ;; are there at least two elements in the list
          (not (null? (rest arg)))
          ;; is the second element of the list a number
          (number? (first (rest arg)))
          ;; are there at least three elements in the list
          (not (null? (rest (rest arg))))
          ;; is the third element of the list a list
          (list? (first (rest (rest arg))))
          ;; is the third element a list with at least one element
          (not (null? (first (rest (rest arg)))))
          ;; is the third element a list with exactly one element
          (null? (rest (first (rest (rest arg)))))
          ;; is the third element a list whose first argument is a string
          (string? (first (first (rest (rest arg)))))
          ;; are there at least four elements in the list 
          (not (null? (rest (rest (rest arg)))))
          ;; is the fourth element in the list a symbol
          (symbol? (first (rest (rest (rest arg)))))
          ;; are there exactly four elements in the list
          (null? (rest (rest (rest (rest arg)))))))

4. Solution to Exercise 4:

   (define (special-list-type-cond? arg)
     (cond ((not (list? arg)) (printf "Expecing a list: ~a~%" arg))
           ((null? arg) (printf "Expecting a non-empty list: ~a~%" arg))
           ((not (number? (first arg)))
            (printf "Expecting the first element to be a number: ~a~%" arg))
           ((null? (rest arg))
            (printf "Expecting a list of length > 1: ~a~%" arg))
	   ((not (number? (first (rest arg))))
            (printf "Expecting the second element to be a number: ~a~%" arg))
           ((null? (rest (rest arg)))
            (printf "Expecting a list of length > 2: ~a~%" arg))
           ((not (list? (first (rest (rest arg)))))
            (printf "Expecting the third element to be a list: ~a~%" arg))
           ((null? (first (rest (rest arg))))
            (printf "Expecting third element to be a non-null list: ~a~%" arg))
           ((not (null? (rest (first (rest (rest arg))))))
            (printf "Expecting the third element to be list with one item: ~a~%" arg))
           ((not (string? (first (first (rest (rest arg))))))
            (printf "The only item in the third element should be a string: ~a~%" arg))
           ((null? (rest (rest (rest arg))))
            (printf "Expecting a list of length 4: ~a~%" arg))
           ((not (symbol? (first (rest (rest (rest arg))))))
            (printf "Expecting the fourth element to be symbol: ~a~%" arg))
	   (else (printf "Just what I was expecting: ~a~%" arg))))


   > (special-list-type-cond? '(1 2 ("foo") a))
   Just what I was expecting: (1 2 (foo) a)
   > (special-list-type-cond? (list 1 "" (list "foo") 'a))
   Expecting the second element to be a number: (1  (foo) a)
   > (special-list-type-cond? (list 1 7 '("foo" "bar") 'a))
   Expecting the third element to be list with one item: (1 7 (foo bar) a)