6.090 IAP '05 - Lecture 4 Solutions

Problem 1:

(define (foo x)
  (+ x 3))
;unspecified

foo
;procedure

(foo 5)
;8

(define bar 5)
;unspec

(define (baz) 5)
;unspec

bar
;5

baz
;procedure

(bar)
;error: 5 not applicable

(baz)
;5

(let ((a 3)
      (b 5))
  (+ a b))
;8

(let ((+ *)
      (* +))
  (+ 3 (* 4 5)))
;27

(define m 3)
(let ((m (+ m 1)))
  (+ m 1))
;5

(define n 4)
(let ((n 12)
      (o (+ n 2)))
  (* n o))
;72

Problem 2:   (gratuitous ASCII art)

+-+-+   +-+-+   +-+-+
|.|.--->|.|.--->|.|\|
+|+-+   +|+-+   +|+-+
 |       |       |
 V       V       V
 1       2       3

+-+-+   +-+-+   +-+-+
|.|.--->|.|.--->|.|\|
+|+-+   +|+-+   +|+-+
 |       |       |
 V       V       V
 3       1       2

+-+-+   +-+-+   +-+-+
|.|.--->|.|.--->|.|\|
+|+-+   +|+-+   +|+-+
 |       |       |
 V       V       V
 1       3       5

+-+-+
|.|\|
+|+-+
 |   
 V   
+-+-+
|.|\|
+|+-+
 |   
 V   
 3   

Problem 3:

(list 1 2 3)
;Value: (1 2 3)

(list (list 1 2) (list 3 4) (list 5 6))
;Value: ((1 2) (3 4) (5 6))

(list (list 4 7) 2)
;Value: ((4 7) 2)

Problem 4:

(define lst (list 7 6 5 4 3 2 1))
(cadddr lst)
;Value: 4
(car (cdr (cdr (cdr lst))))
;Value: 4
(fourth lst)
;Value: 4

(define lst (list (list 7) (list 6 5 4) (list 3 2) 1))
(caddr (cadr lst)
;Value: 4
(third (second lst))
;Value: 4
; the (caddadr lst) won't work.. too many a's and d's (up to 4 only)

(define lst (list 7 (list 6 (list 5 (list 4 (list 3 (list 2 (list 1))))))))
(car (cadr (cadr (cadr lst))))
;Value: 4

(define lst (list 7 (list (list 6 5 (list (list 4)) 3) 2) 1))
(car (car (caddr (car (cadr lst)))))
;Value: 4