CS 135 Tutorials

Tutorial 4: Solutions (October 5, 2007)

1. (and (symbol? 'hello)
        (= (- 5 1) (* 2 3))
        (/ "a string" "another string"))

   ⇒

   (and true
        (= (- 5 1) (* 2 3))
        (/ "a string" "another string"))

   ⇒

   (and (= (- 5 1) (* 2 3))
        (/ "a string" "another string"))

   ⇒

   (and (= 4 (* 2 3))
        (/ "a string" "another string"))

   ⇒

   (and (= 4 6)
        (/ "a string" "another string"))

   ⇒

   (and false
        (/ "a string" "another string"))

   ⇒

   false

2. (define a (+ 2 3))
   (define (foo2 x)
     (cond [(or (> x 1)
   	     (< x -1))
   	 (sqr x)]
   	[(zero? x) 1]))
   (foo2 a)
   (foo2 (/ a a))

   ⇒

   (define a 5)
   (define (foo2 x)
     (cond [(or (> x 1)
   	     (< x -1))
   	 (sqr x)]
   	[(zero? x) 1]))
   (foo2 a)
   (foo2 (/ a a))

   ⇒

   ...
   (foo2 5)
   (foo2 (/ a a))

   ⇒

   ...
   (cond [(or (> 5 1)
   	   (< 5 -1))
          (sqr 5)]
         [(zero? x) 1])
   (foo2 (/ a a))

   ⇒

   ...
   (cond [(or true
   	   (< 5 -1))
          (sqr 5)]
         [(zero? x) 1])
   (foo2 (/ a a))

   ⇒

   ...
   (cond [true
          (sqr 5)]
         [(zero? x) 1])
   (foo2 (/ a a))

   ⇒

   ...
   (sqr 5)
   (foo2 (/ a a))

   ⇒

   ...
   25
   (foo2 (/ a a))

   ⇒

   ...
   25
   (foo2 (/ 5 a))

   ⇒

   ...
   25
   (foo2 (/ 5 5))

   ⇒

   ...
   25
   (foo2 1)

   ⇒

   ...
   25
   (cond [(or (> 1 1)
   	   (< 1 -1))
          (sqr 1)]
         [(zero? 1) 1])

   ⇒

   ...
   25
   (cond [(or false
   	   (< 1 -1))
          (sqr 1)]
         [(zero? 1) 1])

   ⇒

   ...
   25
   (cond [(or (< 1 -1))
          (sqr 1)]
         [(zero? 1) 1])

   ⇒

   ...
   25
   (cond [(or false)
          (sqr 1)]
         [(zero? 1) 1])

   ⇒

   ...
   25
   (cond [(or)
          (sqr 1)]
         [(zero? 1) 1])

   ⇒

   ...
   25
   (cond [false
          (sqr 1)]
         [(zero? 1) 1])

   ⇒

   ...
   25
   (cond [(zero? 1) 1])

   ⇒

   ...
   25
   (cond [false 1])

   ⇒

   ...
   25
   (cond)

   ⇒

   Semantics error (no substitution rule for (cond))

3. (define (foo3 5)
     (+ 1 5))
   (/ (foo3 5)
      0)

   ⇒

   Syntax error: 5 is not a valid variable name

   Note: The division by zero is not even considered because the syntax error is seen first.

4. (define-struct name (first middle last))
   (define (foo4 nme)
     (name-middle (+ nme 1)))
   (name-last (make-name "James" "A" "Garfield"))

   ⇒

   (define-struct name (first middle last))
   (define (foo4 nme)
     (name-middle (+ nme 1)))
   "Garfield"

   Note: The function foo4 will generate a semantics error on every function call, but since it is never called, there is no error here.

5. (define (foo5 x)
     (cond [(= 1 x) 2]
   	[else
   	  (* 2
   	     (foo5 (sub1 x)))]))
   (foo5 3)
   (foo5 -2)

   ⇒

   ...
   (cond [(= 1 3) 2]
         [else
   	(* 2
   	   (foo5 (sub1 3)))])
   (foo5 -2)

   ⇒

   ...
   (cond [false 2]
         [else
   	(* 2
   	   (foo5 (sub1 3)))])
   (foo5 -2)

   ⇒

   ...
   (cond [else
   	(* 2
   	   (foo5 (sub1 3)))])
   (foo5 -2)

   ⇒

   ...
   (* 2
      (foo5 (sub1 3)))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (foo5 2))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (cond [(= 1 2) 2]
   	 [else
   	   (* 2
   	      (foo5 (sub1 2)))]))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (cond [false 2]
   	 [else
   	   (* 2
   	      (foo5 (sub1 2)))]))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (cond [else
   	   (* 2
   	      (foo5 (sub1 2)))]))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (* 2
         (foo5 (sub1 2))))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (* 2
         (foo5 1)))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (* 2
         (foo5 1)))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (* 2
        (cond [(= 1 1) 2]
   	   [else
   	     (* 2
   	        (foo5 (sub1 1)))])))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (* 2
        (cond [true 2]
   	   [else
   	     (* 2
   	        (foo5 (sub1 1)))])))
   (foo5 -2)

   ⇒

   ...
   (* 2
      (* 2
         2))
   (foo5 -2)

   ⇒

   ...
   (* 2
      4)
   (foo5 -2)

   ⇒

   ...
   8
   (foo5 -2)

   ⇒

   Semantics error: infinite loop