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<center><h2>cs150: Notes 8</h2></center>

<h4>Assignments Due</h4>


<ul>
<li> (extended from 29 January) Before Monday, 5 February: Read GEB, <em>Little Harmonic Labyrinth</em> and GEB, Chapter 5
<li> Friday, 2 February (beginning of class): Problem Set 2.  (Note: Problem
Set 2 will be accepted without penalty or any permission required until
the beginning of class on Monday, 5 February, as long as you promise to
still finish reading GEB Chapter 5 before Monday's class.)
</ul>

</ul>

<h4>Tracing</h4>

To enable tracing, evaluate <tt>(require (lib
"trace.ss"))</tt>.  (You can put this in your definitions file, like it
is in <tt>poker.scm</tt>.)  Then,
<blockquote>
<pre>(trace <em>procedure</em>)</pre>
</blockquote>
will enable tracing of the procedure.  The interpreter will print out a
message corresponding to the entrance (showing the parameters) and exit
(showing the resulting value) of the traced procedure.  This is a useful
tool for understanding what is going on when your programs are
evaluated.
<p>

<h4>List Procedures</h4>

<pre>
(define (list? p)
  (if (null? p) 
      #t
      (if (pair? p)
          (list? (cdr p))
          #f)))
</pre>


<pre>
(define (sumlist p)
  (if (null? p)
      0
      (+ (car p) (sumlist (cdr p)))))
</pre>

<pre>
(define (map f p)
  (if (null? p)
      null
      (cons (f (car p)) 
               (map f (cdr p)))))
</pre>
<p class="page"></p>
Here's an example use of <tt>map</tt> in the <tt>choose-n</tt> procedure from PS2:
<pre>
(define (choose-n n lst)
  ;; operands: a number n and a list (of at least n elements)
  ;; result: evaluates to a list of all possible ways 
  ;;     of choosing n elements from lst
  (if (= n 0) 
      (list null) 
      (if (= (length lst) n) 
          (list lst) 
          (append (choose-n n (cdr lst)) 
                  <b>(map (lambda (clst) (cons (car lst) clst)) </b>
                       <b>(choose-n (- n 1) (cdr lst)))))))</b>
</pre>
What is the map application expression doing?
<p><br><p><br><p><br><p><br><p><br>

<pre>
(define (list-cruncher base proc combiner lst)
  (if (null? lst)
      base
      (combiner (proc (car lst))
                     (list-cruncher base proc combiner 
                                         (cdr lst)))))


(define (sumlist p)

  (list-cruncher _____ ___________________  _____ p))

(define (map f p)

  (list-cruncher _______  ______   ______ p))

(define (length p)

  (list-cruncher ______  _____________ + p))
</pre>

Why is it impossible to correctly define <tt>list?</tt> using just <tt>list-cruncher</tt>?
<p><br><p><br><p><br><p><br>

Define <tt>find-closest-number</tt>, a procedure that takes two
parameters, a goal and a list of numbers, and produces the number in the
list numbers list that is closest to goal.

<p><br><p><br><p><br><p><br>

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