<b>CS 61A&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Week 6</b>
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Topic: Generic Operators
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<b>Reading:</b>
Abelson &amp; Sussman, Sections 2.4 through 2.5.2 (pages 169-200)
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<b>Homework:</b>
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Abelson &amp; Sussman, exercises 2.74, 2.75, 2.76, 2.77, 2.79, 2.80, 2.81, 2.83
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Note: Some of these are thought-exercises; you needn't actually run any Scheme
programs for them!  (Some don't ask you to write procedures at all;
others ask for modifications to a program that isn't online.)

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> If you haven't already finished this week's lab exercises that
involve the <tt>scheme-1</tt> interpreter, do it now.  Then write
a <tt>map</tt> primitive for <tt>scheme-1</tt> (call it <tt>map-1</tt> so you
and Scheme don't get confused about which is which) that works
correctly for all mapped procedures.

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> Modify the <tt>scheme-1</tt> interpreter
to add the <tt>let</tt> special form.  Hint: Like a procedure call, <tt>let</tt>
will have to use <tt>substitute</tt> to replace certain variables with their
values.  Don't forget to evaluate the expressions that provide those
values!

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<b>Extra for experts:</b>
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Another approach to the problem of type-handling is <i>type inference</i>.
If, for instance, a procedure includes the expression <tt>(+ n k)</tt>,
one can infer that <tt>n</tt> and <tt>k</tt> have numeric values.
Similarly, the expression <tt>(f a b)</tt> indicates that the value of <tt>f</tt>
is a procedure.

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Write a procedure called <tt>inferred-types</tt> that, given a definition of a
Scheme procedure as argument, returns a list of information about the
parameters of the procedure.  The information list should contain one
element per parameter; each element should be a two-element list whose first
element is the parameter name and whose second element is a word indicating
the type inferred for the parameter.  Possible types are listed on the next
page.

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<b>Continued on next page.</b>

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<b>Week 6 continued...</b>

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<br />
<dl compact="compact">
 <dt>
<tt>?</tt></dt>
<dd>
 (the type can't be inferred)
</dd>
 <dt>
<tt>procedure</tt></dt>
<dd> (the parameter appeared as the first word in an
unquoted expression or as the first argument of <tt>map</tt> or <tt>every</tt>)
</dd>
 <dt>
<tt>number</tt></dt>
<dd> (the parameter appeared as an argument of <tt>+</tt>, <tt>-</tt>,
<tt>max</tt>, or <tt>min</tt>)
</dd>
 <dt>
<tt>list</tt></dt>
<dd> (the parameter appeared as an argument of <tt>append</tt>
or as the second argument of <tt>map</tt> or <tt>member</tt>)
</dd>
 <dt>
<tt>sentence-or-word</tt></dt>
<dd> (the parameter appeared as an argument of <tt>first,</tt>
<tt>butfirst,</tt> <tt>sentence,</tt> or <tt>member?</tt>, or
as the second argument of <tt>every</tt>)
</dd>
 <dt>
<tt>x</tt></dt>
<dd> (conflicting types were inferred)
</dd></dl><br />You should assume for this problem that the body of the procedure to
be examined does not contain any occurrences of <tt>if</tt> or <tt>cond</tt>,
although it may contain arbitrarily nested and quoted expressions.
(A more ambitious inference procedure both would examine a more comprehensive
set of procedures and could infer conditions like "nonempty list".)

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Here's an example of what your inference procedure should return.

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<tt>  <pre>(inferred-types
  '(define (foo a b c d e f)
    (f (append (a b) c '(b c)) (+ 5 d) (sentence (first e) f)) ) )

</pre></tt>

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should return

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<tt>  <pre>((a procedure) (b ?) (c list) (d number)
 (e sentence-or-word) (f x))

</pre></tt>

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If you're <i>really </i> ambitious, you could maintain a database of
inferred argument types and use it when a procedure you've seen is
invoked by another procedure you're examining!

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<br /><hr />
Unix feature of the week: <tt>du</tt>, <tt>df</tt>, <tt>quota</tt>
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Emacs feature of the week: <tt>M-q</tt> (format paragraphs), <tt>C-M-q</tt> (format Scheme code)
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