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);
    }
    div#main {
        margin: 40px auto;
        max-width: 800px;
        line-height: 1.4;
        font-size: 1.1em;
        padding: 1em;
        box-shadow: 0 4px 8px 0 rgba(0, 0, 0, 0.2), 0 6px 20px 0 rgba(0, 0, 0, 0.19);
        border-radius: 0.75em;
        background-color: white;
    }
    img[src*="float_right"] {
      float: right;
      border-radius: 0.75em;
    }
    img[src*="200px"] {
      width: 200px;
    }
		strike     { color: grey                }
		u          { text-decoration: none;
					 background-color: yellow   }
		tt         { color: #2e3436;            }
		pre        { color: #2e3436;
					 margin-left: 20px          }
		h1,h2,h3,h4,h5 {
				color: #cc3b12;
        margin: 0 auto;
    }
		p          { margin-top: 0              }
		span.zim-tag {
			color: #ce5c00;
		}
		div.zim-object {
			border-style:solid;
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	<h1>Common Lisp iteration <a name='Lisp:CommonLispIteration'></a></h1>
	</div>

	<div class='content Lisp:CommonLispIteration'>
	<p>
Created Monday 23 November 2020
</p>
<br>
<p>
Each of the following definitions of a <a href="https://en.wikipedia.org/wiki/Factorial" title="factorial" class="https">factorial</a> function demonstrate a way to <a href="https://en.wikipedia.org/wiki/Iteration#Computing" title="iterate" class="https">iterate</a> in <a href="https://en.wikipedia.org/wiki/Common_Lisp" title="Common Lisp" class="https">Common Lisp</a>, with brief notes. I hope that by demonstrating many different ways that the same thing can be written, you can develop a sense for the character of the constructs afforded by the language, and of the variety of possible styles. Common Lisp is famously syntactically extensible via <a href="https://en.wikipedia.org/wiki/Common_Lisp#Macros" title="macros" class="https">macros</a>, so keep in mind that my examples are by no means the <i>only</i> ways to iterate.
</p>
<br>
<p>
For further reading on the iteration and control structures of Common Lisp, I heartily recommend:
</p>
<br>
<ul>
<li><a href="http://www.gigamonkeys.com/book/macros-standard-control-constructs.html" title="Chapter 7" class="http">Chapter 7</a> and <a href="http://www.gigamonkeys.com/book/loop-for-black-belts.html" title="Chapter 22" class="http">Chapter 22</a> of <a href="https://amzn.to/3nOWKa2" title="Practical Common Lisp" class="https">Practical Common Lisp</a> by Peter Siebel.</li>
<li>A reasonably-priced used copy of <a href="https://amzn.to/2UUTfm3" title="ANSI Common Lisp" class="https">ANSI Common Lisp</a> by Paul Graham.</li>
</ul>
<br>
<p>
<i>Note: several of the examples return nonsensical results for negative inputs. The addition of <tt>(assert (not (minusp n)) </tt>or similar is a good idea, but I have omitted it here for clarity.</i>
</p>
<br>
<h2>DOTIMES<a id="dotimes" class="h_anchor"></a></h2>
<pre>
(defun factorial-dotimes (n &amp;aux (prod 1))
  (dotimes (i n prod)
    (setq prod (* prod (1+ i)))))
</pre>
<br>
<ul>
<li><a href="http://www.lispworks.com/documentation/HyperSpec/Body/03_dae.htm" title="&amp;aux lambda list keyword" class="http"><tt>&amp;aux</tt> lambda list keyword</a> names a local variable <tt>prod</tt>. <a href="http://www.lispworks.com/documentation/HyperSpec/Body/s_let_l.htm" title="LET" class="http"><tt>LET</tt></a> could also be used for this purpose, but at the cost of more indentation.</li>
<li><a href="http://www.lispworks.com/documentation/lw50/CLHS/Body/m_dotime.htm" title="DOTIMES" class="http"><tt>DOTIMES</tt></a> binds <tt>i</tt> successively from 0 to 1-n and finally evaluates to <tt>prod</tt>.</li>
</ul>
<br>
<h2>DO<a id="do" class="h_anchor"></a></h2>
<pre>
(defun factorial-do (n)
  (do ((i 1 (1+ i))
       (prod 1 (* prod i)))
      ((&gt; i n) prod)))
</pre>
<br>
<ul>
<li><a href="http://www.lispworks.com/documentation/lw50/CLHS/Body/m_do_do.htm" title="DO" class="http"><tt>DO</tt></a> binds <tt>i</tt> to 1 and then to (1+ i) in subsequent iterations. <tt>prod</tt> is bound first to 1 and then to <tt>(* prod i)</tt> in subsequent iterations.</li>
<li>When the test clause <tt>(&gt; i n)</tt> becomes true, <tt>prod</tt> is returned. Contrast with the test clause of <tt>for</tt> loops in other languages, which terminate the loop when they become <i>false</i>.</li>
<li>I like the way Paul Graham explains <tt>DO </tt>and<tt> DO*</tt> in <a href="https://amzn.to/2UUTfm3" title="ANSI Common Lisp" class="https">ANSI Common Lisp</a>.</li>
</ul>
<br>
<h2>LOOP<a id="loop" class="h_anchor"></a></h2>
<pre>
(defun factorial-loop (n)
  (loop
     for i from 1 to n
     for prod = 1 then (* prod i)
     finally (return prod)))
</pre>
<br>
<ul>
<li><tt>i</tt> is bound from 1 to <tt>n</tt> inclusive.</li>
<li><tt>prod</tt> is bound to 1 and then <tt>(* prod i)</tt> in subsequent iterations in a manner similar to <tt>DO</tt>.</li>
<li>In the <tt>finally</tt> clause, <tt>prod</tt> is returned by <a href="http://www.lispworks.com/documentation/lw60/CLHS/Body/m_return.htm#return" title="RETURN" class="http"><tt>RETURN</tt></a> once iteration is complete. The <a href="http://www.lispworks.com/documentation/lw60/CLHS/Body/s_block.htm#block" title="BLOCK" class="http"><tt>BLOCK</tt></a> named NIL established by <tt>LOOP</tt> is the point of return.</li>
<li><a href="http://www.lispworks.com/documentation/lw50/CLHS/Body/m_loop.htm" title="LOOP" class="http"><tt>LOOP</tt></a> supports a comprehensive iteration and accumulation <a href="https://en.wikipedia.org/wiki/Domain-specific_language" title="DSL" class="https">DSL</a>. <a href="http://www.gigamonkeys.com/book/loop-for-black-belts.html" title="Chapter 22" class="http">Chapter 22</a> of <a href="https://amzn.to/3nOWKa2" title="Practical Common Lisp" class="https">Practical Common Lisp</a> offers a great introduction.</li>
</ul>
<br>
<p>
The preceding example demonstrates the "extended" form of <tt>LOOP</tt>. There's also "simple" form:
</p>
<br>
<pre>
(defun factorial-simple-loop (n &amp;aux (i 0) (prod 1))
  (loop
    (when (eql i n)
      (return prod))
    (setq prod (* prod (incf i)))))
</pre>
<br>
<h2>Recursion<a id="recursion" class="h_anchor"></a></h2>
<pre>
(defun factorial-recursive (n)
  (if (zerop n)
      1
      (* n (factorial-recursive (1- n)))))
</pre>
<br>
<ul>
<li><tt>FACTORIAL-RECURSIVE</tt> calls itself, but when <tt>n</tt> exceeds the maximum stack size supported by the implementation, an error is signaled.</li>
</ul>
<br>
<pre>
(defun factorial-tail-recursive (n)
  (labels ((recur (n prod)
             (if (zerop n)
                 prod
                 (recur (1- n) (* n prod)))))
    (recur n 1)))
</pre>
<br>
<ul>
<li><tt>FACTORIAL-TAIL-RECURSIVE </tt>does not call itself directly.</li>
<li>Instead, it defines with <a href="http://www.lispworks.com/documentation/HyperSpec/Body/s_flet_.htm" title="LABELS" class="http"><tt>LABELS</tt></a> an internal and recursive helper function, <tt>recur</tt>.</li>
<li>recur <a href="https://en.wikipedia.org/wiki/Tail_call" title="calls itself in tail position" class="https">calls itself in tail position</a> and the stack never overflows in implementations that implement tail-call elimination.</li>
</ul>
<br>
<pre>
(defun factorial-tail-recursive-opt (n &amp;optional (prod 1))
  (if (zerop n)
      prod
    (factorial-tail-recursive-opt (1- n) (* n prod))))
</pre>
<br>
<br>
<ul>
<li><tt>FACTORIAL-TAIL-RECURSIVE-OPT</tt> is also tail recursive, but uses the <tt>&amp;OPTIONAL</tt> lambda list keyword to maintain <tt>prod</tt> across iterations. This approach has the downside of exposing <tt>prod</tt> as part of the public interface of the function. Arguably, <tt>prod</tt> is an implementation detail, best kept internal.</li>
</ul>
<br>
<h2>PROG<a id="prog" class="h_anchor"></a></h2>
<pre>
(defun factorial-prog (n)
  (prog ((i 0) (prod 1))
   begin
   (when (eql i n)
     (return prod))
   (setq prod (* prod (incf i)))
   (go begin)))
</pre>
<br>
<ul>
<li>PROG supports both declaring local lexical variables (<tt>i</tt> and <tt>prod</tt>) and naming GO tags (<tt>begin</tt>).</li>
<li><tt>begin</tt> names a label within the <i>implicit <tt>TAGBODY</tt></i> enclosed by <tt>PROG</tt> that may be jumped to.</li>
<li><a href="http://www.lispworks.com/documentation/HyperSpec/Body/m_when_.htm" title="WHEN" class="http"><tt>WHEN</tt></a> <tt>i</tt> is <a href="http://www.lispworks.com/documentation/HyperSpec/Body/f_eql.htm" title="EQL" class="http"><tt>EQL</tt></a> to <tt>n</tt>, <a href="http://www.lispworks.com/documentation/lw60/CLHS/Body/s_ret_fr.htm" title="RETURN" class="http"><tt>RETURN</tt></a> returns <tt>prod</tt>.</li>
<li><a href="http://www.lispworks.com/documentation/HyperSpec/Body/s_go.htm" title="GO" class="http"><tt>GO</tt></a> jumps to <tt>begin</tt>.</li>
</ul>
<br>
<h2>TAGBODY<a id="tagbody" class="h_anchor"></a></h2>
<pre>
(defun factorial-tagbody (n &amp;aux (i 0) (prod 1))
  (tagbody
     begin
     (when (eql i n)
       (return-from factorial-tagbody prod))
     (setq prod (* prod (incf i)))
     (go begin)))
</pre>
<br>
<ul>
<li><a href="http://www.lispworks.com/documentation/HyperSpec/Body/s_tagbod.htm" title="TAGBODY" class="http"><tt>TAGBODY</tt></a> is the most general but also the lowest-level and most verbose iteration construct.</li>
<li><a href="http://www.lispworks.com/documentation/HyperSpec/Body/03_dae.htm" title="&amp;aux lambda list keyword" class="http"><tt>&amp;aux</tt> lambda list keyword</a> names local variables <tt>i</tt> and <tt>prod</tt>, initializing them to 0 and 1, respectively.</li>
<li><a href="http://www.lispworks.com/documentation/HyperSpec/Body/m_when_.htm" title="WHEN" class="http"><tt>WHEN</tt></a> <tt>i</tt> is <a href="http://www.lispworks.com/documentation/HyperSpec/Body/f_eql.htm" title="EQL" class="http"><tt>EQL</tt></a> to <tt>n</tt>, <a href="http://www.lispworks.com/documentation/lw60/CLHS/Body/s_ret_fr.htm" title="RETURN-FROM" class="http"><tt>RETURN-FROM</tt></a> returns <tt>prod</tt> from the <a href="http://www.lispworks.com/documentation/lw60/CLHS/Body/s_block.htm#block" title="BLOCK" class="http"><tt>BLOCK</tt></a> named after the function by <a href="http://www.lispworks.com/documentation/lw60/CLHS/Body/m_defun.htm" title="DEFUN" class="http"><tt>DEFUN</tt></a>.</li>
<li><a href="http://www.lispworks.com/documentation/HyperSpec/Body/s_go.htm" title="GO" class="http"><tt>GO</tt></a> jumps to <tt>begin</tt>.</li>
</ul>

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