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<a href="./Home">MLton 20130715</a>
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<h1>PrintfGentle</h1>
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  <div id="toctitle">Table of Contents</div>
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<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph"><p>This page provides a gentle introduction and derivation of <a href="Printf">Printf</a>,
with sections and arrangement more suitable to a talk.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_introduction">Introduction</h2>
<div class="sectionbody">
<div class="paragraph"><p>SML does not have <span class="monospaced">printf</span>.  Could we define it ourselves?</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;here&#39;s an int %d and a real %f.</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">13</span><span class="p">,</span><span class="w"> </span><span class="mf">17.0</span><span class="p">)</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;here&#39;s three values (%d, %f, %f).</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">13</span><span class="p">,</span><span class="w"> </span><span class="mf">17.0</span><span class="p">,</span><span class="w"> </span><span class="mf">19.0</span><span class="p">)</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>What could the type of <span class="monospaced">printf</span> be?</p></div>
<div class="paragraph"><p>This obviously can&#8217;t work, because SML functions take a fixed number
of arguments.  Actually they take one argument, but if that&#8217;s a tuple,
it can only have a fixed number of components.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_from_tupling_to_currying">From tupling to currying</h2>
<div class="sectionbody">
<div class="paragraph"><p>What about currying to get around the typing problem?</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="s">&quot;here&#39;s an int %d and a real %f.</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="s">&quot;here&#39;s three values (%d, %f, %f).</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"> </span><span class="mf">19.0</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>That fails for a similar reason.  We need two types for <span class="monospaced">printf</span>.</p></div>
<div class="listingblock">
<div class="content monospaced">
<pre>val printf: string -&gt; int -&gt; real -&gt; unit
val printf: string -&gt; int -&gt; real -&gt; real -&gt; unit</pre>
</div></div>
<div class="paragraph"><p>This can&#8217;t work, because <span class="monospaced">printf</span> can only have one type.  SML doesn&#8217;t
support programmer-defined overloading.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_overloading_and_dependent_types">Overloading and dependent types</h2>
<div class="sectionbody">
<div class="paragraph"><p>Even without worrying about number of arguments, there is another
problem.  The type of <span class="monospaced">printf</span> depends on the format string.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="s">&quot;here&#39;s an int %d and a real %f.</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="s">&quot;here&#39;s a real %f and an int %d.</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"> </span><span class="mf">17.0</span><span class="w"> </span><span class="mi">13</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>Now we need</p></div>
<div class="listingblock">
<div class="content monospaced">
<pre>val printf: string -&gt; int -&gt; real -&gt; unit
val printf: string -&gt; real -&gt; int -&gt; unit</pre>
</div></div>
<div class="paragraph"><p>Again, this can&#8217;t possibly working because SML doesn&#8217;t have
overloading, and types can&#8217;t depend on values.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_idea_express_type_information_in_the_format_string">Idea: express type information in the format string</h2>
<div class="sectionbody">
<div class="paragraph"><p>If we express type information in the format string, then different
uses of <span class="monospaced">printf</span> can have different types.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">type</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w">  </span><span class="cm">(* the type of format strings *)</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">printf</span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
<span class="k">infix</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="n">F</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">fs1</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;here&#39;s an int &quot;</span><span class="n">D</span><span class="s">&quot; and a real &quot;</span><span class="n">F</span><span class="s">&quot;.</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">fs2</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="s">&quot;here&#39;s three values (&quot;</span><span class="n">D</span><span class="s">&quot;, &quot;</span><span class="n">F</span><span class="s">&quot;, &quot;</span><span class="n">F</span><span class="s">&quot;).</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="n">fs1</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="n">fs2</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"> </span><span class="mf">19.0</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>Now, our two calls to <span class="monospaced">printf</span> type check, because the format
string specializes <span class="monospaced">printf</span> to the appropriate type.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_the_types_of_format_characters">The types of format characters</h2>
<div class="sectionbody">
<div class="paragraph"><p>What should the type of format characters <span class="monospaced">D</span> and <span class="monospaced">F</span> be?  Each format
character requires an additional argument of the appropriate type to
be supplied to <span class="monospaced">printf</span>.</p></div>
<div class="paragraph"><p>Idea: guess the final type that will be needed for <span class="monospaced">printf</span> the format
string and verify it with each format character.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">type</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w">   </span><span class="cm">(* &#39;a = rest of type to verify, &#39;b = final type *)</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w">  </span><span class="cm">(* guess the type, which must be verified *)</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">D</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w">  </span><span class="cm">(* consume an int *)</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">F</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w">  </span><span class="cm">(* consume a real *)</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">printf</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>Don&#8217;t worry.  In the end, type inference will guess and verify for us.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_understanding_guess_and_verify">Understanding guess and verify</h2>
<div class="sectionbody">
<div class="paragraph"><p>Now, let&#8217;s build up a format string and a specialized <span class="monospaced">printf</span>.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">infix</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="n">F</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">f0</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">`</span><span class="s">&quot;here&#39;s an int &quot;</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">f1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f0</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="s">&quot; and a real &quot;</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">f2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f1</span><span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="s">&quot;.</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="n">f2</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>These definitions yield the following types.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="n">f0</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">f1</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">f2</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">p</span><span class="p">:</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>So, <span class="monospaced">p</span> is a specialized <span class="monospaced">printf</span> function.  We could use it as
follows</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="mi">14</span><span class="w"> </span><span class="mf">19.0</span><span class="w"></span>
</pre></div></div></div>
</div>
</div>
<div class="sect1">
<h2 id="_type_checking_this_using_a_functor">Type checking this using a functor</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">signature</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">sig</span><span class="w"></span>
<span class="w">      </span><span class="k">type</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">D</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">F</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">real</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">printf</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>

<span class="k">functor</span><span class="w"> </span><span class="n">Test</span><span class="w"> </span><span class="p">(</span><span class="n">P</span><span class="p">:</span><span class="w"> </span><span class="n">PRINTF</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><span class="k">open</span><span class="w"> </span><span class="n">P</span><span class="w"></span>
<span class="w">      </span><span class="k">infix</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="n">F</span><span class="w"></span>

<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">`</span><span class="s">&quot;here&#39;s an int &quot;</span><span class="n">D</span><span class="s">&quot; and a real &quot;</span><span class="n">F</span><span class="s">&quot;.</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">)</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">`</span><span class="s">&quot;here&#39;s three values (&quot;</span><span class="n">D</span><span class="s">&quot;, &quot;</span><span class="n">F</span><span class="w"> </span><span class="s">&quot;, &quot;</span><span class="n">F</span><span class="s">&quot;).</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">)</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="mf">17.0</span><span class="w"> </span><span class="mf">19.0</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
</div>
</div>
<div class="sect1">
<h2 id="_implementing_span_class_monospaced_printf_span">Implementing <span class="monospaced">Printf</span></h2>
<div class="sectionbody">
<div class="paragraph"><p>Think of a format character as a formatter transformer.  It takes the
formatter for the part of the format string before it and transforms
it into a new formatter that first does the left hand bit, then does
its bit, then continues on with the rest of the format string.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Printf</span><span class="p">:</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><span class="k">datatype</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">())</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="n">s</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">()))</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">         </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">                       </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="n">Int</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">i</span><span class="p">);</span><span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="n">s</span><span class="p">;</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">())))</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">         </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">                       </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="n">Real</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">i</span><span class="p">);</span><span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="n">s</span><span class="p">;</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">())))</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
</div>
</div>
<div class="sect1">
<h2 id="_testing_printf">Testing printf</h2>
<div class="sectionbody">
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Z</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Test</span><span class="w"> </span><span class="p">(</span><span class="n">Printf</span><span class="p">)</span><span class="w"></span>
</pre></div></div></div>
</div>
</div>
<div class="sect1">
<h2 id="_user_definable_formats">User-definable formats</h2>
<div class="sectionbody">
<div class="paragraph"><p>The definition of the format characters is pretty much the same.
Within the <span class="monospaced">Printf</span> structure we can define a format character
generator.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="n">newFormat</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">string</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">fn</span><span class="w"> </span><span class="n">toString</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">   </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="n">toString</span><span class="w"> </span><span class="n">a</span><span class="p">);</span><span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="p">;</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">())))</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">newFormat</span><span class="w"> </span><span class="n">Int</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">z</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">newFormat</span><span class="w"> </span><span class="n">Real</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">z</span><span class="w"></span>
</pre></div></div></div>
</div>
</div>
<div class="sect1">
<h2 id="_a_core_span_class_monospaced_printf_span">A core <span class="monospaced">Printf</span></h2>
<div class="sectionbody">
<div class="paragraph"><p>We can now have a very small <span class="monospaced">PRINTF</span> signature, and define all
the format strings externally to the core module.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">signature</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">sig</span><span class="w"></span>
<span class="w">      </span><span class="k">type</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">newFormat</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">string</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">printf</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>

<span class="k">structure</span><span class="w"> </span><span class="n">Printf</span><span class="p">:</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><span class="k">datatype</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">())</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="n">s</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">()))</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">newFormat</span><span class="w"> </span><span class="n">toString</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">         </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">            </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">               </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="n">toString</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"></span>
<span class="w">                </span><span class="p">;</span><span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="n">s</span><span class="w"></span>
<span class="w">                </span><span class="p">;</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">())))</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
</div>
</div>
<div class="sect1">
<h2 id="_extending_to_fprintf">Extending to fprintf</h2>
<div class="sectionbody">
<div class="paragraph"><p>One can implement fprintf by threading the outstream through all the
transformers.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">signature</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">sig</span><span class="w"></span>
<span class="w">      </span><span class="k">type</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">fprintf</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">TextIO</span><span class="p">.</span><span class="n">outstream</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">newFormat</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">string</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">printf</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>

<span class="k">structure</span><span class="w"> </span><span class="n">Printf</span><span class="p">:</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><span class="k">type</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TextIO</span><span class="p">.</span><span class="n">outstream</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">output</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TextIO</span><span class="p">.</span><span class="n">output</span><span class="w"></span>

<span class="w">      </span><span class="k">datatype</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">(</span><span class="n">out</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">fprintf</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">out</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">())</span><span class="w"> </span><span class="n">out</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">fprintf</span><span class="w"> </span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="n">TextIO</span><span class="p">.</span><span class="n">stdOut</span><span class="p">)</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">output</span><span class="w"> </span><span class="p">(</span><span class="n">out</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">);</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="n">out</span><span class="p">))</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">newFormat</span><span class="w"> </span><span class="n">toString</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">         </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">            </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">               </span><span class="p">(</span><span class="n">output</span><span class="w"> </span><span class="p">(</span><span class="n">out</span><span class="p">,</span><span class="w"> </span><span class="n">toString</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"></span>
<span class="w">                </span><span class="p">;</span><span class="w"> </span><span class="n">output</span><span class="w"> </span><span class="p">(</span><span class="n">out</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"></span>
<span class="w">                </span><span class="p">;</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="n">out</span><span class="p">)))</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
</div>
</div>
<div class="sect1">
<h2 id="_notes">Notes</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
Lesson: instead of using dependent types for a function, express the
the dependency in the type of the argument.
</p>
</li>
<li>
<p>
If <span class="monospaced">printf</span> is partially applied, it will do the printing then and
there.  Perhaps this could be fixed with some kind of terminator.
</p>
<div class="paragraph"><p>A syntactic or argument terminator is not necessary.  A formatter can
either be eager (as above) or lazy (as below).  A lazy formatter
accumulates enough state to print the entire string.  The simplest
lazy formatter concatenates the strings as they become available:</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">PrintfLazyConcat</span><span class="p">:</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><span class="k">datatype</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">s&#39;</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">(</span><span class="n">s&#39;</span><span class="w"> </span><span class="n">^</span><span class="w"> </span><span class="n">s</span><span class="p">))</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">newFormat</span><span class="w"> </span><span class="n">toString</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">         </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">            </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">s&#39;</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">               </span><span class="n">th</span><span class="w"> </span><span class="p">(</span><span class="n">s&#39;</span><span class="w"> </span><span class="n">^</span><span class="w"> </span><span class="n">toString</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="n">^</span><span class="w"> </span><span class="n">s</span><span class="p">)))</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>It is somewhat more efficient to accumulate the strings as a list:</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">PrintfLazyList</span><span class="p">:</span><span class="w"> </span><span class="n">PRINTF</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><span class="k">datatype</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">app</span><span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="n">o</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">rev</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">ss</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">(</span><span class="n">s::ss</span><span class="p">))</span><span class="w"></span>

<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">newFormat</span><span class="w"> </span><span class="n">toString</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">         </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">            </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">ss</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">               </span><span class="n">th</span><span class="w"> </span><span class="p">(</span><span class="n">s::toString</span><span class="w"> </span><span class="n">a::ss</span><span class="p">)))</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
</li>
</ul></div>
</div>
</div>
<div class="sect1">
<h2 id="_also_see">Also see</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
<a href="Printf">Printf</a>
</p>
</li>
<li>
<p>
<a href="References#Danvy98"> Functional Unparsing</a>
</p>
</li>
</ul></div>
</div>
</div>
</div>
<div id="footnotes"><hr></div>
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