doc/guide/localhost/PrintfGentle

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  22 <a href="./Home">MLton 20180207</a>
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  26 <h1>PrintfGentle</h1>
  27 <div id="toc">
  28   <div id="toctitle">Table of Contents</div>
  29   <noscript><p><b>JavaScript must be enabled in your browser to display the table of contents.</b></p></noscript>
  30 </div>
  31 </div>
  32 <div id="content">
  33 <div id="preamble">
  34 <div class="sectionbody">
  35 <div class="paragraph"><p>This page provides a gentle introduction and derivation of <a href="Printf">Printf</a>,
  36 with sections and arrangement more suitable to a talk.</p></div>
  37 </div>
  38 </div>
  39 <div class="sect1">
  40 <h2 id="_introduction">Introduction</h2>
  41 <div class="sectionbody">
  42 <div class="paragraph"><p>SML does not have <span class="monospaced">printf</span>.  Could we define it ourselves?</p></div>
  43 <div class="listingblock">
  44 <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>
  45 <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>
  46 </pre></div></div></div>
  47 <div class="paragraph"><p>What could the type of <span class="monospaced">printf</span> be?</p></div>
  48 <div class="paragraph"><p>This obviously can&#8217;t work, because SML functions take a fixed number
  49 of arguments.  Actually they take one argument, but if that&#8217;s a tuple,
  50 it can only have a fixed number of components.</p></div>
  51 </div>
  52 </div>
  53 <div class="sect1">
  54 <h2 id="_from_tupling_to_currying">From tupling to currying</h2>
  55 <div class="sectionbody">
  56 <div class="paragraph"><p>What about currying to get around the typing problem?</p></div>
  57 <div class="listingblock">
  58 <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>
  59 <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>
  60 </pre></div></div></div>
  61 <div class="paragraph"><p>That fails for a similar reason.  We need two types for <span class="monospaced">printf</span>.</p></div>
  62 <div class="listingblock">
  63 <div class="content monospaced">
  64 <pre>val printf: string -&gt; int -&gt; real -&gt; unit
  65 val printf: string -&gt; int -&gt; real -&gt; real -&gt; unit</pre>
  66 </div></div>
  67 <div class="paragraph"><p>This can&#8217;t work, because <span class="monospaced">printf</span> can only have one type.  SML doesn&#8217;t
  68 support programmer-defined overloading.</p></div>
  69 </div>
  70 </div>
  71 <div class="sect1">
  72 <h2 id="_overloading_and_dependent_types">Overloading and dependent types</h2>
  73 <div class="sectionbody">
  74 <div class="paragraph"><p>Even without worrying about number of arguments, there is another
  75 problem.  The type of <span class="monospaced">printf</span> depends on the format string.</p></div>
  76 <div class="listingblock">
  77 <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>
  78 <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>
  79 </pre></div></div></div>
  80 <div class="paragraph"><p>Now we need</p></div>
  81 <div class="listingblock">
  82 <div class="content monospaced">
  83 <pre>val printf: string -&gt; int -&gt; real -&gt; unit
  84 val printf: string -&gt; real -&gt; int -&gt; unit</pre>
  85 </div></div>
  86 <div class="paragraph"><p>Again, this can&#8217;t possibly working because SML doesn&#8217;t have
  87 overloading, and types can&#8217;t depend on values.</p></div>
  88 </div>
  89 </div>
  90 <div class="sect1">
  91 <h2 id="_idea_express_type_information_in_the_format_string">Idea: express type information in the format string</h2>
  92 <div class="sectionbody">
  93 <div class="paragraph"><p>If we express type information in the format string, then different
  94 uses of <span class="monospaced">printf</span> can have different types.</p></div>
  95 <div class="listingblock">
  96 <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>
  97 <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>
  98 <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>
  99 <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>
 100 <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>
 101 <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>
 102 <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>
 103 <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>
 104 </pre></div></div></div>
 105 <div class="paragraph"><p>Now, our two calls to <span class="monospaced">printf</span> type check, because the format
 106 string specializes <span class="monospaced">printf</span> to the appropriate type.</p></div>
 107 </div>
 108 </div>
 109 <div class="sect1">
 110 <h2 id="_the_types_of_format_characters">The types of format characters</h2>
 111 <div class="sectionbody">
 112 <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
 113 character requires an additional argument of the appropriate type to
 114 be supplied to <span class="monospaced">printf</span>.</p></div>
 115 <div class="paragraph"><p>Idea: guess the final type that will be needed for <span class="monospaced">printf</span> the format
 116 string and verify it with each format character.</p></div>
 117 <div class="listingblock">
 118 <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>
 119 <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>
 120 <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>
 121 <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>
 122 <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>
 123 </pre></div></div></div>
 124 <div class="paragraph"><p>Don&#8217;t worry.  In the end, type inference will guess and verify for us.</p></div>
 125 </div>
 126 </div>
 127 <div class="sect1">
 128 <h2 id="_understanding_guess_and_verify">Understanding guess and verify</h2>
 129 <div class="sectionbody">
 130 <div class="paragraph"><p>Now, let&#8217;s build up a format string and a specialized <span class="monospaced">printf</span>.</p></div>
 131 <div class="listingblock">
 132 <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>
 133 <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>
 134 <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>
 135 <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>
 136 <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>
 137 </pre></div></div></div>
 138 <div class="paragraph"><p>These definitions yield the following types.</p></div>
 139 <div class="listingblock">
 140 <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>
 141 <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>
 142 <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>
 143 <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>
 144 </pre></div></div></div>
 145 <div class="paragraph"><p>So, <span class="monospaced">p</span> is a specialized <span class="monospaced">printf</span> function.  We could use it as
 146 follows</p></div>
 147 <div class="listingblock">
 148 <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>
 149 <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>
 150 </pre></div></div></div>
 151 </div>
 152 </div>
 153 <div class="sect1">
 154 <h2 id="_type_checking_this_using_a_functor">Type checking this using a functor</h2>
 155 <div class="sectionbody">
 156 <div class="listingblock">
 157 <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>
 158 <span class="w">   </span><span class="k">sig</span><span class="w"></span>
 159 <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>
 160 <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>
 161 <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>
 162 <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>
 163 <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>
 164 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 165
 166 <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>
 167 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
 168 <span class="w">      </span><span class="k">open</span><span class="w"> </span><span class="n">P</span><span class="w"></span>
 169 <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>
 170
 171 <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>
 172 <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>
 173 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 174 </pre></div></div></div>
 175 </div>
 176 </div>
 177 <div class="sect1">
 178 <h2 id="_implementing_span_class_monospaced_printf_span">Implementing <span class="monospaced">Printf</span></h2>
 179 <div class="sectionbody">
 180 <div class="paragraph"><p>Think of a format character as a formatter transformer.  It takes the
 181 formatter for the part of the format string before it and transforms
 182 it into a new formatter that first does the left hand bit, then does
 183 its bit, then continues on with the rest of the format string.</p></div>
 184 <div class="listingblock">
 185 <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>
 186 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
 187 <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>
 188
 189 <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>
 190
 191 <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>
 192
 193 <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>
 194 <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>
 195 <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>
 196
 197 <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>
 198 <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>
 199 <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>
 200 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 201 </pre></div></div></div>
 202 </div>
 203 </div>
 204 <div class="sect1">
 205 <h2 id="_testing_printf">Testing printf</h2>
 206 <div class="sectionbody">
 207 <div class="listingblock">
 208 <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>
 209 </pre></div></div></div>
 210 </div>
 211 </div>
 212 <div class="sect1">
 213 <h2 id="_user_definable_formats">User-definable formats</h2>
 214 <div class="sectionbody">
 215 <div class="paragraph"><p>The definition of the format characters is pretty much the same.
 216 Within the <span class="monospaced">Printf</span> structure we can define a format character
 217 generator.</p></div>
 218 <div class="listingblock">
 219 <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>
 220 <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>
 221 <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>
 222 <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>
 223 <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>
 224 </pre></div></div></div>
 225 </div>
 226 </div>
 227 <div class="sect1">
 228 <h2 id="_a_core_span_class_monospaced_printf_span">A core <span class="monospaced">Printf</span></h2>
 229 <div class="sectionbody">
 230 <div class="paragraph"><p>We can now have a very small <span class="monospaced">PRINTF</span> signature, and define all
 231 the format strings externally to the core module.</p></div>
 232 <div class="listingblock">
 233 <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>
 234 <span class="w">   </span><span class="k">sig</span><span class="w"></span>
 235 <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>
 236 <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>
 237 <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>
 238 <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>
 239 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 240
 241 <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>
 242 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
 243 <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>
 244
 245 <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>
 246
 247 <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>
 248
 249 <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>
 250 <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>
 251 <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>
 252 <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>
 253 <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>
 254 <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>
 255 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 256 </pre></div></div></div>
 257 </div>
 258 </div>
 259 <div class="sect1">
 260 <h2 id="_extending_to_fprintf">Extending to fprintf</h2>
 261 <div class="sectionbody">
 262 <div class="paragraph"><p>One can implement fprintf by threading the outstream through all the
 263 transformers.</p></div>
 264 <div class="listingblock">
 265 <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>
 266 <span class="w">   </span><span class="k">sig</span><span class="w"></span>
 267 <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>
 268 <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>
 269 <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>
 270 <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>
 271 <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>
 272 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 273
 274 <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>
 275 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
 276 <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>
 277 <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>
 278
 279 <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>
 280
 281 <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>
 282
 283 <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>
 284
 285 <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>
 286
 287 <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>
 288 <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>
 289 <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>
 290 <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>
 291 <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>
 292 <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>
 293 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 294 </pre></div></div></div>
 295 </div>
 296 </div>
 297 <div class="sect1">
 298 <h2 id="_notes">Notes</h2>
 299 <div class="sectionbody">
 300 <div class="ulist"><ul>
 301 <li>
 302 <p>
 303 Lesson: instead of using dependent types for a function, express the
 304 the dependency in the type of the argument.
 305 </p>
 306 </li>
 307 <li>
 308 <p>
 309 If <span class="monospaced">printf</span> is partially applied, it will do the printing then and
 310 there.  Perhaps this could be fixed with some kind of terminator.
 311 </p>
 312 <div class="paragraph"><p>A syntactic or argument terminator is not necessary.  A formatter can
 313 either be eager (as above) or lazy (as below).  A lazy formatter
 314 accumulates enough state to print the entire string.  The simplest
 315 lazy formatter concatenates the strings as they become available:</p></div>
 316 <div class="listingblock">
 317 <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>
 318 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
 319 <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>
 320
 321 <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>
 322
 323 <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>
 324
 325 <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>
 326 <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>
 327 <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>
 328 <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>
 329 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 330 </pre></div></div></div>
 331 <div class="paragraph"><p>It is somewhat more efficient to accumulate the strings as a list:</p></div>
 332 <div class="listingblock">
 333 <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>
 334 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
 335 <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>
 336
 337 <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>
 338
 339 <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>
 340
 341 <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>
 342 <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>
 343 <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>
 344 <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>
 345 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 346 </pre></div></div></div>
 347 </li>
 348 </ul></div>
 349 </div>
 350 </div>
 351 <div class="sect1">
 352 <h2 id="_also_see">Also see</h2>
 353 <div class="sectionbody">
 354 <div class="ulist"><ul>
 355 <li>
 356 <p>
 357 <a href="Printf">Printf</a>
 358 </p>
 359 </li>
 360 <li>
 361 <p>
 362 <a href="References#Danvy98"> Functional Unparsing</a>
 363 </p>
 364 </li>
 365 </ul></div>
 366 </div>
 367 </div>
 368 </div>
 369 <div id="footnotes"><hr></div>
 370 <div id="footer">
 371 <div id="footer-text">
 372 </div>
 373 <div id="footer-badges">
 374 </div>
 375 </div>
 376 </body>
 377 </html>