<!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <meta name="generator" content="AsciiDoc 8.6.8"> <title>PrintfGentle</title> <link rel="stylesheet" href="./asciidoc.css" type="text/css"> <link rel="stylesheet" href="./pygments.css" type="text/css"> <script type="text/javascript" src="./asciidoc.js"></script> <script type="text/javascript"> /*<![CDATA[*/ asciidoc.install(2); /*]]>*/ </script> <link rel="stylesheet" href="./mlton.css" type="text/css"/> </head> <body class="article"> <div id="banner"> <div id="banner-home"> <a href="./Home">MLton 20130715</a> </div> </div> <div id="header"> <h1>PrintfGentle</h1> <div id="toc"> <div id="toctitle">Table of Contents</div> <noscript><p><b>JavaScript must be enabled in your browser to display the table of contents.</b></p></noscript> </div> </div> <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">"here's an int %d and a real %f.</span><span class="se">\n</span><span class="s">"</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">"here's three values (%d, %f, %f).</span><span class="se">\n</span><span class="s">"</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’t work, because SML functions take a fixed number of arguments. Actually they take one argument, but if that’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">"here's an int %d and a real %f.</span><span class="se">\n</span><span class="s">"</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">"here's three values (%d, %f, %f).</span><span class="se">\n</span><span class="s">"</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 -> int -> real -> unit val printf: string -> int -> real -> real -> unit</pre> </div></div> <div class="paragraph"><p>This can’t work, because <span class="monospaced">printf</span> can only have one type. SML doesn’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">"here's an int %d and a real %f.</span><span class="se">\n</span><span class="s">"</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">"here's a real %f and an int %d.</span><span class="se">\n</span><span class="s">"</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 -> int -> real -> unit val printf: string -> real -> int -> unit</pre> </div></div> <div class="paragraph"><p>Again, this can’t possibly working because SML doesn’t have overloading, and types can’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">'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">'a</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">'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">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></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">"here's an int "</span><span class="n">D</span><span class="s">" and a real "</span><span class="n">F</span><span class="s">".</span><span class="se">\n</span><span class="s">"</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">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></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">"here's three values ("</span><span class="n">D</span><span class="s">", "</span><span class="n">F</span><span class="s">", "</span><span class="n">F</span><span class="s">").</span><span class="se">\n</span><span class="s">"</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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="cm">(* 'a = rest of type to verify, '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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">'a</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">'a</span><span class="w"></span> </pre></div></div></div> <div class="paragraph"><p>Don’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’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">"here's an int "</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">" and a real "</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">".</span><span class="se">\n</span><span class="s">"</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">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></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">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></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">-></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">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></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">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></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">-></span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">'a</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">'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">"here's an int "</span><span class="n">D</span><span class="s">" and a real "</span><span class="n">F</span><span class="s">".</span><span class="se">\n</span><span class="s">"</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">"here's three values ("</span><span class="n">D</span><span class="s">", "</span><span class="n">F</span><span class="w"> </span><span class="s">", "</span><span class="n">F</span><span class="s">").</span><span class="se">\n</span><span class="s">"</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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'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">=></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">=></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">=></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">=></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">=></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">=></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">=></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">=></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">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">string</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'b</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'b</span><span class="p">,</span><span class="w"> </span><span class="n">'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">=></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">=></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">=></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">=></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">=></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">=></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">=></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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">string</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'b</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'b</span><span class="p">,</span><span class="w"> </span><span class="n">'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">'a</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">'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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'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">=></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">=></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">=></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">=></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">=></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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">'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">-></span><span class="w"> </span><span class="n">'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">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">string</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'b</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="p">(</span><span class="n">'b</span><span class="p">,</span><span class="w"> </span><span class="n">'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">'a</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">'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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">)</span><span class="w"> </span><span class="p">-></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">'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">=></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">=></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">=></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">=></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">=></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">=></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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">)</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">-></span><span class="w"> </span><span class="n">'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">""</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">=></span><span class="w"> </span><span class="k">fn</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="n">s'</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">=></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'</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">a</span><span class="w"> </span><span class="p">=></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'</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">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'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">-></span><span class="w"> </span><span class="n">'a</span><span class="p">)</span><span class="w"> </span><span class="p">-></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">-></span><span class="w"> </span><span class="n">'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">=></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">=></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">=></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">=></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">=></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> <div id="footer"> <div id="footer-text"> </div> <div 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