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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>
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">"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>
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">"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>
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’t work, because SML functions take a fixed number
49 of arguments. Actually they take one argument, but if that’s a tuple,
50 it can only have a fixed number of components.</p></div>
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">"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>
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">"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>
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 -> int -> real -> unit
65 val printf: string -> int -> real -> real -> unit</pre>
67 <div class="paragraph"><p>This can’t work, because <span class="monospaced">printf</span> can only have one type. SML doesn’t
68 support programmer-defined overloading.</p></div>
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">"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>
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">"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>
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 -> int -> real -> unit
84 val printf: string -> real -> int -> unit</pre>
86 <div class="paragraph"><p>Again, this can’t possibly working because SML doesn’t have
87 overloading, and types can’t depend on values.</p></div>
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">'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">'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>
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">-></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>
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">-></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>
101 <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>
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>
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">'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>
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">-></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>
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">-></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>
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">-></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>
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">'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>
123 </pre></div></div></div>
124 <div class="paragraph"><p>Don’t worry. In the end, type inference will guess and verify for us.</p></div>
128 <h2 id="_understanding_guess_and_verify">Understanding guess and verify</h2>
129 <div class="sectionbody">
130 <div class="paragraph"><p>Now, let’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">"here's an int "</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">" and a real "</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">".</span><span class="se">\n</span><span class="s">"</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">-></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>
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">-></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>
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">-></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>
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">-></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>
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
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>
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">'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>
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">-></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>
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">-></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>
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">-></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>
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">'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>
164 <span class="w"> </span><span class="k">end</span><span class="w"></span>
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>
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">"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>
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">"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>
173 <span class="w"> </span><span class="k">end</span><span class="w"></span>
174 </pre></div></div></div>
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">'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>
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">=></span><span class="w"> </span><span class="p">())</span><span class="w"></span>
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">=></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>
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">=></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>
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>
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">=></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>
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>
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>
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
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">'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>
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">=></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>
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">=></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>
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">=></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">=></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>
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">'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>
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">-></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>
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">'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>
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">'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>
239 <span class="w"> </span><span class="k">end</span><span class="w"></span>
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">'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>
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">=></span><span class="w"> </span><span class="p">())</span><span class="w"></span>
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">=></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>
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">=></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">=></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>
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>
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">'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>
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">-></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>
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">'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>
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">'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>
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">'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>
272 <span class="w"> </span><span class="k">end</span><span class="w"></span>
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>
279 <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>
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">=></span><span class="w"> </span><span class="p">())</span><span class="w"> </span><span class="n">out</span><span class="w"></span>
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>
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">=></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>
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">=></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">=></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>
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>
298 <h2 id="_notes">Notes</h2>
299 <div class="sectionbody">
300 <div class="ulist"><ul>
303 Lesson: instead of using dependent types for a function, express the
304 the dependency in the type of the argument.
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.
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">'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>
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">""</span><span class="w"></span>
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">=></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>
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">=></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'</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>
328 <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>
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">'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>
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>
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">=></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>
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">=></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">=></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>
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>
352 <h2 id="_also_see">Also see</h2>
353 <div class="sectionbody">
354 <div class="ulist"><ul>
357 <a href="Printf">Printf</a>
362 <a href="References#Danvy98"> Functional Unparsing</a>
369 <div id="footnotes"><hr></div>
371 <div id="footer-text">
373 <div id="footer-badges">