doc/guide/localhost/ObjectOrientedProgramming

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  26 <h1>ObjectOrientedProgramming</h1>
  27 </div>
  28 <div id="content">
  29 <div id="preamble">
  30 <div class="sectionbody">
  31 <div class="paragraph"><p><a href="StandardML">Standard ML</a> does not have explicit support for
  32 object-oriented programming.  Here are some papers that show how to
  33 express certain object-oriented concepts in SML.</p></div>
  34 <div class="ulist"><ul>
  35 <li>
  36 <p>
  37 <a href="References#Berthomieu00"> OO Programming styles in ML</a>
  38 </p>
  39 </li>
  40 <li>
  41 <p>
  42 <a href="References#ThorupTofte94"> Object-oriented programming and Standard ML</a>
  43 </p>
  44 </li>
  45 <li>
  46 <p>
  47 <a href="References#LarsenNiss04"> mGTK: An SML binding of Gtk+</a>
  48 </p>
  49 </li>
  50 <li>
  51 <p>
  52 <a href="References#FluetPucella06"> Phantom Types and Subtyping</a>
  53 </p>
  54 </li>
  55 </ul></div>
  56 <div class="paragraph"><p>The question of OO programming in SML comes up every now and then.
  57 The following discusses a simple object-oriented (OO) programming
  58 technique in Standard ML.  The reader is assumed to be able to read
  59 Java and SML code.</p></div>
  60 </div>
  61 </div>
  62 <div class="sect1">
  63 <h2 id="_motivation">Motivation</h2>
  64 <div class="sectionbody">
  65 <div class="paragraph"><p>SML doesn&#8217;t provide subtyping, but it does provide parametric
  66 polymorphism, which can be used to encode some forms of subtyping.
  67 Most articles on OO programming in SML concentrate on such encoding
  68 techniques.  While those techniques are interesting&#8201;&#8212;&#8201;and it is
  69 recommended to read such articles&#8201;&#8212;&#8201;and sometimes useful, it seems
  70 that basically all OO gurus agree that (deep) subtyping (or
  71 inheritance) hierarchies aren&#8217;t as practical as they were thought to
  72 be in the early OO days.  "Good", flexible, "OO" designs tend to have
  73 a flat structure</p></div>
  74 <div class="listingblock">
  75 <div class="content monospaced">
  76 <pre>         Interface
  77              ^
  78              |
  79 - - -+-------+-------+- - -
  80      |       |       |
  81    ImplA   ImplB   ImplC</pre>
  82 </div></div>
  83 <div class="paragraph"><p>and deep inheritance hierarchies</p></div>
  84 <div class="listingblock">
  85 <div class="content monospaced">
  86 <pre>ClassA
  87   ^
  88   |
  89 ClassB
  90   ^
  91   |
  92 ClassC
  93   ^
  94   |</pre>
  95 </div></div>
  96 <div class="paragraph"><p>tend to be signs of design mistakes.  There are good underlying
  97 reasons for this, but a thorough discussion is not in the scope of
  98 this article.  However, the point is that perhaps the encoding of
  99 subtyping is not as important as one might believe.  In the following
 100 we ignore subtyping and rather concentrate on a very simple and basic
 101 dynamic dispatch technique.</p></div>
 102 </div>
 103 </div>
 104 <div class="sect1">
 105 <h2 id="_dynamic_dispatch_using_a_recursive_record_of_functions">Dynamic Dispatch Using a Recursive Record of Functions</h2>
 106 <div class="sectionbody">
 107 <div class="paragraph"><p>Quite simply, the basic idea is to implement a "virtual function
 108 table" using a record that is wrapped inside a (possibly recursive)
 109 datatype.  Let&#8217;s first take a look at a simple concrete example.</p></div>
 110 <div class="paragraph"><p>Consider the following Java interface:</p></div>
 111 <div class="listingblock">
 112 <div class="content monospaced">
 113 <pre>public interface Counter {
 114   public void inc();
 115   public int get();
 116 }</pre>
 117 </div></div>
 118 <div class="paragraph"><p>We can translate the <span class="monospaced">Counter</span> interface to SML as follows:</p></div>
 119 <div class="listingblock">
 120 <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Counter</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">{</span><span class="n">inc</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">,</span><span class="w"> </span><span class="n">get</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">int</span><span class="p">}</span><span class="w"></span>
 121 </pre></div></div></div>
 122 <div class="paragraph"><p>Each value of type <span class="monospaced">counter</span> can be thought of as an object that
 123 responds to two messages <span class="monospaced">inc</span> and <span class="monospaced">get</span>.  To actually send messages
 124 to a counter, it is useful to define auxiliary functions</p></div>
 125 <div class="listingblock">
 126 <div class="content"><div class="highlight"><pre><span class="k">local</span><span class="w"></span>
 127 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">mk</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">(</span><span class="n">Counter</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">()</span><span class="w"></span>
 128 <span class="k">in</span><span class="w"></span>
 129 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">cGet</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">mk</span><span class="p">#</span><span class="n">get</span><span class="w"></span>
 130 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">cInc</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">mk</span><span class="p">#</span><span class="n">inc</span><span class="w"></span>
 131 <span class="k">end</span><span class="w"></span>
 132 </pre></div></div></div>
 133 <div class="paragraph"><p>that basically extract the "function table" <span class="monospaced">t</span> from a counter object
 134 and then select the specified method <span class="monospaced">m</span> from the table.</p></div>
 135 <div class="paragraph"><p>Let&#8217;s then implement a simple function that increments a counter until a
 136 given maximum is reached:</p></div>
 137 <div class="listingblock">
 138 <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">incUpto</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">cGet</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="n">&lt;</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="n">cInc</span><span class="w"> </span><span class="n">counter</span><span class="w"></span>
 139 </pre></div></div></div>
 140 <div class="paragraph"><p>You can easily verify that the above code compiles even without any
 141 concrete implementation of a counter, thus it is clear that it doesn&#8217;t
 142 depend on a particular counter implementation.</p></div>
 143 <div class="paragraph"><p>Let&#8217;s then implement a couple of counters.  First consider the
 144 following Java class implementing the <span class="monospaced">Counter</span> interface given earlier.</p></div>
 145 <div class="listingblock">
 146 <div class="content monospaced">
 147 <pre>public class BasicCounter implements Counter {
 148   private int cnt;
 149   public BasicCounter(int initialCnt) { this.cnt = initialCnt; }
 150   public void inc() { this.cnt += 1; }
 151   public int get() { return this.cnt; }
 152 }</pre>
 153 </div></div>
 154 <div class="paragraph"><p>We can translate the above to SML as follows:</p></div>
 155 <div class="listingblock">
 156 <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">newBasicCounter</span><span class="w"> </span><span class="n">initialCnt</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">let</span><span class="w"></span>
 157 <span class="w">       </span><span class="k">val</span><span class="w"> </span><span class="n">cnt</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="n">initialCnt</span><span class="w"></span>
 158 <span class="w">    </span><span class="k">in</span><span class="w"></span>
 159 <span class="w">       </span><span class="n">Counter</span><span class="w"> </span><span class="p">{</span><span class="n">inc</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="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">cnt</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">!cnt</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"></span>
 160 <span class="w">                </span><span class="n">get</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="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">!cnt</span><span class="p">}</span><span class="w"></span>
 161 <span class="w">    </span><span class="k">end</span><span class="w"></span>
 162 </pre></div></div></div>
 163 <div class="paragraph"><p>The SML function <span class="monospaced">newBasicCounter</span> can be described as a constructor
 164 function for counter objects of the <span class="monospaced">BasicCounter</span> "class".  We can
 165 also have other counter implementations.  Here is the constructor for
 166 a counter decorator that logs messages:</p></div>
 167 <div class="listingblock">
 168 <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">newLoggedCounter</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
 169 <span class="w">    </span><span class="n">Counter</span><span class="w"> </span><span class="p">{</span><span class="n">inc</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="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="s">&quot;inc</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"> </span><span class="p">;</span><span class="w"> </span><span class="n">cInc</span><span class="w"> </span><span class="n">counter</span><span class="p">),</span><span class="w"></span>
 170 <span class="w">             </span><span class="n">get</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="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">print</span><span class="w"> </span><span class="s">&quot;get</span><span class="se">\n</span><span class="s">&quot;</span><span class="w"> </span><span class="p">;</span><span class="w"> </span><span class="n">cGet</span><span class="w"> </span><span class="n">counter</span><span class="p">)}</span><span class="w"></span>
 171 </pre></div></div></div>
 172 <div class="paragraph"><p>The <span class="monospaced">incUpto</span> function works just as well with objects of either
 173 class:</p></div>
 174 <div class="listingblock">
 175 <div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="n">aCounter</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">newBasicCounter</span><span class="w"> </span><span class="mi">0</span><span class="w"></span>
 176 <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">incUpto</span><span class="w"> </span><span class="n">aCounter</span><span class="w"> </span><span class="mi">5</span><span class="w"></span>
 177 <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">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="p">(</span><span class="n">cGet</span><span class="w"> </span><span class="n">aCounter</span><span class="p">)</span><span class="w"> </span><span class="n">^</span><span class="s">&quot;</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">)</span><span class="w"></span>
 178
 179 <span class="k">val</span><span class="w"> </span><span class="n">aCounter</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">newLoggedCounter</span><span class="w"> </span><span class="p">(</span><span class="n">newBasicCounter</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"></span>
 180 <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">incUpto</span><span class="w"> </span><span class="n">aCounter</span><span class="w"> </span><span class="mi">5</span><span class="w"></span>
 181 <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">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="p">(</span><span class="n">cGet</span><span class="w"> </span><span class="n">aCounter</span><span class="p">)</span><span class="w"> </span><span class="n">^</span><span class="s">&quot;</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">)</span><span class="w"></span>
 182 </pre></div></div></div>
 183 <div class="paragraph"><p>In general, a dynamic dispatch interface is represented as a record
 184 type wrapped inside a datatype.  Each field of the record corresponds
 185 to a public method or field of the object:</p></div>
 186 <div class="listingblock">
 187 <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">interface</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
 188 <span class="w">   </span><span class="n">Interface</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">{</span><span class="n">method</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">t1</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">t2</span><span class="p">,</span><span class="w"></span>
 189 <span class="w">                 </span><span class="n">immutableField</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">t</span><span class="p">,</span><span class="w"></span>
 190 <span class="w">                 </span><span class="n">mutableField</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">ref</span><span class="p">}</span><span class="w"></span>
 191 </pre></div></div></div>
 192 <div class="paragraph"><p>The reason for wrapping the record inside a datatype is that records,
 193 in SML, can not be recursive.  However, SML datatypes can be
 194 recursive.  A record wrapped in a datatype can contain fields that
 195 contain the datatype.  For example, an interface such as <span class="monospaced">Cloneable</span></p></div>
 196 <div class="listingblock">
 197 <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">cloneable</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Cloneable</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">{</span><span class="n">clone</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">cloneable</span><span class="p">}</span><span class="w"></span>
 198 </pre></div></div></div>
 199 <div class="paragraph"><p>can be represented using recursive datatypes.</p></div>
 200 <div class="paragraph"><p>Like in OO languages, interfaces are abstract and can not be
 201 instantiated to produce objects.  To be able to instantiate objects,
 202 the constructors of a concrete class are needed.  In SML, we can
 203 implement constructors as simple functions from arbitrary arguments to
 204 values of the interface type.  Such a constructor function can
 205 encapsulate arbitrary private state and functions using lexical
 206 closure.  It is also easy to share implementations of methods between
 207 two or more constructors.</p></div>
 208 <div class="paragraph"><p>While the <span class="monospaced">Counter</span> example is rather trivial, it should not be
 209 difficult to see that this technique quite simply doesn&#8217;t require a huge
 210 amount of extra verbiage and is more than usable in practice.</p></div>
 211 </div>
 212 </div>
 213 <div class="sect1">
 214 <h2 id="_sml_modules_and_dynamic_dispatch">SML Modules and Dynamic Dispatch</h2>
 215 <div class="sectionbody">
 216 <div class="paragraph"><p>One might wonder about how SML modules and the dynamic dispatch
 217 technique work together.  Let&#8217;s investigate!  Let&#8217;s use a simple
 218 dispenser framework as a concrete example.  (Note that this isn&#8217;t
 219 intended to be an introduction to the SML module system.)</p></div>
 220 <div class="sect2">
 221 <h3 id="_programming_with_sml_modules">Programming with SML Modules</h3>
 222 <div class="paragraph"><p>Using SML signatures we can specify abstract data types (ADTs) such as
 223 dispensers.  Here is a signature for an "abstract" functional (as
 224 opposed to imperative) dispenser:</p></div>
 225 <div class="listingblock">
 226 <div class="content"><div class="highlight"><pre><span class="k">signature</span><span class="w"> </span><span class="n">ABSTRACT_DISPENSER</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">sig</span><span class="w"></span>
 227 <span class="w">   </span><span class="k">type</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
 228 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">bool</span><span class="w"></span>
 229 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">push</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
 230 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="n">option</span><span class="w"></span>
 231 <span class="k">end</span><span class="w"></span>
 232 </pre></div></div></div>
 233 <div class="paragraph"><p>The term "abstract" in the name of the signature refers to the fact that
 234 the signature gives no way to instantiate a dispenser.  It has nothing to
 235 do with the concept of abstract data types.</p></div>
 236 <div class="paragraph"><p>Using SML functors we can write "generic" algorithms that manipulate
 237 dispensers of an unknown type.  Here are a couple of very simple
 238 algorithms:</p></div>
 239 <div class="listingblock">
 240 <div class="content"><div class="highlight"><pre><span class="k">functor</span><span class="w"> </span><span class="n">DispenserAlgs</span><span class="w"> </span><span class="p">(</span><span class="n">D</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">ABSTRACT_DISPENSER</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">struct</span><span class="w"></span>
 241 <span class="w">   </span><span class="k">open</span><span class="w"> </span><span class="n">D</span><span class="w"></span>
 242
 243 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">pushAll</span><span class="w"> </span><span class="p">(</span><span class="n">xs</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">foldl</span><span class="w"> </span><span class="n">push</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="n">xs</span><span class="w"></span>
 244
 245 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">popAll</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">let</span><span class="w"></span>
 246 <span class="w">          </span><span class="k">fun</span><span class="w"> </span><span class="n">lp</span><span class="w"> </span><span class="p">(</span><span class="n">xs</span><span class="p">,</span><span class="w"> </span><span class="n">NONE</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">rev</span><span class="w"> </span><span class="n">xs</span><span class="w"></span>
 247 <span class="w">            </span><span class="p">|</span><span class="w"> </span><span class="n">lp</span><span class="w"> </span><span class="p">(</span><span class="n">xs</span><span class="p">,</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">))</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">lp</span><span class="w"> </span><span class="p">(</span><span class="n">x::xs</span><span class="p">,</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="n">d</span><span class="p">)</span><span class="w"></span>
 248 <span class="w">       </span><span class="k">in</span><span class="w"></span>
 249 <span class="w">          </span><span class="n">lp</span><span class="w"> </span><span class="p">([],</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="n">d</span><span class="p">)</span><span class="w"></span>
 250 <span class="w">       </span><span class="k">end</span><span class="w"></span>
 251
 252 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">cp</span><span class="w"> </span><span class="p">(</span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">pushAll</span><span class="w"> </span><span class="p">(</span><span class="n">popAll</span><span class="w"> </span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">)</span><span class="w"></span>
 253 <span class="k">end</span><span class="w"></span>
 254 </pre></div></div></div>
 255 <div class="paragraph"><p>As one can easily verify, the above compiles even without any concrete
 256 dispenser structure.  Functors essentially provide a form a static
 257 dispatch that one can use to break compile-time dependencies.</p></div>
 258 <div class="paragraph"><p>We can also give a signature for a concrete dispenser</p></div>
 259 <div class="listingblock">
 260 <div class="content"><div class="highlight"><pre><span class="k">signature</span><span class="w"> </span><span class="n">DISPENSER</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">sig</span><span class="w"></span>
 261 <span class="w">   </span><span class="k">include</span><span class="w"> </span><span class="n">ABSTRACT_DISPENSER</span><span class="w"></span>
 262 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
 263 <span class="k">end</span><span class="w"></span>
 264 </pre></div></div></div>
 265 <div class="paragraph"><p>and write any number of concrete structures implementing the signature.
 266 For example, we could implement stacks</p></div>
 267 <div class="listingblock">
 268 <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Stack</span><span class="w"> </span><span class="p">:&gt;</span><span class="w"> </span><span class="n">DISPENSER</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">struct</span><span class="w"></span>
 269 <span class="w">   </span><span class="k">type</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">list</span><span class="w"></span>
 270 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span><span class="w"></span>
 271 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">null</span><span class="w"></span>
 272 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">push</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">op</span><span class="w"> </span><span class="n">::</span><span class="w"></span>
 273 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">getItem</span><span class="w"></span>
 274 <span class="k">end</span><span class="w"></span>
 275 </pre></div></div></div>
 276 <div class="paragraph"><p>and queues</p></div>
 277 <div class="listingblock">
 278 <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Queue</span><span class="w"> </span><span class="p">:&gt;</span><span class="w"> </span><span class="n">DISPENSER</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">struct</span><span class="w"></span>
 279 <span class="w">   </span><span class="k">datatype</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</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="n">&#39;a</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">list</span><span class="w"></span>
 280 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">empty</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="w"> </span><span class="p">[])</span><span class="w"></span>
 281 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">isEmpty</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">T</span><span class="w"> </span><span class="p">([],</span><span class="w"> </span><span class="p">_)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">true</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">false</span><span class="w"></span>
 282 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">normalize</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="w"> </span><span class="n">ys</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">rev</span><span class="w"> </span><span class="n">ys</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">q</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">q</span><span class="w"></span>
 283 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">push</span><span class="w"> </span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="n">xs</span><span class="p">,</span><span class="w"> </span><span class="n">ys</span><span class="p">))</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="n">normalize</span><span class="w"> </span><span class="p">(</span><span class="n">xs</span><span class="p">,</span><span class="w"> </span><span class="n">y::ys</span><span class="p">))</span><span class="w"></span>
 284 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">pop</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="p">(</span><span class="n">x::xs</span><span class="p">,</span><span class="w"> </span><span class="n">ys</span><span class="p">))</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">(</span><span class="n">normalize</span><span class="w"> </span><span class="p">(</span><span class="n">xs</span><span class="p">,</span><span class="w"> </span><span class="n">ys</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="p">=&gt;</span><span class="w"> </span><span class="n">NONE</span><span class="w"></span>
 285 <span class="k">end</span><span class="w"></span>
 286 </pre></div></div></div>
 287 <div class="paragraph"><p>One can now write code that uses either the <span class="monospaced">Stack</span> or the <span class="monospaced">Queue</span>
 288 dispenser.  One can also instantiate the previously defined functor to
 289 create functions for manipulating dispensers of a type:</p></div>
 290 <div class="listingblock">
 291 <div class="content"><div class="highlight"><pre><span class="k">structure</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">DispenserAlgs</span><span class="w"> </span><span class="p">(</span><span class="n">Stack</span><span class="p">)</span><span class="w"></span>
 292 <span class="k">val</span><span class="w"> </span><span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">S</span><span class="p">.</span><span class="n">popAll</span><span class="w"> </span><span class="p">(</span><span class="n">S</span><span class="p">.</span><span class="n">pushAll</span><span class="w"> </span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span><span class="w"> </span><span class="n">Stack</span><span class="p">.</span><span class="n">empty</span><span class="p">))</span><span class="w"></span>
 293
 294 <span class="k">structure</span><span class="w"> </span><span class="n">Q</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">DispenserAlgs</span><span class="w"> </span><span class="p">(</span><span class="n">Queue</span><span class="p">)</span><span class="w"></span>
 295 <span class="k">val</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Q</span><span class="p">.</span><span class="n">popAll</span><span class="w"> </span><span class="p">(</span><span class="n">Q</span><span class="p">.</span><span class="n">pushAll</span><span class="w"> </span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span><span class="w"> </span><span class="n">Queue</span><span class="p">.</span><span class="n">empty</span><span class="p">))</span><span class="w"></span>
 296 </pre></div></div></div>
 297 <div class="paragraph"><p>There is no dynamic dispatch involved at the module level in SML.  An
 298 attempt to do dynamic dispatch</p></div>
 299 <div class="listingblock">
 300 <div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Q</span><span class="p">.</span><span class="n">push</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">Stack</span><span class="p">.</span><span class="n">empty</span><span class="p">)</span><span class="w"></span>
 301 </pre></div></div></div>
 302 <div class="paragraph"><p>will give a type error.</p></div>
 303 </div>
 304 <div class="sect2">
 305 <h3 id="_combining_sml_modules_and_dynamic_dispatch">Combining SML Modules and Dynamic Dispatch</h3>
 306 <div class="paragraph"><p>Let&#8217;s then combine SML modules and the dynamic dispatch technique
 307 introduced in this article.  First we define an interface for
 308 dispensers:</p></div>
 309 <div class="listingblock">
 310 <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Dispenser</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">struct</span><span class="w"></span>
 311 <span class="w">   </span><span class="k">datatype</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
 312 <span class="w">      </span><span class="n">I</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">{</span><span class="n">isEmpty</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">bool</span><span class="p">,</span><span class="w"></span>
 313 <span class="w">            </span><span class="n">push</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="p">,</span><span class="w"></span>
 314 <span class="w">            </span><span class="n">pop</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="n">option</span><span class="p">}</span><span class="w"></span>
 315
 316 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">O</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">(</span><span class="n">I</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="n">t</span><span class="w"></span>
 317
 318 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">isEmpty</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">O</span><span class="p">#</span><span class="n">isEmpty</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">()</span><span class="w"></span>
 319 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">push</span><span class="w"> </span><span class="p">(</span><span class="n">v</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">O</span><span class="p">#</span><span class="n">push</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="n">v</span><span class="w"></span>
 320 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">pop</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">O</span><span class="p">#</span><span class="n">pop</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">()</span><span class="w"></span>
 321 <span class="k">end</span><span class="w"></span>
 322 </pre></div></div></div>
 323 <div class="paragraph"><p>The <span class="monospaced">Dispenser</span> module, which we can think of as an interface for
 324 dispensers, implements the <span class="monospaced">ABSTRACT_DISPENSER</span> signature using
 325 the dynamic dispatch technique, but we leave the signature ascription
 326 until later.</p></div>
 327 <div class="paragraph"><p>Then we define a <span class="monospaced">DispenserClass</span> functor that makes a "class" out of
 328 a given dispenser module:</p></div>
 329 <div class="listingblock">
 330 <div class="content"><div class="highlight"><pre><span class="k">functor</span><span class="w"> </span><span class="n">DispenserClass</span><span class="w"> </span><span class="p">(</span><span class="n">D</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">DISPENSER</span><span class="p">)</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">DISPENSER</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">struct</span><span class="w"></span>
 331 <span class="w">   </span><span class="k">open</span><span class="w"> </span><span class="n">Dispenser</span><span class="w"></span>
 332
 333 <span class="w">   </span><span class="k">fun</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
 334 <span class="w">       </span><span class="n">I</span><span class="w"> </span><span class="p">{</span><span class="n">isEmpty</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="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">D</span><span class="p">.</span><span class="n">isEmpty</span><span class="w"> </span><span class="n">d</span><span class="p">,</span><span class="w"></span>
 335 <span class="w">          </span><span class="n">push</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">x</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="p">(</span><span class="n">D</span><span class="p">.</span><span class="n">push</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">)),</span><span class="w"></span>
 336 <span class="w">          </span><span class="n">pop</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="w"> </span><span class="p">=&gt;</span><span class="w"></span>
 337 <span class="w">                   </span><span class="k">case</span><span class="w"> </span><span class="n">D</span><span class="p">.</span><span class="n">pop</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="k">of</span><span class="w"></span>
 338 <span class="w">                      </span><span class="n">NONE</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">NONE</span><span class="w"></span>
 339 <span class="w">                    </span><span class="p">|</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="n">d</span><span class="p">)}</span><span class="w"></span>
 340
 341 <span class="w">   </span><span class="k">val</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
 342 <span class="w">       </span><span class="n">I</span><span class="w"> </span><span class="p">{</span><span class="n">isEmpty</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="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">true</span><span class="p">,</span><span class="w"></span>
 343 <span class="w">          </span><span class="n">push</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">x</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="p">(</span><span class="n">D</span><span class="p">.</span><span class="n">push</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">D</span><span class="p">.</span><span class="n">empty</span><span class="p">)),</span><span class="w"></span>
 344 <span class="w">          </span><span class="n">pop</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="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">NONE</span><span class="p">}</span><span class="w"></span>
 345 <span class="k">end</span><span class="w"></span>
 346 </pre></div></div></div>
 347 <div class="paragraph"><p>Finally we seal the <span class="monospaced">Dispenser</span> module:</p></div>
 348 <div class="listingblock">
 349 <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Dispenser</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">ABSTRACT_DISPENSER</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Dispenser</span><span class="w"></span>
 350 </pre></div></div></div>
 351 <div class="paragraph"><p>This isn&#8217;t necessary for type safety, because the unsealed <span class="monospaced">Dispenser</span>
 352 module does not allow one to break encapsulation, but makes sure that
 353 only the <span class="monospaced">DispenserClass</span> functor can create dispenser classes
 354 (because the constructor <span class="monospaced">Dispenser.I</span> is no longer accessible).</p></div>
 355 <div class="paragraph"><p>Using the <span class="monospaced">DispenserClass</span> functor we can turn any concrete dispenser
 356 module into a dispenser class:</p></div>
 357 <div class="listingblock">
 358 <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">StackClass</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">DispenserClass</span><span class="w"> </span><span class="p">(</span><span class="n">Stack</span><span class="p">)</span><span class="w"></span>
 359 <span class="k">structure</span><span class="w"> </span><span class="n">QueueClass</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">DispenserClass</span><span class="w"> </span><span class="p">(</span><span class="n">Queue</span><span class="p">)</span><span class="w"></span>
 360 </pre></div></div></div>
 361 <div class="paragraph"><p>Each dispenser class implements the same dynamic dispatch interface
 362 and the <span class="monospaced">ABSTRACT_DISPENSER</span> -signature.</p></div>
 363 <div class="paragraph"><p>Because the dynamic dispatch <span class="monospaced">Dispenser</span> module implements the
 364 <span class="monospaced">ABSTRACT_DISPENSER</span>-signature, we can use it to instantiate the
 365 <span class="monospaced">DispenserAlgs</span>-functor:</p></div>
 366 <div class="listingblock">
 367 <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">DispenserAlgs</span><span class="w"> </span><span class="p">(</span><span class="n">Dispenser</span><span class="p">)</span><span class="w"></span>
 368 </pre></div></div></div>
 369 <div class="paragraph"><p>The resulting <span class="monospaced">D</span> module, like the <span class="monospaced">Dispenser</span> module, works with
 370 any dispenser class and uses dynamic dispatch:</p></div>
 371 <div class="listingblock">
 372 <div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">D</span><span class="p">.</span><span class="n">popAll</span><span class="w"> </span><span class="p">(</span><span class="n">D</span><span class="p">.</span><span class="n">pushAll</span><span class="w"> </span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">],</span><span class="w"> </span><span class="n">StackClass</span><span class="p">.</span><span class="n">empty</span><span class="p">))</span><span class="w"></span>
 373 <span class="k">val</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">D</span><span class="p">.</span><span class="n">popAll</span><span class="w"> </span><span class="p">(</span><span class="n">D</span><span class="p">.</span><span class="n">pushAll</span><span class="w"> </span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">],</span><span class="w"> </span><span class="n">QueueClass</span><span class="p">.</span><span class="n">empty</span><span class="p">))</span><span class="w"></span>
 374 </pre></div></div></div>
 375 </div>
 376 </div>
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