doc/guide/localhost/EqualityType

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  26 <h1>EqualityType</h1>
  27 </div>
  28 <div id="content">
  29 <div id="preamble">
  30 <div class="sectionbody">
  31 <div class="paragraph"><p>An equality type is a type to which <a href="PolymorphicEquality">PolymorphicEquality</a> can be
  32 applied.  The <a href="DefinitionOfStandardML">Definition</a> and the
  33 <a href="BasisLibrary">Basis Library</a> precisely spell out which types are
  34 equality types.</p></div>
  35 <div class="ulist"><ul>
  36 <li>
  37 <p>
  38 <span class="monospaced">bool</span>, <span class="monospaced">char</span>, <span class="monospaced">IntInf.int</span>, <span class="monospaced">Int<em>&lt;N&gt;</em>.int</span>, <span class="monospaced">string</span>, and <span class="monospaced">Word<em>&lt;N&gt;</em>.word</span> are equality types.
  39 </p>
  40 </li>
  41 <li>
  42 <p>
  43 for any <span class="monospaced">t</span>, both <span class="monospaced">t array</span> and <span class="monospaced">t ref</span> are equality types.
  44 </p>
  45 </li>
  46 <li>
  47 <p>
  48 if <span class="monospaced">t</span> is an equality type, then <span class="monospaced">t list</span>, and <span class="monospaced">t vector</span> are equality types.
  49 </p>
  50 </li>
  51 <li>
  52 <p>
  53 if <span class="monospaced">t1</span>, &#8230;, <span class="monospaced">tn</span> are equality types, then <span class="monospaced">t1 * ... * tn</span> and <span class="monospaced">{l1: t1, ..., ln: tn}</span> are equality types.
  54 </p>
  55 </li>
  56 <li>
  57 <p>
  58 if <span class="monospaced">t1</span>, &#8230;, <span class="monospaced">tn</span> are equality types and <span class="monospaced">t</span> <a href="AdmitsEquality">AdmitsEquality</a>, then <span class="monospaced">(t1, ..., tn) t</span> is an equality type.
  59 </p>
  60 </li>
  61 </ul></div>
  62 <div class="paragraph"><p>To check that a type t is an equality type, use the following idiom.</p></div>
  63 <div class="listingblock">
  64 <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">S</span><span class="p">:</span><span class="w"> </span><span class="k">sig</span><span class="w"> </span><span class="k">eqtype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="k">end</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  65 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
  66 <span class="w">      </span><span class="k">type</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>
  67 <span class="w">   </span><span class="k">end</span><span class="w"></span>
  68 </pre></div></div></div>
  69 <div class="paragraph"><p>Notably, <span class="monospaced">exn</span> and <span class="monospaced">real</span> are not equality types.  Neither is <span class="monospaced">t1 -&gt; t2</span>, for any <span class="monospaced">t1</span> and <span class="monospaced">t2</span>.</p></div>
  70 <div class="paragraph"><p>Equality on arrays and ref cells is by identity, not structure.
  71 For example, <span class="monospaced">ref 13 = ref 13</span> is <span class="monospaced">false</span>.
  72 On the other hand, equality for lists, strings, and vectors is by
  73 structure, not identity.  For example, the following equalities hold.</p></div>
  74 <div class="listingblock">
  75 <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="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="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="n">::</span><span class="w"> </span><span class="p">[</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>
  76 <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="s">&quot;foo&quot;</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">concat</span><span class="w"> </span><span class="p">[</span><span class="s">&quot;f&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;o&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;o&quot;</span><span class="p">]</span><span class="w"></span>
  77 <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">Vector</span><span class="p">.</span><span class="n">fromList</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="p">=</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">tabulate</span><span class="w"> </span><span class="p">(</span><span class="mi">3</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">=&gt;</span><span class="w"> </span><span class="n">i</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>
  78 </pre></div></div></div>
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