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MLton
20241230
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<h1>EqualityType</h1>
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<div class="paragraph">
<p>An equality type is a type to which <a href="PolymorphicEquality">PolymorphicEquality</a> can be
applied.  The <a href="DefinitionOfStandardML">Definition</a> and the
<a href="BasisLibrary">Basis Library</a> precisely spell out which types are
equality types.</p>
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<ul>
<li>
<p><code>bool</code>, <code>char</code>, <code>IntInf.int</code>, <code>Int<em>&lt;N&gt;</em>.int</code>, <code>string</code>, and <code>Word<em>&lt;N&gt;</em>.word</code> are equality types.</p>
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<p>for any <code>t</code>, both <code>t array</code> and <code>t ref</code> are equality types.</p>
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<p>if <code>t</code> is an equality type, then <code>t list</code>, and <code>t vector</code> are equality types.</p>
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<li>
<p>if <code>t1</code>, &#8230;&#8203;, <code>tn</code> are equality types, then <code>t1 * &#8230;&#8203; * tn</code> and <code>{l1: t1, &#8230;&#8203;, ln: tn}</code> are equality types.</p>
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<li>
<p>if <code>t1</code>, &#8230;&#8203;, <code>tn</code> are equality types and <code>t</code> <a href="AdmitsEquality">AdmitsEquality</a>, then <code>(t1, &#8230;&#8203;, tn) t</code> is an equality type.</p>
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<p>To check that a type t is an equality type, use the following idiom.</p>
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<pre class="rouge highlight"><code data-lang="sml"><span class="kr">structure</span> <span class="nn">S</span><span class="p">:</span> <span class="kr">sig</span> <span class="kr">eqtype</span> <span class="kt">t</span> <span class="kr">end</span> <span class="p">=</span>
   <span class="kr">struct</span>
      <span class="kr">type</span> <span class="kt">t</span> <span class="p">=</span> <span class="p">...</span>
   <span class="kr">end</span></code></pre>
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<p>Notably, <code>exn</code> and <code>real</code> are not equality types.  Neither is <code>t1 -&gt; t2</code>, for any <code>t1</code> and <code>t2</code>.</p>
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<p>Equality on arrays and ref cells is by identity, not structure.
For example, <code>ref 13 = ref 13</code> is <code>false</code>.
On the other hand, equality for lists, strings, and vectors is by
structure, not identity.  For example, the following equalities hold.</p>
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<pre class="rouge highlight"><code data-lang="sml"><span class="kr">val</span> <span class="nv">_</span> <span class="p">=</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="p">=</span> <span class="mi">1</span> <span class="n">::</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="kr">val</span> <span class="nv">_</span> <span class="p">=</span> <span class="s2">"foo"</span> <span class="p">=</span> <span class="n">concat</span> <span class="p">[</span><span class="s2">"f"</span><span class="p">,</span> <span class="s2">"o"</span><span class="p">,</span> <span class="s2">"o"</span><span class="p">]</span>
<span class="kr">val</span> <span class="nv">_</span> <span class="p">=</span> <span class="nn">Vector</span><span class="p">.</span><span class="n">fromList</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="p">=</span> <span class="nn">Vector</span><span class="p">.</span><span class="n">tabulate</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="kr">fn</span> <span class="n">i</span> <span class="p">=&gt;</span> <span class="n">i</span> <span class="n">+</span> <span class="mi">1</span><span class="p">)</span></code></pre>
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Last updated Thu Oct 21 15:53:06 2021 -0400 by Matthew Fluet.
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