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<title>EqualityType - MLton Standard ML Compiler (SML Compiler)</title>
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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. 
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<p>
 <tt>bool</tt>, <tt>char</tt>, <tt>IntInf.int</tt>, <tt>Int</tt>&lt;N&gt;<tt>.int</tt>,  <tt>string</tt>, and <tt>Word</tt>&lt;N&gt;<tt>.word</tt> are equality types.  
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 for any <tt>t</tt>, both <tt>t&nbsp;array</tt> and <tt>t&nbsp;ref</tt> are equality  types.  
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 if <tt>t</tt> is an equality type, then <tt>t&nbsp;list</tt>, and   <tt>t&nbsp;vector</tt> are equality types. 
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 if <tt>t1</tt>, ..., <tt>tn</tt> are equality types, then  <tt>t1&nbsp;*&nbsp;...&nbsp;*&nbsp;tn</tt>  and <tt>{l1:&nbsp;t1,&nbsp;...,&nbsp;ln:&nbsp;tn}&nbsp;</tt>  are equality types. 
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 if <tt>t1</tt>, ..., <tt>tn</tt> are equality types and <tt>t</tt>   <a href="AdmitsEquality">AdmitsEquality</a>, then <tt>(t1,&nbsp;...,&nbsp;tn)&nbsp;t</tt> is an equality type. 
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To check that a type t is an equality type, use the following idiom. 
<pre class=code>
<B><FONT COLOR="#0000FF">structure</FONT></B> S: <B><FONT COLOR="#0000FF">sig</FONT></B> <B><FONT COLOR="#A020F0">eqtype</FONT></B><B><FONT COLOR="#228B22"> t </FONT></B><B><FONT COLOR="#0000FF">end</FONT></B> =
   <B><FONT COLOR="#0000FF">struct</FONT></B>
      <B><FONT COLOR="#A020F0">type</FONT></B><B><FONT COLOR="#228B22"> t </FONT></B>=<B><FONT COLOR="#228B22"> </FONT></B>...
   <B><FONT COLOR="#0000FF">end</FONT></B>
</PRE>
 
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Notably, <tt>exn</tt> and <tt>real</tt> are not equality types.  Neither is <tt>t1&nbsp;-&gt;&nbsp;t2</tt>, for any <tt>t1</tt> and <tt>t2</tt>. 
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Equality on arrays and ref cells is by identity, not structure.  For example, <tt>ref&nbsp;13&nbsp;=&nbsp;ref&nbsp;13</tt> is <tt>false</tt>. On the other hand, equality for lists, strings, and vectors is by structure, not identity.  For example, the following equalities hold. 
</p>

<pre>[1, 2, 3] = 1 :: [2, 3]
"foo" = concat ["f", "o", "o"]
Vector.fromList [1, 2, 3] = Vector.tabulate (3, fn i =&gt; i + 1)
</pre></div>



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Last edited on 2007-08-15 22:05:47 by <span title="fenrir.uchicago.edu"><a href="MatthewFluet">MatthewFluet</a></span>.
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