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EqualityType
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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><N><tt>.int</tt>, <tt>string</tt>, and <tt>Word</tt><N><tt>.word</tt> are equality types.
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for any <tt>t</tt>, both <tt>t array</tt> and <tt>t ref</tt> are equality types.
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if <tt>t</tt> is an equality type, then <tt>t list</tt>, and <tt>t vector</tt> are equality types.
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if <tt>t1</tt>, ..., <tt>tn</tt> are equality types, then <tt>t1 * ... * tn</tt> and <tt>{l1: t1, ..., ln: tn} </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, ..., tn) t</tt> is an equality type.
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To check that a type t is an equality type, use the following idiom.
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<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 -> 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 13 = ref 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.
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<pre>[1, 2, 3] = 1 :: [2, 3]
"foo" = concat ["f", "o", "o"]
Vector.fromList [1, 2, 3] = Vector.tabulate (3, fn i => 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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