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In <a href="StandardML">Standard ML</a>, a type constructor is a function from types to types.  Type constructors can be <em>nullary</em>, meaning that they take no arguments, as in <tt>char</tt>, <tt>int</tt>, and <tt>real</tt>. Type constructors can be <em>unary</em>, meaning that they take one argument, as in <tt>array</tt>, <tt>list</tt>, and <tt>vector</tt>.  A program can define a new type constructor in two ways: a <tt>type</tt> definition or a <tt>datatype</tt> declaration.  User-defined type constructors can can take any number of arguments. 
<pre class=code>
<B><FONT COLOR="#A020F0">datatype</FONT></B><B><FONT COLOR="#228B22"> t </FONT></B>=<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">T</FONT> <B><FONT COLOR="#A020F0">of</FONT></B> int * real            <I><FONT COLOR="#B22222">(* 0 arguments *)</FONT></I>
</FONT></B><B><FONT COLOR="#A020F0">type</FONT></B><B><FONT COLOR="#228B22"> 'a t </FONT></B>=<B><FONT COLOR="#228B22"> 'a * int                    <I><FONT COLOR="#B22222">(* 1 argument *)</FONT></I>
</FONT></B><B><FONT COLOR="#A020F0">datatype</FONT></B><B><FONT COLOR="#228B22"> ('a, 'b) t </FONT></B>=<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">A</FONT> </FONT></B>|<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">B</FONT> <B><FONT COLOR="#A020F0">of</FONT></B> 'a * 'b  <I><FONT COLOR="#B22222">(* 2 arguments *)</FONT></I>
</FONT></B><B><FONT COLOR="#A020F0">type</FONT></B><B><FONT COLOR="#228B22"> ('a, 'b, 'c) t </FONT></B>=<B><FONT COLOR="#228B22"> 'a * ('b  -&gt; 'c)  <I><FONT COLOR="#B22222">(* 3 arguments *)</FONT></I>
</FONT></B></PRE>
<p>
 
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<p>
Here are the syntax rules for type constructor application. 
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<p>
 Type constructor application is written in postfix.  So, one writes  <tt>int&nbsp;list</tt>, not <tt>list&nbsp;int</tt>.   
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    <li class="gap">
<p>
 Unary type constructors drop the parens, so one writes   <tt>int&nbsp;list</tt>, not <tt>(int)&nbsp;list</tt>.   
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</li>
    <li class="gap">
<p>
 Nullary type constructors drop the argument entirely, so one writes  <tt>int</tt>, not <tt>()&nbsp;int</tt>.  
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    <li class="gap">
<p>
 N-ary type constructors use tuple notation; for example,   <tt>(int,&nbsp;real)&nbsp;t</tt>.  
</p>
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    <li class="gap">
<p>
 Type constructor application associates to the left.  So,  <tt>int&nbsp;ref&nbsp;list</tt> is the same as <tt>(int&nbsp;ref)&nbsp;list</tt>. 
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<p>
<hr>
Last edited on 2005-12-02 04:26:23 by <span title="ppp-71-139-183-221.dsl.snfc21.pacbell.net"><a href="StephenWeeks">StephenWeeks</a></span>.
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