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TypeConstructor
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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> t <B><FONT COLOR="#5F9EA0">=</FONT></B> T <B><FONT COLOR="#A020F0">of</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">*</FONT></B> <B><FONT COLOR="#228B22">real</FONT></B> <I><FONT COLOR="#B22222">(* 0 arguments *)</FONT></I>
<B><FONT COLOR="#A020F0">type</FONT></B> 'a t <B><FONT COLOR="#5F9EA0">=</FONT></B> 'a <B><FONT COLOR="#5F9EA0">*</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> <I><FONT COLOR="#B22222">(* 1 argument *)</FONT></I>
<B><FONT COLOR="#A020F0">datatype</FONT></B> ('a, 'b) t <B><FONT COLOR="#5F9EA0">=</FONT></B> A <B><FONT COLOR="#5F9EA0">|</FONT></B> B <B><FONT COLOR="#A020F0">of</FONT></B> 'a <B><FONT COLOR="#5F9EA0">*</FONT></B> 'b <I><FONT COLOR="#B22222">(* 2 arguments *)</FONT></I>
<B><FONT COLOR="#A020F0">type</FONT></B> ('a, 'b, 'c) t <B><FONT COLOR="#5F9EA0">=</FONT></B> 'a <B><FONT COLOR="#5F9EA0">*</FONT></B> ('b <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'c) <I><FONT COLOR="#B22222">(* 3 arguments *)</FONT></I>
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<p>
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<p>
Here are the syntax rules for type constructor application.
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Type constructor application is written in postfix. So, one writes <tt>int list</tt>, not <tt>list int</tt>.
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Unary type constructors drop the parens, so one writes <tt>int list</tt>, not <tt>(int) list</tt>.
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Nullary type constructors drop the argument entirely, so one writes <tt>int</tt>, not <tt>() int</tt>.
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<p>
N-ary type constructors use tuple notation; for example, <tt>(int, real) t</tt>.
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Type constructor application associates to the left. So, <tt>int ref list</tt> is the same as <tt>(int ref) 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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