doc/guide/localhost/TypeConstructor

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  26 <h1>TypeConstructor</h1>
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  28 <div id="content">
  29 <div id="preamble">
  30 <div class="sectionbody">
  31 <div class="paragraph"><p>In <a href="StandardML">Standard ML</a>, a type constructor is a function from
  32 types to types.  Type constructors can be <em>nullary</em>, meaning that
  33 they take no arguments, as in <span class="monospaced">char</span>, <span class="monospaced">int</span>, and <span class="monospaced">real</span>.
  34 Type constructors can be <em>unary</em>, meaning that they take one
  35 argument, as in <span class="monospaced">array</span>, <span class="monospaced">list</span>, and <span class="monospaced">vector</span>.  A program
  36 can define a new type constructor in two ways: a <span class="monospaced">type</span> definition
  37 or a <span class="monospaced">datatype</span> declaration.  User-defined type constructors can
  38 can take any number of arguments.</p></div>
  39 <div class="listingblock">
  40 <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">real</span><span class="w">            </span><span class="cm">(* 0 arguments *)</span><span class="w"></span>
  41 <span class="k">type</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="w">                    </span><span class="cm">(* 1 argument *)</span><span class="w"></span>
  42 <span class="k">datatype</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">&#39;b</span><span class="w">  </span><span class="cm">(* 2 arguments *)</span><span class="w"></span>
  43 <span class="k">type</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;b</span><span class="w">  </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">)</span><span class="w">  </span><span class="cm">(* 3 arguments *)</span><span class="w"></span>
  44 </pre></div></div></div>
  45 <div class="paragraph"><p>Here are the syntax rules for type constructor application.</p></div>
  46 <div class="ulist"><ul>
  47 <li>
  48 <p>
  49 Type constructor application is written in postfix.  So, one writes
  50  <span class="monospaced">int list</span>, not <span class="monospaced">list int</span>.
  51 </p>
  52 </li>
  53 <li>
  54 <p>
  55 Unary type constructors drop the parens, so one writes
  56  <span class="monospaced">int list</span>, not <span class="monospaced">(int) list</span>.
  57 </p>
  58 </li>
  59 <li>
  60 <p>
  61 Nullary type constructors drop the argument entirely, so one writes
  62  <span class="monospaced">int</span>, not <span class="monospaced">() int</span>.
  63 </p>
  64 </li>
  65 <li>
  66 <p>
  67 N-ary type constructors use tuple notation; for example,
  68  <span class="monospaced">(int, real) t</span>.
  69 </p>
  70 </li>
  71 <li>
  72 <p>
  73 Type constructor application associates to the left.  So,
  74  <span class="monospaced">int ref list</span> is the same as <span class="monospaced">(int ref) list</span>.
  75 </p>
  76 </li>
  77 </ul></div>
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