File: GenerativeDatatype

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<h1>GenerativeDatatype</h1>
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<div class="paragraph"><p>In <a href="StandardML">Standard ML</a>, datatype declarations are said to be
<em>generative</em>, because each time a datatype declaration is evaluated,
it yields a new type.  Thus, any attempt to mix the types will lead to
a type error at compile-time.  The following program, which does not
type check, demonstrates this.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span class="k">functor</span><span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><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="w">   </span><span class="k">end</span><span class="w"></span>
<span class="k">structure</span><span class="w"> </span><span class="n">S1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="p">()</span><span class="w"></span>
<span class="k">structure</span><span class="w"> </span><span class="n">S2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="p">()</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">_:</span><span class="w"> </span><span class="n">S1</span><span class="p">.</span><span class="n">t</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">S2</span><span class="p">.</span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">x</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>Generativity also means that two different datatype declarations
define different types, even if they define identical constructors.
The following program does not type check due to this.</p></div>
<div class="listingblock">
<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">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">val</span><span class="w"> </span><span class="n">a1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="w"></span>
<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">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">val</span><span class="w"> </span><span class="n">a2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="w"></span>
<span class="k">val</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">true</span><span class="w"> </span><span class="k">then</span><span class="w"> </span><span class="n">a1</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="n">a2</span><span class="w"></span>
</pre></div></div></div>
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<div class="sect1">
<h2 id="_also_see">Also see</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
<a href="GenerativeException">GenerativeException</a>
</p>
</li>
</ul></div>
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