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<a href="./Home">MLton 20130715</a>
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<h1>GenerativeException</h1>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph"><p>In <a href="StandardML">Standard ML</a>, exception declarations are said to be
<em>generative</em>, because each time an exception declaration is evaluated,
it yields a new exception.</p></div>
<div class="paragraph"><p>The following program demonstrates the generativity of exceptions.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span></span><span class="kr">exception</span> <span class="nc">E</span>
<span class="kr">val</span> <span class="nv">e1</span> <span class="p">=</span> <span class="n">E</span>
<span class="kr">fun</span> <span class="nf">isE1</span> <span class="p">(</span><span class="n">e</span><span class="p">:</span> <span class="n">exn</span><span class="p">):</span> <span class="n">bool</span> <span class="p">=</span>
   <span class="kr">case</span> <span class="n">e</span> <span class="kr">of</span>
      <span class="n">E</span> <span class="p">=&gt;</span> <span class="n">true</span>
    <span class="n">|</span> <span class="p">_</span> <span class="p">=&gt;</span> <span class="n">false</span>
<span class="kr">exception</span> <span class="nc">E</span>
<span class="kr">val</span> <span class="nv">e2</span> <span class="p">=</span> <span class="n">E</span>
<span class="kr">fun</span> <span class="nf">isE2</span> <span class="p">(</span><span class="n">e</span><span class="p">:</span> <span class="n">exn</span><span class="p">):</span> <span class="n">bool</span> <span class="p">=</span>
   <span class="kr">case</span> <span class="n">e</span> <span class="kr">of</span>
      <span class="n">E</span> <span class="p">=&gt;</span> <span class="n">true</span>
    <span class="n">|</span> <span class="p">_</span> <span class="p">=&gt;</span> <span class="n">false</span>
<span class="kr">fun</span> <span class="nf">pb</span> <span class="p">(</span><span class="n">b</span><span class="p">:</span> <span class="n">bool</span><span class="p">):</span> <span class="n">unit</span> <span class="p">=</span>
   <span class="n">print</span> <span class="p">(</span><span class="n">concat</span> <span class="p">[</span><span class="nn">Bool</span><span class="p">.</span><span class="n">toString</span> <span class="n">b</span><span class="p">,</span> <span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">])</span>
<span class="kr">val</span> <span class="p">()</span> <span class="nv">=</span> <span class="p">(</span><span class="n">pb</span> <span class="p">(</span><span class="n">isE1</span> <span class="n">e1</span><span class="p">)</span>
          <span class="p">;</span><span class="n">pb</span> <span class="p">(</span><span class="n">isE1</span> <span class="n">e2</span><span class="p">)</span>
          <span class="p">;</span> <span class="n">pb</span> <span class="p">(</span><span class="n">isE2</span> <span class="n">e1</span><span class="p">)</span>
          <span class="p">;</span> <span class="n">pb</span> <span class="p">(</span><span class="n">isE2</span> <span class="n">e2</span><span class="p">))</span>
</pre></div></div></div>
<div class="paragraph"><p>In the above program, two different exception declarations declare an
exception <span class="monospaced">E</span> and a corresponding function that returns <span class="monospaced">true</span> only on
that exception.  Although declared by syntactically identical
exception declarations, <span class="monospaced">e1</span> and <span class="monospaced">e2</span> are different exceptions.  The
program, when run, prints <span class="monospaced">true</span>, <span class="monospaced">false</span>, <span class="monospaced">false</span>, <span class="monospaced">true</span>.</p></div>
<div class="paragraph"><p>A slight modification of the above program shows that even a single
exception declaration yields a new exception each time it is
evaluated.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span></span><span class="kr">fun</span> <span class="nf">f</span> <span class="p">():</span> <span class="n">exn</span> <span class="n">*</span> <span class="p">(</span><span class="n">exn</span> <span class="p">-&gt;</span> <span class="n">bool</span><span class="p">)</span> <span class="p">=</span>
   <span class="kr">let</span>
      <span class="kr">exception</span> <span class="nc">E</span>
   <span class="kr">in</span>
      <span class="p">(</span><span class="n">E</span><span class="p">,</span> <span class="kr">fn</span> <span class="n">E</span> <span class="p">=&gt;</span> <span class="n">true</span> <span class="n">|</span> <span class="p">_</span> <span class="p">=&gt;</span> <span class="n">false</span><span class="p">)</span>
   <span class="kr">end</span>
<span class="kr">val</span> <span class="p">(</span><span class="n">e1</span><span class="p">,</span> <span class="n">isE1</span><span class="p">)</span> <span class="nv">=</span> <span class="n">f</span> <span class="p">()</span>
<span class="kr">val</span> <span class="p">(</span><span class="n">e2</span><span class="p">,</span> <span class="n">isE2</span><span class="p">)</span> <span class="nv">=</span> <span class="n">f</span> <span class="p">()</span>
<span class="kr">fun</span> <span class="nf">pb</span> <span class="p">(</span><span class="n">b</span><span class="p">:</span> <span class="n">bool</span><span class="p">):</span> <span class="n">unit</span> <span class="p">=</span>
   <span class="n">print</span> <span class="p">(</span><span class="n">concat</span> <span class="p">[</span><span class="nn">Bool</span><span class="p">.</span><span class="n">toString</span> <span class="n">b</span><span class="p">,</span> <span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="p">])</span>
<span class="kr">val</span> <span class="p">()</span> <span class="nv">=</span> <span class="p">(</span><span class="n">pb</span> <span class="p">(</span><span class="n">isE1</span> <span class="n">e1</span><span class="p">)</span>
          <span class="p">;</span> <span class="n">pb</span> <span class="p">(</span><span class="n">isE1</span> <span class="n">e2</span><span class="p">)</span>
          <span class="p">;</span> <span class="n">pb</span> <span class="p">(</span><span class="n">isE2</span> <span class="n">e1</span><span class="p">)</span>
          <span class="p">;</span> <span class="n">pb</span> <span class="p">(</span><span class="n">isE2</span> <span class="n">e2</span><span class="p">))</span>
</pre></div></div></div>
<div class="paragraph"><p>Each call to <span class="monospaced">f</span> yields a new exception and a function that returns
<span class="monospaced">true</span> only on that exception.  The program, when run, prints <span class="monospaced">true</span>,
<span class="monospaced">false</span>, <span class="monospaced">false</span>, <span class="monospaced">true</span>.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_type_safety">Type Safety</h2>
<div class="sectionbody">
<div class="paragraph"><p>Exception generativity is required for type safety.  Consider the
following valid SML program.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span></span><span class="kr">fun</span> <span class="nf">f</span> <span class="p">():</span> <span class="p">(</span><span class="nd">&#39;a</span> <span class="p">-&gt;</span> <span class="n">exn</span><span class="p">)</span> <span class="n">*</span> <span class="p">(</span><span class="n">exn</span> <span class="p">-&gt;</span> <span class="nd">&#39;a</span><span class="p">)</span> <span class="p">=</span>
   <span class="kr">let</span>
      <span class="kr">exception</span> <span class="nc">E</span> <span class="kr">of</span> <span class="nd">&#39;a</span>
   <span class="kr">in</span>
      <span class="p">(</span><span class="n">E</span><span class="p">,</span> <span class="kr">fn</span> <span class="n">E</span> <span class="n">x</span> <span class="p">=&gt;</span> <span class="n">x</span> <span class="n">|</span> <span class="p">_</span> <span class="p">=&gt;</span> <span class="kr">raise</span> <span class="n">Fail</span> <span class="s2">&quot;f&quot;</span><span class="p">)</span>
   <span class="kr">end</span>
<span class="kr">fun</span> <span class="nf">cast</span> <span class="p">(</span><span class="n">a</span><span class="p">:</span> <span class="nd">&#39;a</span><span class="p">):</span> <span class="nd">&#39;b</span> <span class="p">=</span>
   <span class="kr">let</span>
      <span class="kr">val</span> <span class="p">(</span><span class="n">make:</span> <span class="nd">&#39;a</span> <span class="n">-&gt;</span> <span class="n">exn</span><span class="p">,</span> <span class="err">_</span><span class="p">)</span> <span class="nv">=</span> <span class="n">f</span> <span class="p">()</span>
      <span class="kr">val</span> <span class="p">(</span><span class="err">_</span><span class="p">,</span> <span class="n">get:</span> <span class="n">exn</span> <span class="n">-&gt;</span> <span class="nd">&#39;b</span><span class="p">)</span> <span class="nv">=</span> <span class="n">f</span> <span class="p">()</span>
   <span class="kr">in</span>
      <span class="n">get</span> <span class="p">(</span><span class="n">make</span> <span class="n">a</span><span class="p">)</span>
   <span class="kr">end</span>
<span class="kr">val</span> <span class="p">_</span> <span class="p">=</span> <span class="p">((</span><span class="n">cast</span> <span class="mi">13</span><span class="p">):</span> <span class="n">int</span> <span class="p">-&gt;</span> <span class="n">int</span><span class="p">)</span> <span class="mi">14</span>
</pre></div></div></div>
<div class="paragraph"><p>If exceptions weren&#8217;t generative, then each call <span class="monospaced">f ()</span> would yield
the same exception constructor <span class="monospaced">E</span>.  Then, our <span class="monospaced">cast</span> function could
use <span class="monospaced">make: 'a -&gt; exn</span> to convert any value into an exception and then
<span class="monospaced">get: exn -&gt; 'b</span> to convert that exception to a value of arbitrary
type.  If <span class="monospaced">cast</span> worked, then we could cast an integer as a function
and apply.  Of course, because of generative exceptions, this program
raises <span class="monospaced">Fail "f"</span>.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_applications">Applications</h2>
<div class="sectionbody">
<div class="paragraph"><p>The <span class="monospaced">exn</span> type is effectively a <a href="UniversalType">universal type</a>.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_also_see">Also see</h2>
<div class="sectionbody">
<div class="ulist"><ul>
<li>
<p>
<a href="GenerativeDatatype">GenerativeDatatype</a>
</p>
</li>
</ul></div>
</div>
</div>
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