doc/guide/localhost/GenerativeException

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  22 <a href="./Home">MLton 20180207</a>
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  26 <h1>GenerativeException</h1>
  27 </div>
  28 <div id="content">
  29 <div id="preamble">
  30 <div class="sectionbody">
  31 <div class="paragraph"><p>In <a href="StandardML">Standard ML</a>, exception declarations are said to be
  32 <em>generative</em>, because each time an exception declaration is evaluated,
  33 it yields a new exception.</p></div>
  34 <div class="paragraph"><p>The following program demonstrates the generativity of exceptions.</p></div>
  35 <div class="listingblock">
  36 <div class="content"><div class="highlight"><pre><span class="k">exception</span><span class="w"> </span><span class="n">E</span><span class="w"></span>
  37 <span class="k">val</span><span class="w"> </span><span class="n">e1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">E</span><span class="w"></span>
  38 <span class="k">fun</span><span class="w"> </span><span class="n">isE1</span><span class="w"> </span><span class="p">(</span><span class="n">e</span><span class="p">:</span><span class="w"> </span><span class="n">exn</span><span class="p">):</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  39 <span class="w">   </span><span class="k">case</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="k">of</span><span class="w"></span>
  40 <span class="w">      </span><span class="n">E</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">true</span><span class="w"></span>
  41 <span class="w">    </span><span class="p">|</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">false</span><span class="w"></span>
  42 <span class="k">exception</span><span class="w"> </span><span class="n">E</span><span class="w"></span>
  43 <span class="k">val</span><span class="w"> </span><span class="n">e2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">E</span><span class="w"></span>
  44 <span class="k">fun</span><span class="w"> </span><span class="n">isE2</span><span class="w"> </span><span class="p">(</span><span class="n">e</span><span class="p">:</span><span class="w"> </span><span class="n">exn</span><span class="p">):</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  45 <span class="w">   </span><span class="k">case</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="k">of</span><span class="w"></span>
  46 <span class="w">      </span><span class="n">E</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">true</span><span class="w"></span>
  47 <span class="w">    </span><span class="p">|</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">false</span><span class="w"></span>
  48 <span class="k">fun</span><span class="w"> </span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="p">:</span><span class="w"> </span><span class="n">bool</span><span class="p">):</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  49 <span class="w">   </span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="n">concat</span><span class="w"> </span><span class="p">[</span><span class="n">Bool</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">])</span><span class="w"></span>
  50 <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="p">(</span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE1</span><span class="w"> </span><span class="n">e1</span><span class="p">)</span><span class="w"></span>
  51 <span class="w">          </span><span class="p">;</span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE1</span><span class="w"> </span><span class="n">e2</span><span class="p">)</span><span class="w"></span>
  52 <span class="w">          </span><span class="p">;</span><span class="w"> </span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE2</span><span class="w"> </span><span class="n">e1</span><span class="p">)</span><span class="w"></span>
  53 <span class="w">          </span><span class="p">;</span><span class="w"> </span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE2</span><span class="w"> </span><span class="n">e2</span><span class="p">))</span><span class="w"></span>
  54 </pre></div></div></div>
  55 <div class="paragraph"><p>In the above program, two different exception declarations declare an
  56 exception <span class="monospaced">E</span> and a corresponding function that returns <span class="monospaced">true</span> only on
  57 that exception.  Although declared by syntactically identical
  58 exception declarations, <span class="monospaced">e1</span> and <span class="monospaced">e2</span> are different exceptions.  The
  59 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>
  60 <div class="paragraph"><p>A slight modification of the above program shows that even a single
  61 exception declaration yields a new exception each time it is
  62 evaluated.</p></div>
  63 <div class="listingblock">
  64 <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">():</span><span class="w"> </span><span class="n">exn</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="p">(</span><span class="n">exn</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">bool</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  65 <span class="w">   </span><span class="k">let</span><span class="w"></span>
  66 <span class="w">      </span><span class="k">exception</span><span class="w"> </span><span class="n">E</span><span class="w"></span>
  67 <span class="w">   </span><span class="k">in</span><span class="w"></span>
  68 <span class="w">      </span><span class="p">(</span><span class="n">E</span><span class="p">,</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">E</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">true</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">false</span><span class="p">)</span><span class="w"></span>
  69 <span class="w">   </span><span class="k">end</span><span class="w"></span>
  70 <span class="k">val</span><span class="w"> </span><span class="p">(</span><span class="n">e1</span><span class="p">,</span><span class="w"> </span><span class="n">isE1</span><span class="p">)</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>
  71 <span class="k">val</span><span class="w"> </span><span class="p">(</span><span class="n">e2</span><span class="p">,</span><span class="w"> </span><span class="n">isE2</span><span class="p">)</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>
  72 <span class="k">fun</span><span class="w"> </span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="p">:</span><span class="w"> </span><span class="n">bool</span><span class="p">):</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  73 <span class="w">   </span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="n">concat</span><span class="w"> </span><span class="p">[</span><span class="n">Bool</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">])</span><span class="w"></span>
  74 <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="p">(</span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE1</span><span class="w"> </span><span class="n">e1</span><span class="p">)</span><span class="w"></span>
  75 <span class="w">          </span><span class="p">;</span><span class="w"> </span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE1</span><span class="w"> </span><span class="n">e2</span><span class="p">)</span><span class="w"></span>
  76 <span class="w">          </span><span class="p">;</span><span class="w"> </span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE2</span><span class="w"> </span><span class="n">e1</span><span class="p">)</span><span class="w"></span>
  77 <span class="w">          </span><span class="p">;</span><span class="w"> </span><span class="n">pb</span><span class="w"> </span><span class="p">(</span><span class="n">isE2</span><span class="w"> </span><span class="n">e2</span><span class="p">))</span><span class="w"></span>
  78 </pre></div></div></div>
  79 <div class="paragraph"><p>Each call to <span class="monospaced">f</span> yields a new exception and a function that returns
  80 <span class="monospaced">true</span> only on that exception.  The program, when run, prints <span class="monospaced">true</span>,
  81 <span class="monospaced">false</span>, <span class="monospaced">false</span>, <span class="monospaced">true</span>.</p></div>
  82 </div>
  83 </div>
  84 <div class="sect1">
  85 <h2 id="_type_safety">Type Safety</h2>
  86 <div class="sectionbody">
  87 <div class="paragraph"><p>Exception generativity is required for type safety.  Consider the
  88 following valid SML program.</p></div>
  89 <div class="listingblock">
  90 <div class="content"><div class="highlight"><pre><span class="k">fun</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="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">exn</span><span class="p">)</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="p">(</span><span class="n">exn</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  91 <span class="w">   </span><span class="k">let</span><span class="w"></span>
  92 <span class="w">      </span><span class="k">exception</span><span class="w"> </span><span class="n">E</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
  93 <span class="w">   </span><span class="k">in</span><span class="w"></span>
  94 <span class="w">      </span><span class="p">(</span><span class="n">E</span><span class="p">,</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">E</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><span class="p">|</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="n">Fail</span><span class="w"> </span><span class="s">&quot;f&quot;</span><span class="p">)</span><span class="w"></span>
  95 <span class="w">   </span><span class="k">end</span><span class="w"></span>
  96 <span class="k">fun</span><span class="w"> </span><span class="n">cast</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">):</span><span class="w"> </span><span class="n">&#39;b</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
  97 <span class="w">   </span><span class="k">let</span><span class="w"></span>
  98 <span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="p">(</span><span class="n">make</span><span class="p">:</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">exn</span><span class="p">,</span><span class="w"> </span><span class="p">_)</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>
  99 <span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="p">(_,</span><span class="w"> </span><span class="n">get</span><span class="p">:</span><span class="w"> </span><span class="n">exn</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">)</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>
 100 <span class="w">   </span><span class="k">in</span><span class="w"></span>
 101 <span class="w">      </span><span class="n">get</span><span class="w"> </span><span class="p">(</span><span class="n">make</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"></span>
 102 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 103 <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="p">((</span><span class="n">cast</span><span class="w"> </span><span class="mi">13</span><span class="p">):</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">int</span><span class="p">)</span><span class="w"> </span><span class="mi">14</span><span class="w"></span>
 104 </pre></div></div></div>
 105 <div class="paragraph"><p>If exceptions weren&#8217;t generative, then each call <span class="monospaced">f ()</span> would yield
 106 the same exception constructor <span class="monospaced">E</span>.  Then, our <span class="monospaced">cast</span> function could
 107 use <span class="monospaced">make: 'a -&gt; exn</span> to convert any value into an exception and then
 108 <span class="monospaced">get: exn -&gt; 'b</span> to convert that exception to a value of arbitrary
 109 type.  If <span class="monospaced">cast</span> worked, then we could cast an integer as a function
 110 and apply.  Of course, because of generative exceptions, this program
 111 raises <span class="monospaced">Fail "f"</span>.</p></div>
 112 </div>
 113 </div>
 114 <div class="sect1">
 115 <h2 id="_applications">Applications</h2>
 116 <div class="sectionbody">
 117 <div class="paragraph"><p>The <span class="monospaced">exn</span> type is effectively a <a href="UniversalType">universal type</a>.</p></div>
 118 </div>
 119 </div>
 120 <div class="sect1">
 121 <h2 id="_also_see">Also see</h2>
 122 <div class="sectionbody">
 123 <div class="ulist"><ul>
 124 <li>
 125 <p>
 126 <a href="GenerativeDatatype">GenerativeDatatype</a>
 127 </p>
 128 </li>
 129 </ul></div>
 130 </div>
 131 </div>
 132 </div>
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