HCoop / hcoop / debian / mlton.git / blame
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| 22 | <a href="./Home">MLton 20180207</a>\r | |
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| 25 | <div id="header">\r | |
| 26 | <h1>GenerativeException</h1>\r | |
| 27 | </div>\r | |
| 28 | <div id="content">\r | |
| 29 | <div id="preamble">\r | |
| 30 | <div class="sectionbody">\r | |
| 31 | <div class="paragraph"><p>In <a href="StandardML">Standard ML</a>, exception declarations are said to be\r | |
| 32 | <em>generative</em>, because each time an exception declaration is evaluated,\r | |
| 33 | it yields a new exception.</p></div>\r | |
| 34 | <div class="paragraph"><p>The following program demonstrates the generativity of exceptions.</p></div>\r | |
| 35 | <div class="listingblock">\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 40 | <span class="w"> </span><span class="n">E</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">true</span><span class="w"></span>\r | |
| 41 | <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="w"> </span><span class="n">false</span><span class="w"></span>\r | |
| 42 | <span class="k">exception</span><span class="w"> </span><span class="n">E</span><span class="w"></span>\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 46 | <span class="w"> </span><span class="n">E</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">true</span><span class="w"></span>\r | |
| 47 | <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="w"> </span><span class="n">false</span><span class="w"></span>\r | |
| 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>\r | |
| 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">"</span><span class="se">\n</span><span class="s">"</span><span class="p">])</span><span class="w"></span>\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 54 | </pre></div></div></div>\r | |
| 55 | <div class="paragraph"><p>In the above program, two different exception declarations declare an\r | |
| 56 | exception <span class="monospaced">E</span> and a corresponding function that returns <span class="monospaced">true</span> only on\r | |
| 57 | that exception. Although declared by syntactically identical\r | |
| 58 | exception declarations, <span class="monospaced">e1</span> and <span class="monospaced">e2</span> are different exceptions. The\r | |
| 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>\r | |
| 60 | <div class="paragraph"><p>A slight modification of the above program shows that even a single\r | |
| 61 | exception declaration yields a new exception each time it is\r | |
| 62 | evaluated.</p></div>\r | |
| 63 | <div class="listingblock">\r | |
| 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">-></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>\r | |
| 65 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 66 | <span class="w"> </span><span class="k">exception</span><span class="w"> </span><span class="n">E</span><span class="w"></span>\r | |
| 67 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 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">=></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">=></span><span class="w"> </span><span class="n">false</span><span class="p">)</span><span class="w"></span>\r | |
| 69 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 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">"</span><span class="se">\n</span><span class="s">"</span><span class="p">])</span><span class="w"></span>\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 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>\r | |
| 78 | </pre></div></div></div>\r | |
| 79 | <div class="paragraph"><p>Each call to <span class="monospaced">f</span> yields a new exception and a function that returns\r | |
| 80 | <span class="monospaced">true</span> only on that exception. The program, when run, prints <span class="monospaced">true</span>,\r | |
| 81 | <span class="monospaced">false</span>, <span class="monospaced">false</span>, <span class="monospaced">true</span>.</p></div>\r | |
| 82 | </div>\r | |
| 83 | </div>\r | |
| 84 | <div class="sect1">\r | |
| 85 | <h2 id="_type_safety">Type Safety</h2>\r | |
| 86 | <div class="sectionbody">\r | |
| 87 | <div class="paragraph"><p>Exception generativity is required for type safety. Consider the\r | |
| 88 | following valid SML program.</p></div>\r | |
| 89 | <div class="listingblock">\r | |
| 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">'a</span><span class="w"> </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">*</span><span class="w"> </span><span class="p">(</span><span class="n">exn</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'a</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 91 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 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">'a</span><span class="w"></span>\r | |
| 93 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 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">=></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">=></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">"f"</span><span class="p">)</span><span class="w"></span>\r | |
| 95 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 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">'a</span><span class="p">):</span><span class="w"> </span><span class="n">'b</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 97 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 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">'a</span><span class="w"> </span><span class="p">-></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>\r | |
| 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">-></span><span class="w"> </span><span class="n">'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>\r | |
| 100 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 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>\r | |
| 102 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 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">-></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>\r | |
| 104 | </pre></div></div></div>\r | |
| 105 | <div class="paragraph"><p>If exceptions weren’t generative, then each call <span class="monospaced">f ()</span> would yield\r | |
| 106 | the same exception constructor <span class="monospaced">E</span>. Then, our <span class="monospaced">cast</span> function could\r | |
| 107 | use <span class="monospaced">make: 'a -> exn</span> to convert any value into an exception and then\r | |
| 108 | <span class="monospaced">get: exn -> 'b</span> to convert that exception to a value of arbitrary\r | |
| 109 | type. If <span class="monospaced">cast</span> worked, then we could cast an integer as a function\r | |
| 110 | and apply. Of course, because of generative exceptions, this program\r | |
| 111 | raises <span class="monospaced">Fail "f"</span>.</p></div>\r | |
| 112 | </div>\r | |
| 113 | </div>\r | |
| 114 | <div class="sect1">\r | |
| 115 | <h2 id="_applications">Applications</h2>\r | |
| 116 | <div class="sectionbody">\r | |
| 117 | <div class="paragraph"><p>The <span class="monospaced">exn</span> type is effectively a <a href="UniversalType">universal type</a>.</p></div>\r | |
| 118 | </div>\r | |
| 119 | </div>\r | |
| 120 | <div class="sect1">\r | |
| 121 | <h2 id="_also_see">Also see</h2>\r | |
| 122 | <div class="sectionbody">\r | |
| 123 | <div class="ulist"><ul>\r | |
| 124 | <li>\r | |
| 125 | <p>\r | |
| 126 | <a href="GenerativeDatatype">GenerativeDatatype</a>\r | |
| 127 | </p>\r | |
| 128 | </li>\r | |
| 129 | </ul></div>\r | |
| 130 | </div>\r | |
| 131 | </div>\r | |
| 132 | </div>\r | |
| 133 | <div id="footnotes"><hr></div>\r | |
| 134 | <div id="footer">\r | |
| 135 | <div id="footer-text">\r | |
| 136 | </div>\r | |
| 137 | <div id="footer-badges">\r | |
| 138 | </div>\r | |
| 139 | </div>\r | |
| 140 | </body>\r | |
| 141 | </html>\r |